Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
XIAODONG WANG
DESIGNING, MODELLING AND TESTING OF JOINTS AND ATTACHMENT SYSTEMS FOR THE
USE OF OSB IN UPHOLSTERED FURNITURE FRAMES
Thèse présentée à la Faculté des études supérieures de l’Université Laval
dans le cadre du programme de doctorat en sciences du bois pour l’obtention du grade de Philosophiae Doctor (Ph.D.)
DÉPARTEMENT DES SCIENCES DU BOIS ET DE LA FORÊT FACULTÉ DE FORESTERIE ET DE GÉOMATIQUE
UNIVERSITÉ LAVAL QUÉBEC
2007 © Xiaodong Wang, 2007
Résumé court L'objectif général de l'étude est l’optimisation de la conception structurale des joints utilisés
dans les armatures des meubles rembourrés construites avec des panneaux OSB. Les
propriétés des matières premières OSB, MDF et PB, ont été étudiées. Les résultats
montrent que l'OSB a obtenu la variation de densité la plus élevée dans le plan et en
épaisseur, avec une résistance plus critique avec les vis qu’avec les agrafes. La densité des
panneaux MDF a moins varié, conférant une résistance plus homogène. On a également
déterminé la résistance en flexion des joints de gousset et de plaque métallique avec
différentes configurations sous les charges statique et de fatigue. La présence d’adhésif est
le facteur le plus important affectant l'efficacité des joints. Enfin trois configurations
d'armature de sofa trois-places en OSB avec deux types de joints et trois niveaux de charges
ont été modélisées en utilisant le logiciel SAP2000. Le modèle optimal s’avère utilisable en
chargement léger, moindrement pour un chargement moyen et inutilisable pour un
chargement élevé.
ii
Résumé long L'objectif de l'étude est de développer l'information requise pour la conception structurale
des joints utilisés dans les armatures des meubles rembourrés construites avec des
panneaux OSB. On présente trois niveaux d'essais: 1) le matériau, avec interaction matériau
/ attaches (vis et agrafe), 2) le joint (plaques gousset et métallique), et 3) modélisation d'une
structure de sofa en OSB.
En premier, les essais des propriétés des matières premières OSB, MDF et PB, notamment
l'effet de la densité localisée sur la performance en résistance de l'attache dans les panneaux
à base de bois, sous les chargements statique et cyclique ont été examinés. Les résultats
montrent que l'OSB a obtenu la variation de densité la plus élevée dans le plan et en
épaisseur, avec une résistance plus critique avec les vis qu’avec les agrafes. La densité des
panneaux MDF a moins varié, conférant une résistance plus homogène.
En second, on a déterminé la résistance en flexion dans le plan et dehors du plan des joints
de gousset et de plaque métallique avec différentes configurations sous les charges statique
et de fatigue. Les résultats indiquent que l'adhésif est le facteur le plus important affectant
l'efficacité des joints. Une augmentation de longueur des goussets de 102 à 203 mm (4 à 8
po) a accru la charge maximale pour le joint collé et pour le joint sans colle. L'utilisation de
deux paires de plaques était le facteur prédominant dans l'efficacité des joints avec métal.
Un rapport de résistance statique-à-fatigue peut être adopté comme rapport de dépassement
pour la conception des armatures de meubles rembourrés avec les joints réalisés avec des
goussets (2,1) et plaques métalliques (2,5). En général, la résistance en flexion dans le plan
était beaucoup plus grande que la résistance en flexion en dehors du plan pour les joints
réalisés avec des plaques métalliques et avec goussets.
Finalement, trois configurations d'armature de sofa trois-places fait en OSB avec deux
types de joints et trois niveaux de charges ont été modélisés en utilisant le logiciel
SAP2000. Le modèle optimal s’avère utilisable en chargement léger, moindrement pour un
chargement moyen et inutilisable pour un chargement élevé.
iii
Abstract The objective of the study was to develop the information needed for the engineered design
of joints used in upholstered frames constructed of OSB. Presented are three levels of tests:
1) material level, including interaction of material/fasteners (screw and staple), 2) joints
level (gusset-plate and metal-plate), and 3) modeling of a sofa frame made of OSB.
First, tests of basic material properties of OSB, MDF and PB, and localized density
effecting on fastener holding capacities in wood-based panels under static and cyclic
loading were examined. Results showed that in both static and cyclic loads, OSB had the
highest density variation in plane and through thickness, which was more critical to the
screw than to the staple holding capacities. The density of MDF panels varied the least,
leading to a more uniform fastener holding capacity.
Second, in-plane and out-of-plane moment capacities of OSB gusset-plate and metal-plate
joints with different configurations were determined under static and fatigue loads. Results
indicated that application of glue was the most important factor affecting the performance
of the joints. An increase in length of gusset-plate from 102 to 203-mm (4 to 8-in)
increased the peak load for both glued and unglued joints. For metal-plates, the use of two
pairs of plates was the most important factor that affected the performance of the joints. For
fatigue tests, the average values of 2.1 and 2.5 can be used as the passing static-to-fatigue
ratio for design of upholstered furniture frames with OSB gusset-plate and metal-plate
joints, respectively. In general, in-plane moment capacities were found to be 4 to 6 times
higher than out-of-plane moment capacities for both metal-plate and gusset-plate joints.
Finally, three configurations of three-seat sofa frame made of OSB with two types of joints
under three levels of service acceptance loads were modeled using the finite element
program SAP2000. The results demonstrated that the sofa frame model can pass light-
service acceptance level load; there is the limit to pass medium-service acceptance level
load; and it could not serve the heavy-service acceptance level load.
Foreword
This thesis includes seven scientific papers, which are presented in Chapters III to VI, The
first article has been published in the first issue of 2007 of the Forest Products Journal. The
second and third articles were accepted by the Forest Products Journal in December 2006.
The fourth and fifth articles were submitted to the Forest Products Journal in February
2007, and the sixth and seventh articles were also submitted to the Forest Products Journal
in May 2007. The summary description of these articles is given below:
Chapter 3:
Article 1:
Wang X., A. Salenikovich, and M. Mohammad. 2007. Localized density effects on fastener
holding capacities in wood-based panels. Forest Prod. J. 57(1/2): 103-109.
Article 6:
Wang X., A. Salenikovich, M. Mohammad. Localized density effects on fastener holding
capacities in wood-based panels. Part 2: Cyclic tests. (Submitted to the Forest Products
Journal, May 2007).
Chapter 4:
Article 2:
Wang X., A. Salenikovich, M. Mohammad, C. Echavarria, J. Zhang. Moment capacity of
oriented strandboard gusset-plate joints for upholstered furniture. Part 1. Static Load.
Forest Prod. J. 57(7/8): 39-45.
Article 3:
Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Moment capacity of oriented
strandboard gusset-plate joints for upholstered furniture. Part 2. Fatigue Load. Forest Prod.
J. 57(7/8): 46-50.
v
Chapter 5:
Article 4:
Wang X., M. Mohammad, A. Salenikovich, R. Knudson, J. Zhang. Static bending
resistance of metal-plated joints constructed of oriented strandboard for upholstered
furniture frames. (Submitted to the Forest Products Journal, February 2007).
Article 5:
Wang X., M. Mohammad, A. Salenikovich, R. Knudson, J. Zhang. Fatigue bending
resistance of metal-plated joints constructed of oriented strandboard for upholstered
furniture frames. (Accepted by Forest Products Journal, February 2007).
Chapter 6:
Article 7:
Wang X., A. Salenikovich, M. Mohammad. Out-of-plane static bending resistance of
gusset-plate and metal-plate joints constructed of oriented strandboard for upholstered
furniture frames. (Submitted to the Forest Products Journal, May 2007).
The roles of the authors of each article mentioned above are as follows: the first author had
responsibility to do the literature review and to define the methods, conducted all the
experimental and technical work, performed various statistical analyses, interpreted the
results and wrote the manuscripts, Dr. Salenikovich, Dr. Mohammad, Dr. Zhang, Dr.
Echavarria and Dr. Knudson as co-authors defined the overall project at the beginning,
facilitated the sampling and laboratory work, reviewed and revised the manuscripts.
The results of my Ph. D research work were also presented in the following international
conferences:
1. Wang X., M. Mohammad, L. Hu, A. Salenikovich. Evaluation of density distribution
in wood-based panels using x-ray scanning. 14th International Symposium of Non
Destructive Testing of wood. Hannover, Germany (May 2nd- 4th, 2005).
vi
2. Wang X., M. Mohammad, A. Salenikovich. Localized fastener-material interaction
in panels for upholstered furniture frames. 59th Forest Products Society Annual
Meeting. Quebec, Canada (June 19-22, 2005).
3. Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Capacité de moment de joints
agrafés de goussets construits avec du panneau de plaquettes orientées (OSB) pour les
structures de meubles rembourrés. 74ème Congrès ACFAS, Montréal, Canada. (May
19, 2006).
4. Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Moment capacity of stapled
gusset-plate joints constructed of oriented strandboard for upholstered furniture
frames. 60th Forest Products Society Annual Meeting. Newport Beach, California,
USA (June 25-28, 2006).
5. Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Finite element model of sofa
frame made of OSB. Received the 2nd Place Forest Products Society – Eastern
Canadian Section Student Poster Award. Forest Products Society Eastern
Canadian Section Spring Meeting 2007. May 16th and 17th, Pembroke, Ontario,
Canada.
Acknowledgements
I would like to express my deep appreciation to the individuals and organizations that
helped me in this endeavor. It is an honor and the great delight of my life to be affiliated
with all these wonderful people.
I am deeply grateful to everyone who has helped me in the preparation of my thesis. I will
always be thankful to my supervisor, Prof. Alexandre Salenikovich, whose wide
knowledge and logical way of thinking was invaluable on a number of key issues during
the full course of my study. His understanding, encouraging and personal guidance have
provided a good basis for the present thesis. I wish to express my warm and sincere
appreciation to my co-directors, Dr. Mohammad Mohammad from FPInnovations
Forintek Division, Québec lab, and Prof. Jilei Zhang from Mississippi State University for
their detailed and constructive comments, their tremendous support and encouragement
throughout this work.
I give my special appreciation to my master adviser Prof. Yves Fortin who offered and
made it possible for me to come from Vancouver to Quebec, and who encouraged me to
finish my master and to continue my Ph. D study. Special thanks to Prof. Robert
Beauregard, it was him who brought me this Ph. D subject and financially supported my
study for all these years, it is very important for me. I also would like to give my grateful
thanks to my friend Prof. Tatjana Stevanovic, for her personal advises and cares.
My sincere thanks are to my committee, Prof. Alain Cloutier, from the Wood Research
Center of the Université Laval, Prof. Eva Haviarova from Purdue University for their
detailed review, constructive criticism and excellent advice during the preparation of this
thesis.
First part of the experimental work of localized density effects on fastener holding
capacities was carried out and supported by FPInnovations Forintek Division, Québec lab. I
would like to thank the people in this organization who gave me a lot of help.
Acknowledgements are also to Mr. Richard Desjardin, the manager of the Building System
viii
Department, and Dr. Lin Hu, for their support and advice towards trial the arrangement and
testing, and so forth.
My warm appreciations are to Dr. Hui Wan and Dr. Tony Zhang, FPInnovations Forintek
Division, for their valuable advices and friendly help. Their extensive discussions around
my work have been very helpful for this study. I wish to express my thanks to Dr.
Chuangming Liu for his kind help on statistical analysis of the experiment results.
Additionally, I would like to express my appreciation for the following personnel for their
technical support, Mr. Jean-Claude Garant, Mr. Anes Omeranovic, Mr. Olivier Bäes, and
Ms. Francine Coté at FPInnovations Forintek Division.
I would like to express my thanks to all members in the Département de sciences du bois et
de la forêt, Centre de recherches sur le bois (CRB) for their help and cooperation. My
sincere appreciations to Mr. Sylvain Auger, Mr. Daniel Bourgault, Mr. Luc Germain, and
Mr. Éric Rousseau, for their technical support during my experimental work. Mr. Etienne
Simard, Mr. Alireza Kaboorani, and Mr. Maxime Bouchard-Deschênes for their help with
some tests. Thanks go to all professors (Bernard Riedl, Michel Beaudoin, and Roger
Hernández), all technologists (Yves Bédard, and David Lagueux), and all staff (Colette
Bourcier, Guylaine Bélanger, Marie-Noël Gagnon, Guillaume Giroud, Aziz Laghdir, and
Virginie St-Onge).
I appreciate a lot the help and encouragement that I received from my friends: Cesar
Echavarria, Alireza Kaboorani, Damien Voinot, Gaspard Houziaux, Williams Manuel
Munoz Toro, Benoit St-Pierre, Myriam Drouin, Julie Cool, Katherina Beck, Étienne
Simard, Maxime Bouchard-Deschênes, Pierre Bossis, Xiaojing Guo, Suying Xing,
Yongmin Zhang, Yan Jiang, Xiaolin Cai, Wenhua Liu and his daughter Yao Liu, etc.
I respectfully acknowledge the financial support given by CIBISA, FPInnovations Forintek
Division and Université Laval (Fonds de soutien au doctorat) for this project.
Last, but not least thanks to my families, relatives both in China and Canada for their
support and encouragement, my boy friend - Francois Magny and my little son Yann who
taught me to be patient.
Table of Contents Résumé court ...........................................................................................................................i Résumé long .......................................................................................................................... ii Abstract................................................................................................................................. iii Foreword................................................................................................................................iv Acknowledgements.............................................................................................................. vii Table of Contents...................................................................................................................ix List of Tables ....................................................................................................................... xii List of Figures.......................................................................................................................xv Chapter 1 Background.........................................................................................................1
1.1 Introduction.............................................................................................................2 1.1.1 Purposes ..........................................................................................................2 1.1.2 Needs ..............................................................................................................3 1.1.3 Objectives .......................................................................................................3 1.1.4 Significance ....................................................................................................4 1.1.5 Scope and limitation .......................................................................................4 1.1.6 Methodology...................................................................................................5 1.1.7 Overview of the dissertation ...........................................................................6
1.2 Literature Review ...................................................................................................9 1.2.1 Design procedure ............................................................................................9 1.2.2 Loads and design philosophies .....................................................................10 1.2.3 Material properties........................................................................................13 1.2.4 Fatigue life ....................................................................................................15 1.2.5 Properties of fasteners and joints ..................................................................21 1.2.6 Frame construction .......................................................................................47 1.2.7 Structure of sofa frames................................................................................47 1.2.8 Structure of other upholstered furniture frames............................................48
Chapter 2 Load Distribution on a Sofa Frame...................................................................49 2.1 Introduction...........................................................................................................50 2.2 General configuration of loads and the construction of the sofa frame................50
2.2.1 Sofa frame construction ................................................................................50 2.2.2 Frame performance tests...............................................................................51 2.2.3 Simplified Sofa Frame Model.......................................................................52 2.2.4 Simplified Analysis of Sofa Structural Joints...............................................53
2.3 Discussion.............................................................................................................53 2.3.1 Seat System...................................................................................................53 2.3.2 Side Rail System...........................................................................................56 2.3.3 Back System .................................................................................................58
2.4 Summary...............................................................................................................59 Chapter 3 Localized density effects on fastener holding capacities in wood-based panels .. ..........................................................................................................................60
3.1 Localized density effects on fastener holding capacities in wood-based panels. Part 1: Static tests..............................................................................................................61
3.1.1 Résumé..........................................................................................................61 3.1.2 Abstract.........................................................................................................61
x
3.1.3 Introduction...................................................................................................62 3.1.4 Materials and Methods..................................................................................64 3.1.5 Results and Discussion .................................................................................66 3.1.6 Conclusions and Recommendations .............................................................75
3.2 Localized density effects on fastener holding capacities in wood-based panels. Part 2: Cyclic tests ............................................................................................................76
3.2.1 Résumé..........................................................................................................76 3.2.2 Abstract.........................................................................................................76 3.2.3 Introduction...................................................................................................77 3.2.4 Materials and Methods..................................................................................78 3.2.5 Results and Discussion .................................................................................83 3.2.6 Conclusions and Recommendations .............................................................93
Chapter 4 Gusset-plate joints.............................................................................................94 4.1 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1: Static load..............................................................................................95
4.1.1 Résumé..........................................................................................................95 4.1.2 Abstract.........................................................................................................95 4.1.3 Introduction...................................................................................................96 4.1.4 Materials and Methods..................................................................................98 4.1.5 Results and discussion ................................................................................105 4.1.6 Conclusion ..................................................................................................110 4.1.7 APPENDIX.................................................................................................110
4.2 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 2: Fatigue load .........................................................................................112
4.2.1 Résumé........................................................................................................112 4.2.2 Abstract.......................................................................................................112 4.2.3 Introduction.................................................................................................113 4.2.4 Materials and Methods................................................................................114 4.2.5 Results and Discussion ...............................................................................119 4.2.6 Conclusions.................................................................................................121 4.2.7 Practicality ..................................................................................................122
Chapter 5 Metal-plate connected joints...........................................................................123 5.1 Static bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames .................................................................124
5.1.1 Résumé........................................................................................................124 5.1.2 Abstract.......................................................................................................124 5.1.3 Introduction.................................................................................................125 5.1.4 Materials and Methods................................................................................127 5.1.5 Results and Discussion ...............................................................................132 5.1.6 Conclusion ..................................................................................................138
5.2 Fatigue bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames .................................................................139
5.2.1 Résumé........................................................................................................139 5.2.2 Abstract.......................................................................................................139 5.2.3 Introduction.................................................................................................139 5.2.4 Materials and Methods................................................................................141
xi
5.2.5 Results and Discussion ...............................................................................146 5.2.6 Conclusions.................................................................................................150 5.2.7 Practicality ..................................................................................................151
Chapter 6 Out-of-plane static bending resistance of gusset-plate and metal-plate joints constructed of oriented strand board for upholstered furniture frames ..............................152
6.1 Résumé................................................................................................................153 6.2 Abstract...............................................................................................................153 6.3 Introduction.........................................................................................................154 6.4 Materials and Methods........................................................................................156 6.5 Results and Discussion .......................................................................................168 6.6 Conclusion ..........................................................................................................174
Chapter 7 Finite element model of sofa frames made of OSB........................................175 7.1 Introduction.........................................................................................................176 7.2 Methodology.......................................................................................................176 7.3 Results and Discussion .......................................................................................188 7.4 Conclusions and Recommendations ...................................................................195
Summary and Conclusions .................................................................................................197 Recommendations for Future Work ...................................................................................204 Bibliography .......................................................................................................................205 APPENDIX I Visiting Several Upholstered Furniture Companies ..................................212 APPENDIX II Tables in finite element modelling...........................................................223
List of Tables Table 1.1 The initial load, load increments, and acceptance levels used in GSA upholstered
furniture performance tests (adapted from GSA 1998) ................................................13 Table 1.2 National Furniture Center Upholstered Furniture Performance-acceptance Level
(adapted from GSA “Bare frame”) ...............................................................................14 Table 1.3 Average values of fatigue life (number of cycles to failure) for each joint material
type at each of bending moment level. (from Zhang et al. 2001a)...............................17 Table 1.4 Calculation of the fatigue life for plywood joints using the Palmgran-Miner rule.
(Adapted from Zhang et al. 2001a) ..............................................................................19 Table 1.5 Comparison of predicted fatigue life with average fatigue life from stepped load
tests. (from Zhang et al. 2001a)....................................................................................19 Table 1.6 Withdrawal strength of dowels in the face of OSB (adapted from Eckelman et al.
2002) .............................................................................................................................27 Table 1.7 Withdrawal strength of dowels in edge of OSB (adapted from Eckelman et al.
2002) .............................................................................................................................27 Table 1.8 Bending strength of two-pin moment-resisting dowel joints (adapted from
Eckelman et al. 2002) ...................................................................................................28 Table 1.9 Results for lateral holding capacity of dowels: Test series 1a (adapted from Zhang
et al. 2002a) ..................................................................................................................30 Table 1.10 Results for lateral holding capacity of dowels: Test series 2 a (adapted from
Zhang et al. 2002a) .......................................................................................................30 Table 1.11 Torsional strength per joint, two multi-groove dowel, symmetrically spaced 25-
mm (1 inch) from edge of rail, i.e. all rails 51-mm (2 inches) wider than dowel spacing a (adapted from Zhang et al. 2002b) .............................................................................32
Table 1.12 Face and edge withdrawal resistance (N) of screws in OSB (adapted from Erdil et al. 2002a) ..................................................................................................................35
Table 1.13 Withdrawal force versus pilot hole diameter (adapted from Erdil et al. 2002a) 35 Table 1.14 Withdrawal strength of staples from OSB (adapted from Erdil et al. 2003a) ....38 Table 1.15 Summary of grade properties on OSB panels (adapted from Forintek’s report
(Wang and Knudson 2002))..........................................................................................39 Table 1.16 Lateral holding strength of the staples (adapted from Erdil et al. 2003a) ..........39 Table 1.17 Moment resisting strength of Douglas-fir plywood gusset and stapled joints
(adapted from Erdil et al. 2003a)..................................................................................40 Table 1.18 Bending strength of gusset-plate joints constructed of wood composites
(adapted from Zhang et al. 2001b). ..............................................................................41 Table 1.19 Summary of grade properties on OSb Panels (adapted from Forintek’s report
(Wang and Knudson 2002))..........................................................................................42 Table 1.20 Bending strength of moment resisting through- bolt with dowel nut joints
(adapted from Erdil et al. 2003b)..................................................................................44 Table 1.21 Holding strength of dowel nut in relation to end distance (adapted from Erdil et
al. 2003b) ......................................................................................................................44 Table 1.22 Bending strengths of moment-resisting toothed metal plate connector joints
(adapted from Eckelman and Erdil, 1998)....................................................................46 Table 1.23 Zhang et al. (2005) evaluated the moment capacity of metal-plate-connected
joints in furniture grade pine plywood..........................................................................46
xiii
Table 2.1 Cyclic load schedules of GSA performance tests for bare frame (adapted from GSA 1998) ....................................................................................................................51
Table 2.2 Estimated joints strengths .....................................................................................54 Table 3.1 Screw and staple holding capacities available in literature. .................................63 Table 3.2 Sampling plan to evaluate the static performance of fasteners in wood based
panels. ...........................................................................................................................65 Table 3.3 Fastener performance with localized density for screws. .....................................70 Table 3.4 Fastener performance with localized density for staples. .....................................72 Table 3.5 Sampling plan to evaluate the cyclic performance of fasteners in wood based
panels. ...........................................................................................................................79 Table 3.6 Reference load levels for cyclic loading...............................................................80 Table 3.7 Test results for screw performance in cyclic loading ...........................................84 Table 3.8 Test results for staple performance in cyclic loading. ..........................................85 Table 3.9 Comparisons for screw and staple performances in static and cyclic loadings....86 Table 4.1 Description of the specimens, load capacities, and failure modes of gusset-plate
joints constructed of OSB. ..........................................................................................100 Table 4.2 Performance-acceptance levels of upholstered furniture referencing to GSA
(1998)..........................................................................................................................102 Table 4.3 Average values (COV%) of physical and mechanical properties of joint members
and gusset-plates. ........................................................................................................106 Table 4.4 Test specimen configurations and results for GSA backrest frame schedule.....115 Table 4.5 Test specimen configurations and results for GSA seat load foundation schedule.
....................................................................................................................................116 Table 4.6 Cyclic stepped load schedule using GSA backrest frame testing schedule........118 Table 4.7 Cyclic stepped load schedule for testing using GSA seat load foundation testing
schedule. .....................................................................................................................118 Table 5.1 Moment capacities of metal-plated joints constructed of plywood available in
literature (Zhang et al. 2005). .....................................................................................126 Table 5.2 Moment capacities of gusset-plate joints constructed of OSB available in
literature (Wang et al. 2007b).....................................................................................127 Table 5.3 Acceptance performance level of upholstered furniture in accordance with GSA
(1998)..........................................................................................................................131 Table 5.4 Physical & mechanical properties of OSB. ........................................................133 Table 5.5 Ultimate load capacity and failure modes of metal-plated joints constructed of
OSB.............................................................................................................................133 Table 5.6 Stiffness of six configurations of metal-plate joints. ..........................................137 Table 5.7 Test specimen configurations. ............................................................................144 Table 5.8 Cyclic stepped load levels using GSA backrest frame testing schedule. ...........145 Table 5.9 Cyclic stepped load levels using GSA seat load foundation testing schedule....146 Table 5.10 Test results using GSA backrest frame schedule..............................................148 Table 5.11 Test results using GSA seat load foundation schedule. ....................................149 Table 6.1 In-plane moment capacities of metal-plated joints constructed of OSB available
in literature (Wang et al. 2007d).................................................................................158 Table 6.2 In-plane moment capacities of gusset-plate joints constructed of OSB available in
literature (Wang et al. 2007b).....................................................................................159
xiv
Table 6.3 Out-of-plane moment capacities and stiffness of metal-plate joints constructed of OSB.............................................................................................................................163
Table 6.4 Out-of-plane moment capacities and stiffness of gusset-plate joints constructed of OSB.............................................................................................................................164
Table 6.5 Acceptance performance level of upholstered furniture in accordance with GSA (1998)..........................................................................................................................165
Table 6.6 Distributed loads applied on each springs per seat of sofa (from Tackett and Zhang 2007). ...............................................................................................................165
Table 6.7 Physical and mechanical properties of OSB.......................................................171 Table 7.1 Material properties of members and joints used in the finite element model.....179 Table 7.2 Acceptance performance level of upholstered furniture in accordance with GSA
(1998)..........................................................................................................................181 Table 7.3 Distributed loads applied on each spring of a sofa seat for light, medium, and
heavy-service acceptance levels (from Tackett and Zhang 2007). .............................181 Table 7.4 Specified Strength, Stiffness, and Rigidity Capacities for Type 1 (Standard)
Design OSB (Nominal thickness 18.5mm, Rating grade B) (Adapted from Table 7.3C CSA-O86) ...................................................................................................................183
Table 7.5 The average short-term strength values ..............................................................184 Table 7.6 Joint displacements under light-service acceptance level load...........................190 Table 7.7 Element joint big forces in the links under light-service acceptance level load.191 Table 7.8 Joint displacements under medium-service acceptance level load.....................193 Table 7.9 Joint displacements under heavy-service acceptance level load. .......................194
xv
List of Figures Figure 1.1 Diagram showing construction of the T-type, two-pin dowel joint specimen in
fatigue test (from Zhang et al. 2001a) ..........................................................................17 Figure 1.2 A specially designed pin rack system with pneumatic cylinder for evaluating
fatigue life of T-shaped joints (from Zhang et al. 2001a) ............................................18 Figure 1.3 Bending moment versus fatigue life (M-N) curve from constant bending tests of
plywood joints (from Zhang et al. 2001a) ....................................................................18 Figure 1.4 Typical configuration of the specimens in the face and edge withdrawal tests of
dowel joints (Eckelman et al. 2002) .............................................................................25 Figure 1.5 General dimensions of the two-pin moment-resisting dowel joints (Eckelman et
al. 2002) ........................................................................................................................26 Figure 1.6 Apparatus for holding specimens in the face and edge withdrawal tests of dowel
joints (Eckelman et al. 2002)........................................................................................26 Figure 1.7 Test apparatus for evaluating the bending strength of the joints (Eckelman et al.
2002). ............................................................................................................................26 Figure 1.8 General configuration of specimens used in lateral dowel strength tests with the
centre rail in: a) flat position b) edge position (adapted from Zhang et al. 2002a) ......28 Figure 1.9 Dimensions of the specimens used in lateral shear strength of dowel joints tested
in edge and flat positions (adapted from Zhang et al. 2002a) ......................................29 Figure 1.10 Methods of testing the lateral face and edge strength of dowels (adapted from
Zhang et al. 2002a) .......................................................................................................29 Figure 1.11 Configurations of the joints tested with the rail in the flat and edge positions
(adapted from Zhang et al. 2002b) ...............................................................................31 Figure 1.12 Apparatus used to test joints in the flat and edge positions (adapted from Zhang
et al. 2002b) ..................................................................................................................31 Figure 1.13 Configuration of screw withdrawal test (adapted from Erdil et al. 2002a).......34 Figure 1.14 Screw withdrawal from edge and face (adapted from Erdil et al. 2002a).........34 Figure 1.15 Specimens with screw embedded to full depth (a) and with tip protruding (b)
(adapted from Erdil et al. 2002a)..................................................................................34 Figure 1.16 General configuration of face (left) and edge (right) withdrawal specimens
(from Erdil et al. 2003a) ...............................................................................................37 Figure 1.17 Geometric dimensions of face and edge staple withdrawal specimens (adapted
from Erdil et al. 2003a).................................................................................................38 Figure 1.18 Apparatus for evaluating face and edge withdrawal strength of staples (adapted
from Erdil et al. 2003a).................................................................................................38 Figure 1.19 Configuration and apparatus of staple lateral holding strength (adapted from
Erdil et al. 2003a) .........................................................................................................39 Figure 1.20 Configuration and apparatus for staple bending strength (adapted from Erdil et
al. 2003a) ......................................................................................................................40 Figure 1.21 Through-bolt with dowel-nut (from Erdil et al. 2003b)....................................43 Figure 1.22 Dimensions of specimens for dowel-nut withdrawal test (from Erdil et al.
2003b) ...........................................................................................................................43 Figure 1.23 Dimensions of moment resisting through-bolt with dowel-nut specimens
(adapted from Erdil et al. 2003b)..................................................................................44
xvi
Figure 1.24 Typical sofa frame construction (from Chen 2003). .........................................48 Figure 2.1 Structural performance test loads of three-seat sofa frames................................52 Figure 2.2 Simplified three-seat sofa frame structural model ..............................................52 Figure 2.3 Front rail to stump joint under vertical loading...................................................55 Figure 2.4 Front rail to stump joint under horizontal sidethrust loading.............................55 Figure 2.5 Front rail to stump joint under out of plane loading............................................56 Figure 2.6 Side rail system under vertical loading ..............................................................57 Figure 2.7 The side rail system under horizontal front to back loading ...............................58 Figure 2.8 Horizontal loads on the top rail to back post joints.............................................59 Figure 3.1 Typical images of horizontal density variation in panels: a) OSB; b) MDF; and
c) PB. ............................................................................................................................67 Figure 3.2 Vertical density profiles of OSB, MDF and PB specimens. ...............................67 Figure 3.3 Average screw withdrawal resistance of OSB, MDF and PB specimens. ..........69 Figure 3.4 Screw head pull-through resistance of OSB panels in relation to average
localized density. ..........................................................................................................74 Figure 3.5 A test set-up for carrying out static (left) and cyclic (right) lateral loading
resistance of screws ......................................................................................................80 Figure 3.6 An example of typical cyclic loading regime for fastener holding capacity tests
of screw face withdrawal on 11-mm OSB panels.........................................................82 Figure 3.7 Example of load-displacement curves of static and cyclic tests of screw head
pull-through on 15-mm OSB panels. ............................................................................87 Figure 3.8 Average cyclic withdrawal resistance of screws in OSB, MDF and PB panels. 87 Figure 3.9 Cyclic head pull-through resistance of staples in OSB panels in relation to
average localized density. .............................................................................................92 Figure 4.1 Schematic of a three-seat sofa frame (Critical joints—Side rail to back post joint
& Back rail to back post joint)......................................................................................97 Figure 4.2 Configuration of a typical staple-glued gusset-plate joint...................................99 Figure 4.3 Placement of staples in gusset-plates of unglued joints (Configurations a-i). ..101 Figure 4.4 GSA load applied on the back rail of a three-seat sofa frame (back rail to back
post joint). ...................................................................................................................103 Figure 4.5 Schematic of a moment-resisting connection....................................................105 Figure 4.6 Forces in fasteners of a moment-resisting connection. .....................................105 Figure 4.7 Typical failure modes of gusset-plate joints......................................................107 Figure 4.8 Experimental reference resistance vs. predicted peak loads of stapled gusset-
plate joint assemblies with/without glue.....................................................................108 Figure 4.9 Schematic of a three-seat sofa frame: a) side rail to back post joint; b) back rail
to back post joint.........................................................................................................117 Figure 4.10 Setup for the fatigue test of gusset-plate connected joint assemblies. ............119 Figure 5.1 An example of metal-plated joint with two LVDTs’ points A and B. ..............128 Figure 5.2 Configurations of metal-plated joints................................................................130 Figure 5.3 Measurement of the angle of rotation, α. ..........................................................131 Figure 5.4 Typical moment-rotation curves of metal-plated joints. ...................................132 Figure 5.5 Typical failure modes of metal-plated joints.....................................................134 Figure 5.6 Experimental mean ultimate loads of metal-plated joints. ................................136 Figure 5.7 Rotational stiffness of metal-plated joints.........................................................137 Figure 5.8 Configurations of metal-plated joints for fatigue tests. .....................................143
xvii
Figure 5.9 Schematic of a three-seat sofa frame. a) side rail to back post joint; b) back rail to back post joint.........................................................................................................144
Figure 5.10 Setup for fatigue test of metal-plate connected joints. ....................................146 Figure 6.1 Configurations of metal-plate joints for out-of-plane moment tests. ................160 Figure 6.2 Configuration of a typical staple-glued gusset-plate joint for out-of-plane
moment tests. ..............................................................................................................161 Figure 6.3 Placement of staples in gusset-plates of unglued joints (Configurations a-i) for
out-of-plane moment tests. .........................................................................................162 Figure 6.4 Schematic of the out-of-plane bending carried by the front rail. ......................165 Figure 6.5 An example of out-of-plane bending test joint with a LVDT point A. .............166 Figure 6.6 Measurement of the angle of rotation, α. ..........................................................166 Figure 6.7 Typical out-of-plane moment-rotation curves: (a) gusset-plate, and (b) metal-
plate joints...................................................................................................................167 Figure 6.8 Typical failure modes of test joints. ..................................................................172 Figure 6.9 Experimental mean ultimate out-of-plane loads of gusset-plated and metal-plated
joints............................................................................................................................173 Figure 6.10 Stiffness of all configurations of gusset-plated and metal-plated joints. ........173 Figure 7.1 Typical three-seat sofa frame. ...........................................................................178 Figure 7.2 Two of 2 x 6 metal-plate joint in-plane and out-of-plane rotation-moments (R3
and R2). .......................................................................................................................180 Figure 7.3 Light-service acceptance level loads distributed on a sofa frame model. .........182 Figure 7.4 Configurations (a), (b) and (c) of a three-seat sofa made of OSB.....................185 Figure 7.5 Types of connections used in sofa frame model. ..............................................187 Figure 7.6 OSB sofa frame with torsion stress bars for configurations (a), (b) and (c). ....189
Chapter 1 Background
2
1.1 Introduction
1.1.1 Purposes Upholstered furniture manufacturers are always looking for ways to cut down on the cost
of the raw material. They always search for a new less expensive material, which of course,
have to be as strong and reliable as the traditional ones. Recently, upholstered furniture
manufacturers are exploring new alternatives to solid wood, especially with the
development of CNC technology, where panels are becoming the good alternative for solid
wood. Oriented Strand Board (OSB) is one of those panel products that have a good
potential in such applications.
OSB is a wood-based flake board product that emerged in the early 1980s. Water resistant
exterior-type resin is applied to long narrow flakes to form a mat of three to five layers.
OSB has only recently started to be investigated for use in furniture framing. There are not
many published reports on the use of OSB in furniture frames. FPInnovations Forintek
Division published a technical report on the “Suitability of OSB for usage in upholstered
furniture” (Wang and Knudson 2002). The results of the study indicate that some
upholstered furniture manufacturers use a limited amount of OSB in their furniture frames.
The main advantages of OSB are the low cost, product consistency, availability, and low
labour requirement. This indicates that OSB deserves careful consideration as a frame
stock for upholstered furniture. On the other hand, the major disadvantages of the product
cited by the furniture manufacturers are a low staple withdrawal resistance on edges, lower
perpendicular to grain strength compared to lumber, rougher surface and faster saw blade
and tool wear. Moreover OSB lacks the bending strength of solid wood (Erdil, 1998),
hence one should be careful with the construction of front rails in sofas, where substitution
for solid wood on a one-to-one basis could lead to serious structural problems.
There is no reason to assume that sound frames cannot be constructed of OSB. We should
further investigate the characteristics and capacities of OSB in order to ensure its rational
use through appropriate design. Upholstered furniture manufacturers are looking for an
alternative to hardwood lumber and plywood, combining low cost, consistent high strength
and a good fastener holding capacity. If OSB manufacturers are able to supply products
3
with those attributes, there will be an opportunity to expand the use of OSB in the
upholstered furniture market.
1.1.2 Needs The upholstered furniture industry is in need for technical information on rational design
sofa frames with OSB, especially the joints design with OSB, since most failures occur at
joints. Joints are the weakest part in the frame. Also, strength design of upholstered
furniture frames should take into account information about joints fatigue strength
properties since most service failures appear to be fatigue related (Eckelman and Zhang
1995). However, the strength properties currently available for the design of upholstered
furniture frames have mostly been determined using static load tests. Research to
determine the fatigue properties of joints subjected to cyclic loads in furniture application
has so far been minimal. Although, fatigue studies have been done in the area of material
(wood and composites) for structural design of furniture frame, studies are rarely
concerning joint fatigue. So, the research of joint fatigue is quite new and we have to carry
out in detail research on this topic.
1.1.3 Objectives This study was focused on issues associated with designing, modelling, and testing of
joints and attachment systems for the use of OSB in upholstered furniture frames. The
primary purpose of this study was to develop technical information needed for strength and
durability design of joints used in upholstered frames constructed of OSB. This study was
intended to add to the previous studies and supplement the results with additional
experimental and mathematical investigations to improve the methodology of joints design
for upholstered sofa frame. The following complementary objectives comprise the purpose
of the study:
1) Examine basic material physical and mechanical properties of OSB, Medium density
fiberboard (MDF) and Particle board (PB), and interaction of material/fastener, including
screw and staple face and edge direct withdrawal resistance, screw lateral resistance, and
4
screw and staple head pull-through resistance under static and cyclic loads, and these
resistances correlations with material localized density.
2) Determine in-plane and out-of-plane bending moment capacities of OSB joints,
including gusset-plate and metal-plate joints under static and fatigue loadings.
3) Estimate load distribution on joints of a full-size structural three-seat sofa frame using
numerical modeling. Different configurations of sofa frames made of OSB with different
types of joints under three levels of service acceptance loads were modeled using finite
element method (SAP2000). Two types of connections were used in the model: rigid and
semi-rigid (with real connectors’ properties).
4) Provide recommendations and improvements based on testing and modeling.
1.1.4 Significance It is postulated that findings from this study will help the upholstered furniture companies
to improve their designs and produce reliable products with good performance/cost ratios
by providing better designs for sofa frames made of OSB and, in particular, for joints made
of OSB.
This study provides tools to support the development of OSB frames for upholstered
furniture and foster the development of niche market for OSB.
1.1.5 Scope and limitation A literature review has been carried out in addition to a study of the various types of joints
for upholstered sofa frame made of OSB. Four upholstered furniture manufacturers in
Quebec area have been visited to learn more about the framing and jointing systems and
potential problems associated with the usage of OSB in such frames.
The material properties and fastener material localized density relationships were studied
using OSB of various thickness and various types of fasteners. The static tests were carried
out according to ASTM standards, and fatigue tests were conducted in accordance with
GSA standard (GSA 1998).
5
The frame structural modeling was limited to a three seats standard sofa frame, other
types of frames, such as recliners, should be the subject of future studies, after validation of
the model.
1.1.6 Methodology To achieve the objectives, the following steps have been done:
1) Based on the literature review of pertinent research and visits of furniture manufacturers,
the decisions on the types of joints and frame configuration to be studied were made.
2) Structural analysis of a typical sofa frame:
This part of study provides background information on how to estimate load distribution on
the joints of a full-size three-seat sofa frame. A simplified three-seat sofa frame structural
model was proposed, including the most critical members needed to resist service loads.
Structural analyses were performed on this frame using the various General Service
Administration (GAS 1998) loading cases (i.e. light duty, medium duty and heavy duty)
and boundary conditions. Internal forces at each connection and stresses in each structural
member were evaluated in two different ways. First, the analysis was performed using
basic structural analysis techniques assuming rigid joints, magnitudes and directions of
internal forces at each connection in the frame model were determined, i.e., type of forces
that those connections were subjected to such as tension and shear force, and bending
moments. Second, finite element analysis software (SAP 2000) was used to analyze the
furniture frame with real joint performance parameters considering semi-rigid joint effect.
3) OSB panel properties and localized fastener characteristics:
Material localized density / fastener holding capacities were studied in this part. Basic
material tests, such as density profile, internal bond, modulus of elasticity (MOE), and
modulus of rupture (MOR) were performed. These data was used as input for the
modelling of the joints and for the sofa frame. The fastener holding capacity and, localized
density, were evaluated. Screws and staples were chosen since they are the common types
of fasteners in the upholstered furniture industry. The fastener experiments under static and
6
cyclic regimes were carried out. These tests were screw and staple face and edge direct
withdrawal, screw lateral, and screw and staple head pull-through. Such information is
crucial for the final model and it is also important in providing some suggestions to the
OSB industry as to how they could improve their panel properties specifically for
upholstered furniture usage.
4) Tests and analysis of joints identified
After identifying the connection points subjected to maximum internal forces in the frame
model, joint configurations were proposed for connecting those being highly stressed
connections. Joint specimens of finally determined configurations were built using OSB
and tested. Two types of joints were investigated, including staple gusset-plate with or
without glue, and metal-plate. In-plane moment capacities of OSB gusset-plate and metal-
plate joints under static and fatigue loads were examined. Then the static out-of-plane
moment capacity of these joints with gusset-plates and metal-plates were determined
experimentally for different configurations. The comparisons between in-plane and out-of-
plane moment capacities were performed.
5) Modeling of sofa frames made of OSB
Three OSB sofa frame configurations were designed. The finite element analysis software
(SAP2000) was used to analyze the sofa frames under three levels of service acceptance
loads. The performances of each frame and joint were studied, and then through analysis,
any possible weaknesses due to OSB properties were identified. Recommendations and
improvements were proposed based on those observations.
1.1.7 Overview of the dissertation Background presented in Chapter 1 continued with a literature review including furniture
frame design procedure; loads and design philosophies. In this study, GSA performance
test loads were used as design loads. Material properties, such as fatigue life were reviewed
based on most recent publications on member and joints fatigue research. Also,
experimental studies that have been completed in the past were discussed for the properties
7
of different types of fastener and joints, including dowel, screw, staple, gusset-plate,
through bolt with dowel nuts, toothed metal connector plates, tenon-mortise, and T-nuts.
Chapter 2 provided information on how to estimate load distribution on the joints of a full-
size three-seat sofa frame. A simplified three-seat sofa frame structural model was
analyzed. Internal forces at each connection were evaluated using structural analysis
techniques. Finite element analysis (SAP 2000) would be performed later, in Chapter 7,
using parameters determined during the experimental study.
In Chapter 3, the material localized density effects on fastener holding capacities in wood-
based panels were discussed. Some basic materials tests, such as density profile, internal
bond, and bending MOE and MOR, and localized density / fastener holding capacities
were investigated. Fastener holding capacities - localized density relationship tests were
presented in this chapter, including screw and staple face and edge withdrawal, screw
lateral resistance, and screw and staple head pull-through under static and cyclic regimes.
Two journal articles were written based on the test results in this chapter. Article 1:
localized density effects on fastener holding capacities in wood-based panels; Article 6:
localized density effects on fastener holding capacities in wood-based panels. Part 2:
Cyclic tests.
In Chapter 4, tests and analysis of gusset-plate joints made of OSB were reported. Joints
most commonly used and/or with the most potential use in industry, e.g. stapled gusset-
plate with/without glue were selected. Such joints were tested using static and fatigue
loadings. Experiments of OSB stapled gusset-plate with/without glue joint static and
fatigue bending tests were performed. Two articles were written in this part. Articles 2 and
3 described static and fatigue tests of critical joints of sofa frame made of OSB. 1) Moment
capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1: Static
Load; 2) Moment capacity of oriented strandboard gusset-plate joints for upholstered
furniture. Part 2: Fatigue Load.
Similar to Chapter 4, Chapter 5 studies OSB metal-plate joints under static and fatigue
bending tests. Two articles were written in this part (Article 4 and 5) that discussed static
and fatigue tests of metal-plate joints of sofa frame made of OSB. The article 4 titled static
8
bending resistance of metal-plate joints constructed of oriented strandboard for upholstered
furniture frames. The article 5 titled fatigue bending resistance of metal-plate joints
constructed of oriented strandboard for upholstered furniture frames.
Chapter 6 demonstrated the test results of static out-of-plane moments capacity of T-
shaped joints with gusset-plate and metal-plate joints made of OSB for different
configurations. The results from out-of-plane were compared with in-plane moment
capacities. Out-of-plane moment capacities were needed for modeling of the sofa frame.
This chapter yielded the last article from the thesis.
Chapter 7 discussed the finite element model of a typical sofa frame made of OSB. Three
configurations of a three-seat sofa frame made of OSB with two types of joints under three
levels of service acceptance loads were modeled using the finite element method
(SAP2000). Two types of connections are used in the model: rigid (fixed) and semi-rigid
(with real connectors’ properties). Comparing the results of experimental test and finite
element analysis for three-seat sofa frame could be a future project.
In the summary and conclusions section, an overview of the research and achieved results
are presented and some conclusions are provided. This section also included
recommendations and improvements based on research findings, and suggestions for future
research.
1.2 Literature Review Although there is much literature pertaining to various aspects of furniture design, there are
very few publications related the structural analysis and design of upholstered furniture
frames. Nevertheless, the last fifty years saw valuable studies related to the structural
analysis and design of furniture and its components, which can be applied to OSB as well.
It is worthwhile to review these studies in order to develop basic guidelines for the
structural design of upholstered furniture frames of OSB. Studies of interest may be
divided into the following subgroups according to the major topics covered:
1.2.1 Design procedure At the early age in recorded history, man had already developed furniture design and
constructions differing little from those in use today. In 1963, chairs, cabinets and even a
folding bed were found in the tomb of the Ancient Egyptian King Tutankhamen's tomb
(Desroches-Noblecourt, 1963). After the 10th century, as a result of innovations borrowed
from the field of architecture, both the aesthetic and functional design of furniture vastly
improved. Immediately after the Middle Age, almost every new idea introduced in
architecture was incorporated into furniture, especially in Europe. In other words, the
renaissance affected both architecture and furniture design in Europe (Erdil 1998).
There are actually 3 areas of furniture design (In the text book of Eckelman 1991, Chapter
I, p. 1-2). The first is aesthetic design, that is, the artistic development of a structural form
that is appealing to consumers and which will culturally enrich their lives. This area is still
of most importance today. The second is function design, planning the structure so that it
will perform its intended function as efficiently as possible. The third one is engineering
design which involves devising the structure so that it can safely resist the load imposed
upon it in service.
Engineering design of a piece of furniture, just as that of any other structures, consists of
carrying out the following procedures:
1) Determining the loads which will be imposed upon the structure in service
10
2) Designing the size of the members or parts required to carry these loads and “draw
up” a “prototype” structure
3) Analyzing the magnitude and distribution of the internal forces arising in this trial
structure under the action of the external loads
4) Redesigning the trial structure and repeating steps 2 through 4, until no part is
overstressed
5) Designing the joints so that they can safely carry the internal and external loads
acting upon them in service
The real situation is a little different from the above in that the aesthetic design of an artist
constitutes the first step in the design procedure. In fact the artist’s sketch corresponds to
the first attempt at a trial structure. Nonetheless, the formerly described procedure will
form the basis of the computer-aided design system not taking into account the aesthetic
design step.
1.2.2 Loads and design philosophies The first step in any design procedure involves the determination of the external loads
which the piece of furniture must be able to withstand in service. Such loads are not always
predictable, and determining them is often more difficult than the design of the structure
itself. In order to select these loads, the designer must have a thorough knowledge of the
conditions the furniture will encounter in service. We must know not only how it is used,
but also how it is abused. To be more exact, we need to know the nature of the static and
dynamic forces that will be encountered in service, i.e., their magnitude, direction and
frequency of occurrence. In the case of sofas, for instance, we need to know the forces
arising when users sit down, lean backwards, and then move around as they settle. We also
need to know which forces are imposed on the sofas when they are transported or moved.
Such forces could be quite high, and furniture is often damaged in transit. We also need to
know whether the sofa will be shoved across a floor, or whether if it will be lifted and
carried from one location to the next, whether it is to be moved in an upright position or
standing on end. Obviously, it is important that we anticipate as many potential uses of the
furniture as possible. Many failures occur in service simply because the ways the furniture
were to be used were not foreseen.
11
Structural design can be defined as a procedure for determining member and joint
configurations to ensure that external loads do not exceed the resistance of a structure.
Safety, function, and economy are the three major goals of design. Normally, a factor of
safety of 3 is assumed (Eckelman 1970a, 1974) for allowable design stresses in furniture
designs. This may be increased to 6 if fatigue and creep conditions are considered.
There are two philosophies applied in current structure (Geschwindner et al. 1994; Salmon
and Johnson 1990). The first is Allowable Stress Design (ASD), also called “working
stress design”. ASD is a classical approach to structural design, not only for wood
structures, but also for the design of reinforced concrete and steel structures. ASD is based
on the concept that the maximum stress in a member will not exceed an allowable stress,
which incorporates a factor of safety (FS) under normal service conditions. All load effects
are determined by elastic analysis of the structure. Both the factor of safety and the
resulting allowable stress depend on the governing limit stress, with allowable stress
expressed as follows:
Governing limit stress
Allowable stress = ------------------------------ (1.1) Factor of safety The governing limit stress depends on the structural element type and stress condition
being considered. Importantly, there may be limit stresses which must be checked
individually for each element.
ASD has been the primary philosophy used for over a century, but it has been replaced by
Limit States Design (LSD) in many countries, including Canada. The actual level of safety
is not known, however. During the past 20 years, structural design has been developing a
more rational, probability-based, economic design procedure called “limit state” design.
Load and resistance factor design (LRFD) is an example of such recently developed limit
state design in the USA.
In the United States, LRFD has been accepted for steel design with the adoption of the
1986 AISC Load and Resistance Factor Design Specification. For engineered wood
construction both formats (ASD and LRFD) are currently in use. LRFD explicitly
12
incorporates the effects of the random variability of strength and load. The basic LRFD
design criterion can be summarized as follows:
Φ Rn ≥ Σ Γi Qi (1.2)
Where
Φ: resistance factor (strength reduction factor)
Rn: nominal resistance
Γi: overload factors
Qi: various load effects
The quantity of Φ Rn (called resistance or strength) must be more than the load effects, i.e.,
Qi multiplied by Γi, to fulfill the safety requirement.
Rosowsky and Hunt (1995) also showed that structural wood composites benefit from the
introduction of LRFD concepts into wood design, especially in the potential for the control
of material property distributions through product design, manufacturing process control,
and quality control.
Unfortunately, a systematic scientific investigation of the loads that act on a sofa frame has
never been undertaken. Therefore, relatively few service loads have been thoroughly
evaluated, and there is a scarcity of pertinent quantitative data. At this time, the
information required to design furniture on a scientific basis is still too imperfect to rely
totally on strength design methods. For instance, design loads are simply not available for
the design of a sofa frame.
Fortunately, furniture frame performance test standards such as General Services
Administration (GSA 1998) and the Business and Institutional Furniture Manufacturer’s
Association (BIFMA) are available to evaluate the durability of a furniture frame
construction including components such as joints and members. Therefore, the loads used
for the performance tests could be the best available candidates for the determination of
design loads for furniture frame components. Efforts in determining design loads based on
available engineering design information for a sofa frame to meet specified frame
performance test requirements, for instance GSA performance test, were explored in this
13
study. Tables 1.1 and 1.2 show the initial load, load increments, and acceptance levels used
in GSA general upholstered furniture performance and “BARE” frame tests.
1.2.3 Material properties Because of the particular structure of OSB, bending properties of oriented strand board (in
the direction of alignment) are generally superior to those of a randomly oriented flake
board. As with any particle panel product, the properties of OSB depend strongly on the
manufacturing process. It has been manufactured primarily for structural purposes such as
wall sheathing, floors, and roofs of conventional buildings. However, recently, OSB
products are increasingly used in upholstered furniture frame construction in place of solid
wood and plywood as some studies have demonstrated (Wang and Knudson 2002).
Even though, many studies have examined and evaluated properties of OSB, most of those
have dealt with the use of OSB as structural materials in conventional structures (i.e.,
sheathing). If its mechanical properties are closely controlled, and structurally evaluated as
a furniture framing material, OSB may find more use in the furniture industry.
From furniture engineering design point of view, research relating the structural
performance of OSB to its properties is limited. Eckelman (1987) carried a study to
determine the bending strength, fatigue strength, stiffness and allowable design stresses for
engineered strand-lumber (ESL), engineered strand-panel (ESP) and OSB.
Table 1.1 The initial load, load increments, and acceptance levels used in GSA upholstered furniture performance tests (adapted from GSA 1998)
Acceptance levels light Medium Heavy
Description of test No. of loads
Initial load (N)
Load increment
(N) (N) (N) (N) Seat Load
Foundation 3 667 167 1334 1668 1835
Backrest Foundation 3 222 56 500 556 667 Backrest Frame 3 334 111 334 445 667
Front to Back on Leg 1 667 222 667 890 1334 Sidethrust on Arm 1 222 111 334 667 890 Sidethrust on legs 1 890 222 890 1112 1557
14
Table 1.2 National Furniture Center Upholstered Furniture Performance-acceptance Level (adapted from GSA “Bare frame”)
Test Initial load (N)
Load increments
(N)
Number of loads
Light- service
acceptance level (N)
Medium-service
acceptance level (N)
Heavy-service
acceptance level (N)
Cyclic Front to Back Load Test on Top
Rails 334 111 3 334 445 667
Cyclic Sidethrust
Load
Test on Arm -- Inward 222 111 1 334 778 1001
-- Outward 222 111 1 334 667 890
Cyclic Vertical Load 445 445 2 1779 2669 3558 Test on Arm
Cyclic Vertical Load Test on -- Front Rail 445 445 3 1334 1779 2669
-- Back Rail 445 445 3 890 1334 2224
Cyclic Torsional Inward 445 445 3 1334 1779 2669
Pull Test on Seat Rails
Cyclic Frame Racking Test 445 445 1 445 890 1779
Cyclic Front to Back Load Test on Legs 445 222 2 667 890 1334
Cyclic Sidethrust
Load
Test on Legs -- Inward 445 222 1 890 1112 1557
-- Outward 445 222 1 445 667 1112
Cyclic Vertical Load Test on Legs 667 667 4 2002 2669 4003
In that study, tests were carried out to determine the allowable design stress of such
materials when they are used as furniture framing components. Particularly, lateral and
withdrawal strength of dowels and screws were investigated for these materials. In
addition, Eckelman evaluated the impact and long term performance of bending specimens.
Based on the results, it was concluded that ESL, ESP and OSB could be used to build
sound furniture frames.
15
Similar research was carried out ten years later by Erdil (1998) for plywood and OSB. The
withdrawal, lateral, torsional and bending strength of dowels and the holding strength of
screws, staples and T-nuts in such materials were determined for upholstered furniture
frames. The study concluded that plywood and OSB could be used in the construction of
upholstered furniture frames. Models were developed in that study, which could be used in
the engineering design of such frames.
1.2.4 Fatigue life In carrying out a structural design, a furniture designer, like any other structural designer,
must select a material and choose the size of structural members to perform a specified
function without failure. Safety is one of the most important considerations. Failure of
material under fluctuating or cyclic loading conditions is known as fatigue failure.
Importantly, such failure can occur well below the ultimate static strength of the material
(Eckelman, 1987). Therefore, knowing the behaviour of the furniture parts under both
static and cyclic loading and having a set of allowable design stresses for wood composites
are fundamental to the design of furniture. That is true for both wood material and joint
fatigue strength. Studies on joint fatigue strength include joints with different types of
fasteners (i.e. staple, staple-glue-block, dowel, screw, gusset-plate and metal plate).
Material studies include plywood, Timberstrand, Engineered Strand Lumber (ESL),
oriented strand board (OSB), particleboard, oak and yellow poplar (Zhang 2000).
1.2.4.1 Wood material fatigue life Bao and Eckelman (1995) studied the fatigue life and allowable design stresses for wood
composites used in furniture. They tested MDF, OSB, and particleboard in edgewise in
order to determine their resistance to fatigue. They concluded that the relationship between
the level of stress and fatigue life was in inverse proportion. An anticipated, fatigue life
was found to decrease as the level of stress increases. Fatigue life amounted to over a
million cycles when the stress level was 30 percent of MOR, but decreased to about 400
cycles for MDF, and to about 11,000 cycles for OSB respectively at a stress level of 70
percent of MOR. The result of the study suggests that allowable design stress for the
16
composite materials included in the study could likely be derived from a consideration of
their fatigue resistance at various load levels.
1.2.4.2 Wood joints fatigue life Strength design of upholstered furniture frames requires information about joint fatigue
strength properties since most service failures of such frames appear to be fatigue related
and the most common failure to the frames occurs at the joints (Eckelman and Zhang
1995).
Eckelman (1970a) studied the fatigue life of two-dowel joints subjected to a constant cyclic
loading. He tested sugar maple joints with an average ultimate static bending load of 359
N-m (3,180 lbf-in) under two different cyclic load schedules, alternating fully-reversed
loads and one sided loads. Fatigue loads were applied to joints at a rate of 40 cycles per
minute. No failures were found at the 56.5 N-m (500 lbf-in) load level in either set of
specimens after 1,000,000 cycles. At the 113.0 N-m (1,000 lbf-in) load level (about 30% of
ultimate static bending capacity), joints failed at about 200,000 cycles, and at 169.5 N-m
(1,500 lbf-in) level (about 50% of ultimate static bending capacity), the value was about
12,000 cycles. Results clearly demonstrated that specimens were subject to fatigue damage,
and an endurance limit existed for the joints. The suggested design strength for two-pin
dowel joints should be limited to no more than one-third of joint ultimate static bending
capacity.
Few studies were found on the fatigue life of furniture frame joints subjected to cyclic
stepped loads. Zhang et al. (2001a) studied the fatigue strength properties of furniture
frame joints subjected to one-sided constant and stepped cyclic bending loads. In that
study, T-shaped, two-pin moment-resisting dowel joints constructed of red oak, yellow-
poplar, southern yellow pine plywood, aspen engineered strand lumber, and particleboard
subjected to constant and stepped cyclic bending loads were evaluated. Table 1.3
summarizes average values of fatigue life (number of cycles to failure) for each joint
material type at each of the bending moment levels. Joint fatigue life was below 25,000
cycles at the bending moment level of 70 percent of joint ultimate bending capacity. It is
expected that at 30 percent, the joint could have a fatigue life over 1 million cycles.
17
Regression of M-N data (moment versus log number of cycles to failure) of each joint
material type subjected to constant cyclic bending loads resulted in linear equations for M-
N curves. Figures 1.1 and 1.2 demonstrate the configuration and special testing system for
fatigue tests of dowels. Figure 1.3 shows the results of constant load fatigue tests of
plywood as a log-linear plot, i. e. M-N curve, the following regression equation was used
to fit individual representation of it:
M = C + D log10 Nf (1.3) Where,
M = bending moment (lb.-in.);
Nf = number of cycles to failure;
C, D = fitting constants.
Table 1.3 Average values of fatigue life (number of cycles to failure) for each joint material type at each of bending moment level. (from Zhang et al. 2001a)
Bending moment level
(%) Red oak Yellow-
poplar Plywood ESL Particleboard
90 286 (109)a 5,406 (92) 72 (43) 318 (132) 1,406 (64)
70 1,013 (114) 17,011 (100) 1,088(112) 5,263 (90) 7,491 (132)
50 82,382 (121) 301,026 (82) 84,633 (73) 121,705 (37) 152,307 (66)
30 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000
a Values in parentheses are coefficients of variation, in percent.
Figure 1.1 Diagram showing construction of the T-type, two-pin dowel joint specimen in fatigue test (from Zhang et al. 2001a)
18
Figure 1.2 A specially designed pin rack system with pneumatic cylinder for evaluating fatigue life of T-shaped joints (from Zhang et al. 2001a)
Figure 1.3 Bending moment versus fatigue life (M-N) curve from constant bending tests of plywood joints (from Zhang et al. 2001a)
To predict the fatigue life of a joint subjected to cyclic stepped bending loads based on its
M-N curve, the Palmgren-Miner rule may be used with the following unity summation of
life fractions (Zhang et al. 2001a):
13
3
2
2
1
1 ==⋅⋅⋅+++ ∑fj
j
fff NN
NN
NN
NN
(1.4)
Where
Nj = number of cycles applied to a joint at the bending moment Mj;
Nfj = number of cycles to failure from the joint M-N curve for the bending moment Mj.
19
The proposed equation indicates that for a given stepped load schedule and a known M-N
curve, joint failure is expected when the life fractions sum to unity, that is, when 100
percent of life is exhausted. The fatigue life of a joint under a given stepped bending load
schedule could be estimated from its M-N curve.
Table 1.4 shows fatigue life calculations for plywood joints subjected to cyclic stepped
loads Mj. According to the regression equation of the M-N curve for plywood joints, M =
2991 - 338 log10 Nf, the number of cycles to failure Nfj for each bending moment level is
first calculated. Then the life fractions Nj/Nfj are determined based on a known number of
cycles applied to the joint Nj. Finally, the sum of Nj/Nfj ratios is determined and made equal
to unity, the number of cycles applied (N4) at the bending moment of 169.5 N-m (1,500
lbf-in) can be calculated, which is 22,065. So the total number of cycles applied to joint
failure is 97,065 with summation of column Nj. Table 1.5 summarizes fatigue life of both
predicted and tested results of joints subjected to cyclic stepped loads.
Table 1.4 Calculation of the fatigue life for plywood joints using the Palmgran-Miner rule. (Adapted from Zhang et al. 2001a)
J Mj Nfj Nj Nj/Nfj (N-m)
1 68 11,856,718 25,000 0.002 2 102 1,535,998 25,000 0.016 3 136 198,983 25,000 0.126 4 170 25,778 N4 N4/25,778
Table 1.5 Comparison of predicted fatigue life with average fatigue life from stepped load tests. (from Zhang et al. 2001a)
Red oak Yellow-poplar Plywood ESL Particleboard
Average number of cycles to
failure 102,537(21)a 103,557 (4) 102,242(9) 88,167 (13) 71,232 (12)
Predicted number of cycles
to failure 102,068 107,440 97,065 79,945 64,739
Means difference (%) -0.5 3.6 -5.3 -10.3 -10.0
a Values in parentheses are coefficients of variation, in percent.
20
Zhang et al. (2001a) found that for fatigue life of dowel joints subjected to a given stepped
cyclic bending schedule, joints constructed of particleboard had significantly lower fatigue
life than joints made of red oak, yellow poplar, plywood, and ESL. No evidence of
significant differences existed in fatigue life among joints constructed of red oak, yellow-
poplar, plywood, and ESL. Results of static bending tests, however, showed significant
differences in bending capacity among them. They suggest that joint resistance to fatigue
failure should be taken into account in strength design of furniture frames that are
subjected to repeated loading. Fatigue strength property data such as M-N curves should be
obtained for joints commonly used in the furniture frame construction so that analyzing
and designing furniture frames for fatigue failure would be made possible.
Later on, Zhang et al. (2003) investigated the bending fatigue behaviour of T-shaped, end
to side, two-pin dowel joints constructed of furniture grade, 19.1 mm (3/4 in) thick 5-ply
southern yellow pine plywood under one-sided constant and stepped fatigue load
conditions. Results indicated that the fatigue life of dowel joints averaged 131,253; 78,122;
31,617; 11,023; 4,161; and 329 cycles for load levels of 40; 50; 60; 70; 80; and 90 percent
of their ultimate static bending capacity, respectively. Also fatigue life comparisons among
joint groups with different static bending capacity indicated that a significant increase in
ultimate static bending capacity might not yield a significant fatigue life increase when
joints were subjected to cyclic stepped loads. Joint resistance to fatigue failure should be
taken into account in strength design of furniture frames that are subjected to repeated load.
Most recently, Zhang et al. (2006) studied bending fatigue life of metal-plate-connected
(MPC) joints in furniture-grade pine plywood. Tested joints were subjected to one-sided
cyclic stepped bending loads. The purpose of the study was to obtain joint static to fatigue
moment capacity ratios. Performance test results showed that a MPC plywood joint would
fail within 25,000 cycles when a stepped load level reached 46 percent of the static
moment capacity of the tested joint. Joints failed mainly due to tooth fatigue shear at the
roots. The static to fatigue moment capacity ratio for tested joints averaged 2.5 with a
coefficient of variation of 11 percent and a range of 2.2 to 3.1.
21
1.2.5 Properties of fasteners and joints The design of joints in a furniture frame is the most important step in the whole design
process. The strength and stiffness of joints used in the construction normally determine
the strength and rigidity of the furniture frame. Structural failure in furniture is often
associated with weak joints. It is very important that the joints used in the construction of a
particular piece of furniture are properly designed, so that they can safely carry the forces
imposed upon them in service. Current advances in furniture mechanics and design have
now made it possible to relate joint strength requirements to service loads in furniture
(Eckelman 1968). Some important joints and fasteners have been studied during the past
half century. Eckelman (1978a) developed design formulas for one-pin dowels (Eckelman
1969), two-pin dowels (Eckelman 1971a), and tenon-mortise joints (Hill and Eckelman
1973) for both bending and withdrawal strength of typical mechanical fasteners such as
screws, staples, and nails. Eckelman (1989a) also carried out tests to determine the bending
strength of through-bolts and dowel-nuts and developed expressions to predict their
strength. Erdil (1998) developed design formulas for dowel screws, staples and T-nuts used
with plywood and OSB to predict the withdrawal and holding strength. The characteristics
of some joints and fasteners along with studies of their design formulas are given below:
1.2.5.1 Dowel joints A dowel is a small diameter wooden pin used to fasten two furniture components together
with or without the help of other fasteners and glue. Dowels are among the most commonly
used connectors to assemble furniture. Because of their favourable cost and production
characteristics, dowels have long been a favourite connector in the furniture industry and
good for both mass and small shop productions of furniture. They are simple in design and
require only a drilling operation to form a joint. They have high initial strength, are self-
aligning and can also be used to joint parts of almost any shape that come together at
nearly any angle. Dowels are often used as the primary connectors in furniture frames
constructed of both solid wood and composite materials, including plywood and OSB.
Ideally, we would like to be able to design all types of dowel joints on the basis of the axial
and shear properties of the individual dowels used in their assembly (Eckelman 1991). The
22
strength of a dowel depends on the wood it is made of. The other factors affecting dowel
joint strength are the strength of the wood in shear, the internal bond of connected
members, the glue type, gluing conditions, diameter and length of the dowel, and precision
of dowel pin installation (Eckelman 1989b).
In the case of solid wood, substantial research provided the basis for the rational design of
the dowel-based joints used in such frames. Some basic formulae that could be used to
obtain reasonable estimates of their properties have been developed. Eckelman (1969)
proposed the following expression to predict average direct withdrawal strength of a dowel
pin from the side grain surface of a piece of solid wood:
F = 0.834 D L 0.89 (0.95S1 + S2) a b c (1.5)
Where:
F = ultimate withdrawal strength of the dowel, lbf;
D = diameter of the dowel, in;
L = depth of penetration of the dowel in the wooden piece, in;
S1= shear strength of the member parallel to the grain, psi;
S2= shear strength of the dowel parallel to the grain, psi;
a = 1.0 for polyvinyl resins with at least 60 percent solids content;
= 0.9 for polyvinyl resins with less than 60 percent solids content;
= 0.85 for animal glue;
b = correction factor for dowel-hole clearance;
c = 1.0 for plain (smooth surface) dowel;
= 0.9 for spiral-groove and multi-groove dowel (Eckelman and Hill 1971).
It can be clearly seen from this equation, that a strong relationship exists between the
withdrawal strength of a dowel and the shear strength parallel to grain of the solid wood
used in the construction of the joint. In other words, high withdrawal strength is obtained
when dowels are constructed of a high shear strength wood.
Moreover, in modern furniture constructions, two-pin moment-resisting dowel joints are
used more than any other type to give strength and rigidity to furniture frames. The most
common example of the use of these joints is probably the side rail to back post joint in
23
sofas. In the textbook of Eckelman (1991, Chapter VI, p.11) describes the bending strength
and moment rotation characteristics of T-shaped end-to-side grain two-pin moment
resisting dowel joints. Findings indicated that the bending strength of such joints increased
as their shear strength, rail width and dowel spacing increased. According to his
recommendations, the bending moment strength of these joints can be predicted by means
of the expression:
F4 = F2 (d1 + d2 / 2) (1.6)
Where:
F4 = ultimate bending moment strength of the joint, lbf-in;
F2 = withdrawal strength of the dowel loaded in tension, lbf;
d1 = spacing between dowel hole centers, in;
d2 = distance from the centre of the dowel loaded in compression to the corresponding
outside edge of the rail, in.
Using sufficient glue is an important factor for dowel holding strength. Eckelman and
Cassens (1985) carried out a study to determine the withdrawal strength of dowels from
wood composites used in furniture construction. They realized that when an excess amount
of glue was applied and subsequently forced into the substrate as the dowels were inserted
into the holes, the strength increased. They also emphasized the importance of surface
configuration of dowels. Findings indicated that the plain dowel and spiral-groove dowels
provided greater strength than multi-grooved dowels when an excess amount of glue was
applied, as can be seen in equation 1. In addition, they pointed out that the face withdrawal
strength of the dowels was closely related to the internal bond strength of the composite
used in the test.
Eckelman et al. (1979) were first to make a direct study of specific dowel joint strength
related to the upholstered furniture frame construction. They evaluated the utilization of
red oak press-lam as upholstered furniture frame stock. It was found that the shear strength
of press-lam was only 53 percent of frames made of solid red oak. Its dowel withdrawal
strength on the face and edge was found to be 69 percent of solid red oak.
24
Erdil (1998) carried out a study on joint design for upholstered furniture constructed of
plywood and OSB. Zhang et al. (2002a, 2002b), and Eckelman et al. (2002) studied the
fundamental lateral holding, torsional, withdrawal and bending resistances of dowel joints
for plywood and OSB constructions. Figures 1.4 to 1.12 show the configurations and
apparatus used for all dowel tests. They found that equations 1 and 2 provide good
predictions of the withdrawal resistance and bending moment, respectively for dowel joints
made of plywood and OSB. As can be seen in Tables 1.6 to 1.11, results from withdrawal
tests were incorporated into predictive expressions allowing designers to estimate
withdrawal strength as a function of the diameter of the dowels, their embedment depth,
and the density of the composite material. Results from two-pin moment-resisting joint
tests indicate that the bending strength of two-pin dowel joints constructed of plywood and
OSB could be estimated by means of the same expression developed for solid wood.
Results from lateral shear strength tests of dowel joints constructed of plywood and OSB
are sufficiently strong for several frame applications such as top rail to back post joints in
sofa frames. However, joints subjected to high levels of lateral force need to be reinforced.
Such case can be found in the case of a sofa with its front rail equipped with sinusoidal
type spring or other seat foundation materials that impose high front to back loads on the
rails. Results have indicated that torsional strength of the dowel joints increased linearly
with the dowel spacing and rail width. Joints subjected to high torsional forces such as
front rail to stump joints in smooth-front sofas or to side rails in T-front sofas should be
reinforced with glued blocks or gusset plates in order to develop the strength needed to
resist in-service loads.
Summary of predictive expressions developed to calculate the strength of dowel joints in
OSB joints of upholstered frames can be expressed as: (Erdil 1998, Eckelman and Erdil
1998)
1) Withdrawal strength
• On face: Y = 87 D 1.19 L 0.9 W 0.93 (1.7)
Where:
W = density of OSB, lb/ft3.
A simplified form of the expression has been used and is written as: Y = 55 DLW (1.8)
25
• On edge: Y = 0.41 D 1.71 L 0.9 W 2.48 (1.9)
A simplified form is written as: Y = 1.2 DW2 (1.10)
or F2 = 179 D2 L0.5 W (1.11)
2) Bending resistance of two-pin moment resisting dowel joints
Withdrawal strength of a dowel embedded in the edge of OSB may be predicted by means
of expression:
F2 = 179 D2 L0.5 W (1.12)
Then, the bending strength of the joint maybe found by means of expression:
F4 = F2 (d1 + d2 / 2) (1.13)
Figure 1.4 Typical configuration of the specimens in the face and edge withdrawal tests of dowel joints (Eckelman et al. 2002)
26
Figure 1.5 General dimensions of the two-pin moment-resisting dowel joints (Eckelman et al. 2002)
Figure 1.6 Apparatus for holding specimens in the face and edge withdrawal tests of dowel joints (Eckelman et al. 2002)
Figure 1.7 Test apparatus for evaluating the bending strength of the joints (Eckelman et al. 2002).
27
Table 1.6 Withdrawal strength of dowels in the face of OSB (adapted from Eckelman et al. 2002)
Mean face withdrawal strength/standard deviation Material Dowel Depth of embedment in face (mm)
Code Replications Diam. 9.5 12.7 14.3 15.9 19.1 22.2 Density Thick. (mm) ------------------------------------------(N)-------------------------------------------- (kg/m3) (mm)
OSB–1b 8 6.4 1,975/445 2,082/325a 751.3 19.1 8 7.9 1,850/374 2,144/400a 8 9.5 2,905/89 3,407/138a
OSB - 2 8 6.4 1,503/209 2,051/276a 626.3 19.1 8 7.9 1,268/285 2,246/165a 8 9.5 1,882/169 3,158/191a
OSB - 3 20 9.5 2,406/196 3,091/560a 776.9 22.2 5 9.5 4,506/182a
OSB - 4 20 9.5 2,286/151 3,260/520a 680.8 22.2 5 9.5 3,874/480a
OSB - 5 20 9.5 2,317/173 2,887/596a 752.9 19.1 5 9.5 3,821/342a
aThe dowel hole was drilled completely through the specimen bOSB -1 to 5 are oriented strandboard made of Southern pine (Pinus elliottii)
Table 1.7 Withdrawal strength of dowels in edge of OSB (adapted from Eckelman et al. 2002)
Mean edge withdrawal strength/standard deviation Depth of penetration (mm)
Material Dowel 19.1 25.4 31.8 Code Rep. Diam. Random or
end and side
combined
End Side Random or end and
side combined
End Side Random or end and
side combined
End Side
(mm) ----------------------------------------------------(N)------------------------------------------------------ OSB–1b 8 6.4 2,193
/431 2,206 /374
2,180 /543
8 7.9 3,385 /556
3,514 /645
3,260 /512
8 9.5 2,931 /1,010
2,753 /1,023
3,109 /1,116
24 9.5a 4,559 /503
4,533 /672
4,581 /360
5,716 /712
5,738 /898
5,693 /609
5,831 /885
5,640 /116
6,027 /565
OSB-2 8 6.4 1,775 /431
1,646 /489
1,904 /396
8 7.9 2,518 /774
2,006 /245
3,025 /356
8 9.5 2,384 /698
2,420 /823
2,349 /672
24 9.5a 4,114 /405
4,283 /316
3,950 /463
5,418 /787
5,315 /454
5,516 /1,099
5,106 /725
5,062 /116
5,146 /467
OSB-3 15 9.5a 5,200 /827
OSB-4 15 9.5a 4,848 /467
OSB-5 15 9.5a 5,177 /218
aThe dowel hole was drilled completely through the specimen bOSB -1 to 5 are oriented strand board made of Southern pine (Pinus elliottii)
28
Table 1.8 Bending strength of two-pin moment-resisting dowel joints (adapted from Eckelman et al. 2002)
Estimated Ratio : Estimated Ratio : Bending Bending Strength Dowel bending estimated bending estimated
Material strength strength ratio withdrawal strength strength/test strength strength/test code Statistic 102-mm 152-mm 152/102-mm strength 102-mm. strength 152-mm. strength
---------(N-m)--------- (N) (N-m) (N-m) OSB-1 Avg. 393.2 604.6 1.54 5,253 333.7 0.85 600.6 0.99
SD 30.1 132.8 OSB-2 Avg. 281.4 500.6 1.78 4,377 278.0 0.99 500.4 1.0
SD 28.3 64.3 OSB-3 Avg. 344.1 574.9 1.67 5,431 345.0 1.0 620.9 1.08
SD 48.1 84.0
Figure 1.8 General configuration of specimens used in lateral dowel strength tests with the centre rail in: a) flat position b) edge position (adapted from Zhang et al. 2002a)
29
Figure 1.9 Dimensions of the specimens used in lateral shear strength of dowel joints tested in edge and flat positions (adapted from Zhang et al. 2002a)
Figure 1.10 Methods of testing the lateral face and edge strength of dowels (adapted from Zhang et al. 2002a)
30
Table 1.9 Results for lateral holding capacity of dowels: Test series 1a (adapted from Zhang et al. 2002a) Rail position Edge position Flat position Rail width 76-mm 102-mm 51-mm 102-mm
No. of dowels 2 2 1 2 Dowel spacing 25-mm 51-mm 51-mm Density Thickness
Lateral load and standard deviation per dowel (N) (kg/m3) (mm) OSB-1b 1,557 2,366 663 725 751.3 19.1
294 209 76 36 OSB-2 1,414 1,672 596 565 626.3 19.1
169 196 62 31 a All loads are in pounds per dowel bOSB -1 or 2 are oriented strand board made of mixed species
Table 1.10 Results for lateral holding capacity of dowels: Test series 2 a (adapted from Zhang et al. 2002a) Rail position Edge position Flat position Rail width 76-mm 102-mm 76-mm 51-mm
No. of dowels 2 2 2 1 Dowel spacing 38-mm 51-mm 25-mm Density Thickness
Lateral load and standard deviation per dowel (N) (kg/m3) (mm) OSB-3b 1,779 1,841 1,624 1,659 776.9 22.2
89 165 107 205 OSB-4 1,810 1,984 1,068 1,472 680.8 19.1
165 227 107 156 OSB-5 1,664 1,882 1,085 1,361 752.9 22.2
205 40 80 111 a All loads are pounds per dowel bOSB -3 to 5 are oriented strand board made of mixed species
31
Figure 1.11 Configurations of the joints tested with the rail in the flat and edge positions (adapted from Zhang et al. 2002b)
Figure 1.12 Apparatus used to test joints in the flat and edge positions (adapted from Zhang et al. 2002b)
32
Table 1.11 Torsional strength per joint, two multi-groove dowel, symmetrically spaced 25-mm (1 inch) from edge of rail, i.e. all rails 51-mm (2 inches) wider than dowel spacing a (adapted from Zhang et al. 2002b)
Maximum Material Rail Dowel Vertical load Torsional Shear force
Code position Spacing (Fv) per joint moment COV Per dowel Density Thickness (mm) (N) (N-m) (%) (N) (kg/m3) (mm)
First test series
OSB-1b Flat 51 230 58.5 28.2 1,268 751.3 19.1 OSB-2 Flat 51 181 45.9 15.8 992 626.3 19.1
Third test series
OSB-3 Edge 51 212 53.9 8.0 1,063 680.8 19.1 OSB-4 Edge 51 230 58.3 11.0 1,148 752.9 22.2
a n = 4 replications per cell for first and second series, and N = 10 per cell for third series. bOSB -1 to 4 are oriented strandboard made of mixed species
1.2.5.2 Joints with screws Wood screws have been used in furniture construction for about 300 years, primarily to
attach hinges to drop-leaf tables (Textbook of Eckelman 1991, Chapter VI, p. 49). They are
still widely used for fastening hardware to furniture and in replacing other fasteners such as
dowels and nails to structural-load-bearing joints. There is a growing tendency to use
screws in many of the small but highly stressed joints found in upholstered furniture
frames. For example, the highly stressed corners are often reinforced with blocks that are
glued and screwed in place. Many of the highly stressed upright braces to centre rail and
the front rail to stretcher braces are attached with screws. It is very important that these
joints be properly designed in order to safely carry the loads imposed on them in service.
Many investigations into the capacity of screws to withstand withdrawal loads involved
solid wood, particleboard, plywood, OSB and other wood composites. Johnson (1967)
investigated the screw holding capacity of plywood and particleboard with various sizes of
screws. He found out that the resistance of materials varied in proportion to the size of the
screws. The Wood Handbook (1987) contains allowable design formulae for screws used
in wood building constructions for 50 years. However, the design formulae are not
satisfactory for engineering of furniture joints. Eckelman (1978b) investigated type A
panhead sheet-metal screws widely used in furniture construction. He tested the withdrawal
strength of the screws for a wide range of hardwood used in furniture construction,
33
concluding that the withdrawal strength from side grain of wood can be predicted by the
following expression:
F = 3.2 Ds (Ls-Ds)0.75 Sx (1.14)
Where:
F = screw withdrawal strength from side grain of wood (lbf);
Sx = shear strength of the wood;
Ds = screw diameter, in;
Ls = depth of penetration of the threaded portion of the screw, in.
Eckelman (1988a) also investigated the holding strength of various sizes of sheet-metal
screws in face and edge of commercially available medium-density fibreboard. He
concluded that the withdrawal resistance could be predicted by means of mathematical
expressions as given below:
F (face) = 39 (IB) 0.85 Ds 0.5 (Ls-Ds/3)1.25 (1.15)
F (edge) = 18.4 (IB) 0.85 Ds 0.5 (Ls-Ds/3)1.25 (1.16)
Where:
F = withdrawal strength on face or edge, lbf;
IB = internal bonding strength, psi.
He also demonstrated that screw withdrawal strengths were 13 percent higher when
optimum pilot holes were used compared to tests made without holes. Pilot holes not only
help to locate screws, but also facilitate their insertion in a desired direction. The
investigation found that using pilot holes of the proper diameter significantly increases the
holding strength of screws in MDF and particleboard. Rajak and Eckelman (1993)
indicated that pilot holes should be 80 to 85 percent of the root diameter of the screw, but
larger pilot holes should be used with MDF, when compared to particleboard and solid
wood, to avoid splitting. Pilot holes drilled into the edges of MDF should be approximately
equal to the root diameter of the screws and have a depth equal to the depth of embedment
of the screws (Anonymous 1980).
34
Erdil (1998) tested the screw withdrawal resistance both on face and edge for OSB. Later
on, Erdil et al. (2002a) developed estimates of both face and edge screw holding strength
that could be used for the engineering design of furniture frames constructed of OSB. They
determined the effect of pilot hole size on withdrawal strength and the relationship between
withdrawal resistance, screw diameter and depth of penetration. Most importantly, they
developed predictive expressions that could be used to estimate the screw holding
resistance as a function of board properties, screw diameter and depth of penetration.
Figures 1.13 to 1.15 show specimens and test set-up used for evaluating the holding
strength of screws in plywood and OSB (Erdil et al. 2002a). The results are given in Tables
1.12 and 1.13.
Figure 1.13 Configuration of screw withdrawal test (adapted from Erdil et al. 2002a)
Figure 1.14 Screw withdrawal from edge and face (adapted from Erdil et al. 2002a)
Figure 1.15 Specimens with screw embedded to full depth (a) and with tip protruding (b) (adapted from Erdil et al. 2002a)
35
Table 1.12 Face and edge withdrawal resistance (N) of screws in OSB (adapted from Erdil et al. 2002a)
Screw size Material Face-tip not protruding Face-tip protruding Code Statistica 6AB 10AB 10AB 12AB 14AB 6AB 8AB 10AB 12AB 14AB Thickness Density
(mm) (kg/m3) OSB-1 Avg. 2,082 2,335 2,402 2,620 2,771 2,455 2,580 2,811 2,544 3,376 19.1 751.3
SD 458 214 129 254 609 222 311 351 414 53 OSB-2 Avg. 1,419 1,481 1,468 1,334 1,615 1,610 1,704 1,988 1,788 1,868 19.1 626.3
SD 307 133 191 240 485 276 173 289 351 138 OSB-3 Avg. 2,660 3,234 22.2 776.9
SD 449 71 OSB-4 Avg. 2,513 3,038 22.2 680.8
SD 240 427 OSB-5 Avg. 2,518 2,891 19.1 738.5
SD 449 405 Edge-side grain Edge-end grain
OSB-1 Avg. 3,056 3,158 3,225 3,625 3,896 3,300 2,949 3,145 3,661 3,892 19.1 751.3 SD 338 160 574 142 676 200 498 302 276 236
OSB-2 Avg. 1,272 1,339 1,739 1,575 1,882 1,241 1,744 1,681 1,970 1,877 19.1 626.3 SD 289 169 129 102 342 138 294 209 298 111
OSB-3 Avg. 3,158 2,584 22.2 776.9 SD 414 329
OSB-4 Avg. 2,317 1,904 22.2 680.8 SD 1,904 329
OSB-5 Avg. 2,566 2,700 19.1 738.5 SD 209 360
a Statistic: avg. refers to average; SD refers to standard deviation.
Table 1.13 Withdrawal force versus pilot hole diameter (adapted from Erdil et al. 2002a) Pilot hole diameter (mm)
Screw gage 0 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 (major Withdrawal force (N)
Diameter)a Statisticb Face withdrawal – OSB-1 6AB Avg. 1,561 1,615 1,406 1,352 1,223 (3.5) SD 182 160 471 240 240 8AB Avg. 1,459 1,481 1,245 1,245 1,197 (4.2) SD 125 307 62 62 142 10AB Avg. 1,557 1,757 1,757 1,708 1,459 (4.8) SD 160 191 191 147 240 12AB Avg. 1,793 1,788 1,788 2,099 1,681 1,285 (5.5) SD 147 49 49 294 240 298 14AB Avg. 1,890 2,028 2,015 1,988 1,970 (6.1) SD 98 53 178 93 67
Edge withdrawal – OSB-1 6AB Avg. 1,303 1,481 1,134 1,330 (3.5) SD 85 227 280 120 8AB Avg. 1,655 1,668 1,539 1,370 (4.2) SD 120 53 351 116 10AB Avg. 1,686 1,721 1,686 1,410 (4.8) SD 160 214 165 200 12AB Avg. 1,597 2,019 1,655 1,784 (5.5) SD 534 160 173 302 14AB Avg. 1,984 1,699 1,699 1,970 (6.1) SD 58 165 165 67
a Major diameter refer to basic diameter (mm) of screw used in predictive expression b Statistic: avg. refers to average; SD refers to standard deviation
36
Based on the results from the screw withdrawal tests, a regression analysis was carried out
and the following expression was proposed for face and edge withdrawal from OSB:
Y = a D b (L – cD)d We (1.17)
where:
Y = screw holding strength, lb;
a, b, c, d, and e = regression coefficients;
cD = tip effect, loss in strength that occurs because the tip of the screw is not in contact
with the composite when pilot holes are used;
1) For face withdrawal the proposed predictive expression is: Y = 1.99 D 0.5 (L – 2D/3) W1.78 (empirically determined from tests) (1.18)
Y = 0.87 D 0.5 (L – 2D/3) W2 (simplified) (1.19)
2) For edge withdrawal the proposed predictive expression is: Y = 0.032 D 0.547 W2.81 (empirically determined from tests) (1.20)
Y = 0.66 D 0.5 W2 (simplified) (1.21)
It can be clearly observed that the screw diameter and depth of penetration as well as the
density of the board affect the strength of such joints. Results have indicated that high
strength screw joints can be fabricated from OSB.
1.2.5.3 Staples Staples are widely used in the furniture industry. They are frequently used to hold glue
blocks in place until the adhesive dries, as well as in reinforcing joints. Moreover, the
Wood Handbook provides equations to determine the withdrawal and lateral strength of
joints made with staples intended for use in construction, but these equations are based on
static tests on nails and have not been verified for staples. But in Eurocode 5 (2004), the
equations for all metal dowel-type fasteners, such as nails, screw and staples are the same.
Staples are common in the fabrication of upholstered furniture where they are mostly used
in the attachment of fabric to the frame. More recently, staples are being used in the
37
fabrication of the frame itself because they provide a rapid and convenient method of
fabricating joints.
Erdil et al. (2003a) conducted tests and developed basic strength data for staple holding
strength in both plywood and OSB (Figures 1.16 to 1.20 and Tables 1.14 to 1.17). These
could be used in the engineering design of furniture frames constructed of such materials.
Results of the tests showed that the staple holding strength from the face of plywood and
OSB was at least 50 percent higher than that from the edge. Results from the lateral
holding capacity tests of staple on edge for plywood and OSB indicated that the strength
was proportional to the number of staples (Erdil et al. 2003a). In the gusset plate stapled
moment resisting joints, results demonstrated that the size of the gusset plate and the
number of staples were the key factors in the overall strength of joints. The larger were the
dimensions of the plate and the number of the staples, the higher the strength of the joints.
Furthermore, application of glue in the gusset plates could at least double the moment
resisting strength of such joints. Zhang et al. (2001b) studied bending strength of gusset-
plate joints constructed of wood composites, as given in Table 1.18. Results showed that
the bending strength of gusset-plate joints was significantly affected by gusset-plate
thickness, width, and length. Among the plate size parameters, plate width affected joint
bending strength the most. Joint member material type and the number of staples had no
effect on bending strength.
Figure 1.16 General configuration of face (left) and edge (right) withdrawal specimens (from Erdil et al. 2003a)
38
Figure 1.17 Geometric dimensions of face and edge staple withdrawal specimens (adapted from Erdil et al. 2003a)
Figure 1.18 Apparatus for evaluating face and edge withdrawal strength of staples (adapted from Erdil et al. 2003a)
Table 1.14 Withdrawal strength of staples from OSB (adapted from Erdil et al. 2003a) Withdrawal from edge Withdrawal from face
Material 1 staple 2 staples 1 staple 2 staples code DOPa Force
avg./SDb DOPa Force
avg./SDb DOPa Force
avg./SDb DOPa Force
avg./SDb Density Thickness
(mm) (N) (mm) (N) (mm) (N) (mm) (N) (kg/m3) (mm) OSB-1c 19.1 400/111 19.1 867/156 19.1 445/89 19.1 1,134/156 751.3 19.1 OSB-2 19.1 111/22 19.1 534/111 19.1 467/133 19.1 1,023/222 626.3 19.1 OSB-3 15.9 423/89 15.9 N/A 15.9 801/178 15.9 1,979/200 776.9 22.2 OSB-4 25.4 445/151 25.4 645/151 15.9 756/129 15.9 1,245/187 680.8 22.2 OSB-5 25.4 489/116 25.4 667/138 19.1 890/178 19.1 1,735/262 752.9 19.1
a DOP = nominal depth of penetration of staple shakes in the test block b SD = standard deviation c OSB -1 to 5 are oriented strandboard made of mixed softwood
39
Table 1.15 Summary of grade properties on OSB panels (adapted from Forintek’s report (Wang and Knudson 2002))
(ASTM D1037-96a) Staple withdrawal Face Edge (N) (N) Mill A* 426 898 Mill B 621 914 Mill C 595 810 Mill D 564 880 Mill E 427 842 Mill F* 651 1,232 Mill G* 622 942 Mill H 741 1,073 Mill I* 935 1,023 Mill J 786 1,014 Mill K 1,089 1,044 Mill L 645 790 * OSB panels sold for furniture applications
Figure 1.19 Configuration and apparatus of staple lateral holding strength (adapted from Erdil et al. 2003a)
Table 1.16 Lateral holding strength of the staples (adapted from Erdil et al. 2003a) Lateral holding force avg./SDb DOPa(mm) 25.4 28.6 31.8 34.9 25.4 28.6 31.8 34.9 Material code
1 staple 2 staples
------------------------------------------------(N)--------------------------------------------------- OSB-1 792/98 841/111 738/93 676/107 1,317/191 1,615/125 1,499/71 1,570/102 aDOP = nominal depth of penetration of staple shakes in the test block bSD = standard deviation
40
Figure 1.20 Configuration and apparatus for staple bending strength (adapted from Erdil et al. 2003a)
Table 1.17 Moment resisting strength of Douglas-fir plywood gusset and stapled joints (adapted from Erdil et al. 2003a)
Moment resisting strength (avg.)a
No. of staples Gusset dimension With adhesive Without adhesive (mm) ----------------------(N-m)----------------------- 6 102 by 102 by 4.8 425.2 (84.6)a 133.7(7.8) 10 152 by 102 by 4.8 501.5(49.4) 235.9(12.0) 12 203 by 102 by 4.8 508.5(83.8) 308.3(30.3)
a Number between brackets is the standard deviation
41
Table 1.18 Bending strength of gusset-plate joints constructed of wood composites (adapted from Zhang et al. 2001b).
Material type Gusset-plate dimensions Bending strength Coefficient of variation (mm) (N-m.) (%)
6.4 by 76 by 152 630.7 13.1 6.4 by 76 by 254 759.5 18.5 6.4 by 102by 203 1,292.0 14.8 6.4 by 127 by 152 1,649.6 7.1 6.4 by 127 by 254 1,765.1 12.5 9.5 by 76 by 152 940.0 11.3 9.5 by 76by 254 1,228.9 23.7 9.5 by 102by 203 1,477.6 12.8 9.5 by 127 by 152 1,270.5 18.7
Plywood
9.5 by 127 by 254 1,882.6 8.8 6.4 by 76 by 152 710.2 10.3 6.4 by 76 by 254 688.2 17.8 6.4 by 102by 203 1,295.9 18.0 6.4 by 127 by 152 1,712.0 8.8 6.4 by 127 by 254 1,850.7 7.0 9.5 by 76 by 152 997.8 5.5 9.5 by 76by 254 1,254.9 15.8 9.5 by 102by 203 1,549.6 11.3 9.5 by 127 by 152 1,801.6 11.3
Timberstrand
9.5 by 127 by 254 2,242.5 12.4 6.4 by 76 by 152 621.8a 4.7 6.4 by 76 by 254 778.0 12.3 6.4 by 102by 203 1,265.0 10.1 6.4 by 127 by 152 1,065.4 16.6 6.4 by 127 by 254 1,777.5 5.3 9.5 by 76 by 152 902.1 8.9 9.5 by 76by 254 1,114.5 10.0 9.5 by 102by 203 1,149.5 7.2 9.5 by 127 by 152 1,410.2 9.2
ESL
9.5 by 127 by 254 1,904.4 7.4
1.2.5.4 Nails
Nails are not commonly used in furniture construction as structural load bearing fasteners
in areas of high stress; rather, they are used to hold other types of joints such as dowel
joints together until the glue dries.
Sometimes nails are used structurally and are subject to shear and/or withdrawal forces.
When the top rail on a sofa is laid in flat position, nails are often driven through it into the
top of interior uprights. In this case the nails are subjected to both shear and withdrawal
forces. Moreover, nails are often driven through side slats into the ends of the centre rail. In
such cases, nails are primarily subject to lateral shear forces. Nails are frequently used to
attach stretchers to front and back rails. In this type of construction, nails are driven
through the rails into the ends of the members, and are loaded in shear and withdrawal.
42
Twelve types of panels were sampled from different OSB mills in a study carried out at
Forintek using commercial OSB panels (Wang and Knudson 2002). Panels from mill A, F,
G and I were marketed as furniture grade or sold to furniture manufacturers. The nail
withdrawal and lateral nail strength, nail pull-through resistance and planar shear-strength
are given in Table 1.19. From this Table, one can see that commercial OSB panels
currently sold for furniture applications generally have higher fastener holding capacities
than standard construction type OSB panels. There were also differences in properties
between the various OSB furniture panels.
1.2.5.5 Through bolt with dowel nuts
Through-bolts with dowel-nuts are commonly used in furniture construction, both as
primary connectors and also to reinforce weak joints. For instance bed bolts, one form of
through-bolt, have been used for many years to attach bed rails to bed posts in order to
allow transportation of bulky bed frames. Aside from their use in the construction which
must be assembled and disassembled on site, through-bolt with dowel-nut construction is
of particular interest due to its high strength and reliability (Eckelman 1989a, Eckelman
and Erdil 1998, Erdil et al. 2003b). Through-bolts with dowel-nuts are often used in chair
construction, where they are used, to reinforce the critical seat side rail to back post joints.
They are also widely used in bulky furniture where these must be shipped in a partially
Table 1.19 Summary of grade properties on OSb Panels (adapted from Forintek’s report (Wang and Knudson 2002)) (ASTM D 1037-96a) Nail withdrawal Lateral nail resistance
Nail pull-through
Planar shear- shear stress
Face Edge Para Perp N/A Para Perp --------------------------------------------------(N)-------------------------------------------------------
Mill A* 207 359 1,214 1,229 1,180 1,261 1,419 Mill B 164 199 904 1,073 1,418 814 821 Mill C 211 268 1,425 1,188 1,275 739 901 Mill D 243 266 1,148 1,132 1,384 852 829 Mill E 138 229 866 1,229 1,176 809 847 Mill F* 274 531 1,921 1,773 2,063 1,561 1,680 Mill G* 329 320 1,742 1,488 1,469 816 994 Mill H 386 401 1,620 1,808 1,688 975 911 Mill I* 427 361 1,407 1,548 1,711 1,076 1,016 Mill J 396 273 1,431 1,690 1,755 864 667 Mill K 522 418 1,597 1,712 2,311 1,081 1,212 Mill L 367 296 1,524 1,738 1,725 726 779
* Panels sold for furniture applications
43
disassembled condition and where stales are used to attach the ends of legs to steel
mounting plates which are attached to the underside of table top (Eckelman 1977). These
fasteners also have significant potential value in upholstered furniture frame construction
in similar situations where strength and reliability are essential. An obvious use is the
attachment of an arm to a back post where reliability is essential.
Figures 1.21 to 1.23 demonstrated the through-bolt with dowel-nut in Erdil et al. 2003b.
The bending resistance of a number of T-shaped joints constructed with dowel nuts are
given in Table 1.20. The holding strength values of 9.5mm (3/8 inch) diameter dowel nuts
in the end of a rail are given in Table 1.21. Values are given for nuts placed 1, 1.5, and 2
inches from the end of the rail.
Figure 1.21 Through-bolt with dowel-nut (from Erdil et al. 2003b)
Figure 1.22 Dimensions of specimens for dowel-nut withdrawal test (from Erdil et al. 2003b)
44
Figure 1.23 Dimensions of moment resisting through-bolt with dowel-nut specimens (adapted from Erdil et al. 2003b)
Table 1.20 Bending strength of moment resisting through- bolt with dowel nut joints (adapted from Erdil et al. 2003b)
Rail width (mm) Rail width (mm) 51 102 152
No. of nuts 1 2 3 Material
code Statistic Ultimated bending moment
(N-m) Density (kg/m3)
Thickness (mm)
OSB-1a Ave./stdev 121.5/30.1 297.2/29.6 700.6/62.0 751.3 19.1 OSB-2 Ave./stdev 76.3/14.2 268.4/33.8 546.7/82.0 626.3 19.1 OSB-3 Ave./stdev 722.1/56.2 1,037.3/105.3 776.9 22.2 OSB-4 Ave./stdev 445.8/45.4 922.1/130.7 680.8 22.2 OSB-5 Ave./stdev 523.2/43.5 795.5/137.7 738.5 19.1
a OSB -1 to 5 are oriented strand board made of mixed species
Table 1.21 Holding strength of dowel nut in relation to end distance (adapted from Erdil et al. 2003b)
Edge distance Material 25-mm. 38-mm 51-mm
code Statistic -------------------------------(N)-------------------------------- OSB-1a Ave./stdev 5,871/1,379 6,405/1,156 5,649/1,201 OSB-2 Ave./stdev 4,181/400 4,581/311 4,048/578 OSB-3 Ave./stdev 6,850/1,201 7,517/979 7,562/1,023 OSB-4 Ave./stdev 6,316/1,201 6,628/890 6,628/979 OSB-5 Ave./stdev 5,782/578 6,005/890 6,894/845
a OSB -1 to 5 are oriented strand board made of mixed species
45
1.2.5.6 Toothed metal plates
One fastener used to a limited extent in upholstered furniture frame construction is the
toothed metal plate. Typical applications of this connector include the back post to side
seat rail joints in recliner type chairs and in front rail to stump (or front post) joint sofa
frames (Zhang et al. 2005). Both of these joints are highly stressed and thus require high
strength joint - which toothed metal plates can provide. Toothed metal plates also provide a
quality control advantage in that they can be inspected visually to determine if they have
been properly installed. The bending resistance of several plate and rail geometries and
material combinations are given in Tables 1.22 and 1.23. As can be seen, very high
strength values may be achieved with wider plates, particularly when used on both sides of
the joint.
1.2.5.7 Tenon-mortise joints
No literature could be found on the use of tenon and mortise joints in upholstered furniture.
With the expansion of the use of CNC machinery, it might be of interest to further explore
the broader use of such type of joints. It has been found that in certain situations, grooved
components are being used which somehow resemble half tenon and mortise joints.
1.2.5.8 T-nut joints There is very limited published literature on T-nuts joints, in spite of the fact that they are
increasingly finding application in upholstered furniture constructions, such as sofas and
chairs. Information is lacking on both static and dynamic holding strength of T-nuts. Since
such information is essential for the engineering design of furniture frames, Eckelman
(1998) carried out a study to obtain preliminary estimates of the static holding strength of
representative types of T-nuts in a wide variety of domestic wood and wood composites.
He concluded that two types of failure occur when withdrawing T-nuts. Either the nut
failed from the neck, or the material around the nut crushed and the nut pulled through.
Results of such tests have indicated that high strength joints could be constructed with
these fasteners, but that strength tends to vary greatly depending on the style and source of
the nut. Hence, specific performance information is needed for each T-nut. Based on the
46
same study, the T-nut diameter and thickness of the parent material from which it is
manufactured significantly affect the holding strength of this fastener.
Table 1.22 Bending strengths of moment-resisting toothed metal plate connector joints (adapted from Eckelman and Erdil, 1998) Plate on one face Plate on two faces Rail width (mm) Rail width (mm) 76 102 152 76 102 102 152 152 Plate description (mm) Plate description (mm) Material 38 x 114 51 x 114 (2)1-25 x 114 38 x 114 51 x 114 76 x 114 (2)1-25 x 114 (2/1)2-25 x 114
code ----------------------------------------------(N-m)----------------------------------------------- OSB-1 210.2 436.2 529.7 329.4 606.2 1,012.5
30.3 25.1 51.0 15.9 34.5 35.3 OSB-2 187.9 363.1 523.8 318.7 506.0 878.9
11.1 31.9 87.6 14.7 7.6 120.1 OSB-3 1,183.1 1,202.3
45.2 83.6 OSB-4 1,045.3 898.4
108.5 35.0 OSB-5 934.5 965.0
70.1 44.1 (2)1 indicates that two 25mm (1 in) plates were used instead of a single plate (2/1)2 indicates that two 25mm (1 in) plates were used instead of a single plate on one side of the joint and one 25mm (1 in) plate on the other side of the joint a OSB -1 to 5 same as in article Erdil et al. (2003b)
Table 1.23 Zhang et al. (2005) evaluated the moment capacity of metal-plate-connected joints in furniture grade pine plywood.
Metal-plate length Rail width Metal-plate width 76 114 152 191
------------(mm)------------ --------------------------------------(N-m)--------------------------------- 3.5 323.5(5) 352.6 (10) 360.7 (4) 372.9 (5) 4.8 451.0 (5) 523.4 (6) 505.2 (4) 529.4(2) 83 6.1 527.5 (6) 721.4 (4) 742.5 (3) 746.4 (8) 3.5 357.4 (10) 482.2 (2) 480.8 (8) 477.5 (6) 4.8 512.0 (5) 648.2 (7) 647.9 (6) 635.7 (4) 114 6.1 608.1 (5) 884.1 (7) 878.5 (5) 928.6 (4) 3.5 567.0 (9) 691.8 (11) 675.5 (9) 746.9 (9) 4.8 672.0 (11) 850.4 (7) 873.8 (5) 884.3 (6) 152 6.1 806.3 (5) 1,110.6 (8) 1,081.9 (6) 1,062.5 (7) 3.5 731.1 (8) 877.3 (4) 956.0 (6) 1,006.9 (8) 4.8 864.9 (10) 1,120.1 (6) 1,074.0 (4) 1,142.5 (2) 191 6.1 989.9 (8) 1,500.3 (3) 1,550.5 (3) 1,536.6 (5)
47
Erdil (1998) also tested T-nuts in upholstered furniture. From his study, two general types
of failure occurred. Either the nuts themselves failed or the wooden board below the nuts
crushed, allowing the nuts to be pulled deeply into the substrate. With OSB, the nuts were
pulled into the face of the board resulting in failure of the construction. On the other hand,
it was found that the holding strength increases linearly with the thickness of the boards.
1.2.6 Frame construction Before using stiffness matrix method in the structural analysis, Eckelman (1967) used
slope deflection methods to analyze chair frame design. Subsequently, the concepts of
elastically non-linear, semi-rigid joints based on stiffness analysis were applied in his
doctoral research (Eckelman 1968). The frame member stiffness coefficient was modified
owing to the semi-rigid joints, and an iterative approximation technique was applied to the
non-linear joint behaviour. After that, Eckelman (1970b, 1970c, 1971b) modified the
analysis to a wide range of furniture frame problems, where he incorporated these
approaches into a computer program named “CODOFF”. This program serves as the basis
for many other related program moduli in his studies.
1.2.7 Structure of sofa frames Thousands of styles for upholstered sofas are being used in the world, but generally, their
frames may be categorized into a relatively few specific types (Picado 1988). Owing to the
upholstery materials, the sofa frame may be difficult to visualize. Often only a few major
features can be identified, such as the relative positions of the arm and top rail, stump and
arm. But once the type of sofa frame is determined, it can be structurally analyzed.
According to Erdil (1998), a sofa can be structurally analyzed with respect to three
different subsystems: 1) Seat system; 2) Side frame system; 3) Back system (see
details in Chapter 3 Load distribution). A typical sofa frame construction is shown in
Figure 1.24.
48
Top Rail
Front Stump
Top Arm Rail
Back Posts
Front Rail
Front Spring Rail
Stretcher
Upright
Middle Side Rail
Bottom Side Rail
Back Rail Back
SpringRail
BACK FRAME SYSTEM
SEAT FRAME SYSTEM
SIDE FRAME SYSTEMTop Rail
Front Stump
Top Arm Rail
Back Posts
Front Rail
Front Spring Rail
Stretcher
Upright
Middle Side Rail
Bottom Side Rail
Back Rail Back
SpringRail
BACK FRAME SYSTEM
SEAT FRAME SYSTEM
SIDE FRAME SYSTEM
Figure 1.24 Typical sofa frame construction (from Chen 2003).
1.2.8 Structure of other upholstered furniture frames Most of the other types of upholstered furniture frames are in fact of the sofa type but
narrower in width, with one or more seating positions. Hence, these can be modelled using
the general sofa framework described previously. One type of upholstered furniture is very
different from the sofa type, it is the reclining seat. Recliners include several of the same
subsystems presented in the sofa system. The seat, back and side subsystems can be found
too, but there are many features specific for such furniture, including the presence of the
reclining mechanism, which is a metallic device, attached to the furniture frame itself and
where load concentration occurs as well as repetitive dynamic loading. This type of
furniture has not been described in the literature.
Chapter 2 Load Distribution on a Sofa Frame
50
2.1 Introduction This chapter provides background information on how to estimate load distribution on the
joints of a full-size three-seat sofa frame. A simplified three-seat sofa frame structural
model was proposed, including only the most critical members and joints needed to resist
service loads. Structural analyses were performed on this frame using the various GSA
loading cases (i.e. light duty, medium duty and heavy duty) and boundary conditions.
Internal forces at each connection and stresses in each structural member were evaluated in
two ways. First, a simplified analysis was carried out using basic structural analysis
techniques and assuming joints rigid. Internal forces at each connection in the frame model
is determined, i.e., magnitudes and directions of axial and shear forces and bending
moments. The second method is a more rigorous analysis using Finite Element Model
(FEM). For this purpose, commercial software SAP 2000 is chosen. Results of this analysis
are reported in Chapter 7.
2.2 General configuration of loads and the construction of the sofa frame
2.2.1 Sofa frame construction The general configuration of a typical three-seat wooden sofa frame is shown in Figure
1.24. It consists of three basic structural subsystems, a) the seat frame system, b) the back
frame system, and c) the side frame system. The seat frame system includes the principal
structural members, which are: the front and back rails, the front and back spring rails, and
the stretchers. The back frame system consists of the top rail, the back posts, and the back
uprights. The side frame system’s principal members are the front stumps, the top arm
rails, the middle side rails, and the bottom side rails. Common types of joints connecting
frame members utilized in a sofa frame construction are metal fasteners (staples and
screws)-glued blocks, dowels, gusset-plates, metal-plates, mortise and tenon joints, and
metal dowel-nuts..
51
2.2.2 Frame performance tests The loads on the frame were estimated in accordance with the service requirements of such
frames from GSA Specification FNAE-80-214 (see Tables 1.1 and 1.2 in Chapter 1).
These specifications were established for performance testing of upholstered furniture
frames and provide, perhaps, the best estimates of service loads, since it is known that
these specifications were based on a wide range of experimental data. Furniture
performance tests may be defined as accelerated tests that predict the ability of a piece of
furniture to fulfill its intended function. Performance test standards such as the GSA
performance test regime FNAE-80-214A are based on a stepped load model, i.e. tested
frame members and joints are subjected to cyclic stepped loads rather than a constant
cyclic load. Table 2.1 shows five test load configurations for evaluating structural
performance characteristics of upholstered furniture bare frames. These are: Top Rails-
Front to Back, Arms-Outward, Arms-Vertical, Front Rails-Vertical, and Front Spring
Rails-Inward tests. Table 2.1 also gives detailed cyclic load schedules for these tests. The
schedules include initial load, load increments, number of loads, and service acceptance
levels in terms of passed load levels and accumulative numbers of cycles. Figure 2.1 shows
the structural performance test loads of three-seat sofa frame.
Table 2.1 Cyclic load schedules of GSA performance tests for bare frame (adapted from GSA 1998)
Test Initial
load Load
increments Number of loads
Light-service acceptance
level
Medium-service acceptance
level
Heavy-service acceptance
level ---------- (N) --------- -------------------------- (N/cycle) ---------------------- Top Rails- Front to Back
334
111
3
334/25,000
445/50,000
667/100,000
Arms- Outward
222
111
1
334/50,000
667/125,000
890/175,000
Arms- Vertical
445
445
1
1,779/100,000
2,669/150,000
3,558/200,000
Front Spring Rails - Inward
445
445
3
1,334/75,000
1,779/100,000
2,669/150,000
Front Rails-Vertical
445
445
3
1,334/75,000
1,779/100,000
2,669/150,000
52
TOP RAILS-FRONTTO BACK
ARMS-OUTWARD
ARMS-VERTICAL
FRONT RAILS-VERTICAL
SPRING RAILS-INWARD
TOP RAILS-FRONTTO BACK
ARMS-OUTWARD
ARMS-VERTICAL
FRONT RAILS-VERTICAL
SPRING RAILS-INWARD
Figure 2.1 Structural performance test loads of three-seat sofa frames
2.2.3 Simplified Sofa Frame Model Reduced to its basic form and function, the sofa frame (Figure 2.2) consists of the front and
back rails, the front and back spring rails, the top rail, the back posts, the front stumps, the
top arm rails, and the bottom side rails.
Top Arm Rail
72 in.
26 in.
34 in.
18 in.
Top Rail
Front Rail
Front Spring Rail
Back Spring Rail
Back Rail
Back Post
Front Stump
Side Rail
Top Arm Rail
72 in.
26 in.
34 in.
18 in.
Top Rail
Front Rail
Front Spring Rail
Back Spring Rail
Back Rail
Back Post
Front Stump
Side Rail
Figure 2.2 Simplified three-seat sofa frame structural model
53
2.2.4 Simplified Analysis of Sofa Structural Joints The internal forces acting on the joints of these subsystems of the simplified sofa frame
were calculated using basic structural analysis techniques assuming rigid joints. An
analysis of each joint was made under the light level of service conditions indicated in the
GSA specification to satisfy the domestic use requirements. These requirements are based
on the cyclic performance. Since the cyclic joint strength is only equal to about half of the
static joint strength, the static strength requirement must be at least doubled (Eckelman and
Erdil 1998).
2.3 Discussion Results of the analysis are summarized in Table 2.2 Results can be evaluated under the
three structural subsystems: seat system, side system, and back system.
2.3.1 Seat System The seat system is composed of the front and back rails, front and back spring rails. Side
rails and stumps are also supporting components of the seat system. The seat system is
mainly subjected to vertical loads resulting from the sitting action, horizontal loads put
outward on arm, and out-of-plane loads owing to the spring system used as part the seat
foundation system. Generally, sinusoidal springs generate a substantial amount of out-of-
plane loads on the front and back rails. The critical joints in the seat system are the front
rail to stump (Erdil 1998).
Front rail to stump joints
The front rail to stump joints is subjected to three different loadings that can be analyzed in
detail, namely, vertical loading, outward sidethrust loading, and out of plane loading. The
joint strength values and estimated ultimate forces required for the three levels of service
conditions are given in Table 2.2.
Erdil (1998) assumed that in the case of vertical loading (Figure 2.3), the bending moment
acting on the front rail to stump joint is small and it may be neglected. Thus, the shear
strength of the joint which determines its ability to resist vertical loads is of primary
54
Table 2.2 Estimated joints strengths
Joint type Loading direction Cyclic light duty load requirement
Static light duty load requirement
Vertical 2,002 N 4,003 N Horizontal 135.6 N-m 271.2 N-m
Front rail to stump
Out-of plane 1,668 N 3,336 N Vertical 1,334 N 2,669 N Horizontal 723 N 1,446 N
Back post to arm
Out-of plane 288.2 N-m 576.3 N-m Side rail to stump Horizontal 165 N-m 330 N-m
Vertical 2,002 N 4,003 N Top rail to back post Horizontal 500 N 1,001 N
concern. For example, for Front rails (Table 2.1), using light duty category, a single
vertical load is equal to 1334 N (300 lbf). As there are 3 loads acting on the front rail, the
total load becomes 4003 N (900 lbf). However, as the Front rail has two joints with stump,
each joint carries a shear force of 2002 N (450 lbf) of cyclic load. To get to the static loads,
it is necessary to double that load requirement which results in a static load of 4003 N (900
lbf).
Bending forces acting on the front rail to stump joint owing to sidethrust forces applied to
the arms (Figure 2.4) cannot be neglected. As a matter of fact, high bending forces occur in
this joint when a sidethrust load is applied to the arm or the top of the stump. This joint can
be treated as a two-pin moment resisting type of joint for such loading condition. Based on
the design of the sofa frame, it is proposed to take Arms-Outward load in Table 2.1 light
duty being equal to 334 N (75 lbf). Using a single load (Fh), the distance between this load
to the joint is 457-51 mm (18-2 in), 457 mm (18 in) is the height of arm, 51 mm (2 in) is
half of the front rail width). So the ultimate bending strength required for this joint is
estimated at 135.6 N-m (1200 lbf-in). Double that to achieve the load for static
requirement, it becomes 271.2 N-m (2400 lbf-in).
55
Figure 2.3 Front rail to stump joint under vertical loading
Figure 2.4 Front rail to stump joint under horizontal sidethrust loading Front rails of sofas are also subjected to out-of-plane loads which occur due to the
attachment of sinusoidal type seat springs (Figure 2.5). As those springs are normally
attached, each imposes out-of-plane force of approximately 445 N (100 lbf) to the top of
the front and back rail. The average number of springs attached to a 1.83-m (72-in) front
rail is about 15. So total spring stress is 445 x 15 = 6,675 N (100 x 15 = 1,500 lbf), shared
by front and back spring rails, 6,675/2 = 3,337.5 N (1500/2 = 750 lbf), shared by both front
rail to stump joints and 1,669 N (375 lbf) for each joint. But as the spring forces act on the
top edge of the rail whereas the joints are located some distance below the top edge, then it
is necessary to make some minor adjustments. Therefore, the loads transferred to the end
joints should be a bit bigger than 1,669 N (375 lbf), i.e. 1,669 N (375 lbf) is the minimum
force on each front rail to stump joint, doubling that for the static load, the total loads
would be over 3,337.5 (750 lbf).
56
Figure 2.5 Front rail to stump joint under out of plane loading
2.3.2 Side Rail System The side rail system can be analyzed as a two dimensional frame which generally consists
of a stump, back post, arm, and side rails. Side frames are generally subjected to vertical
forces due to sitting action on the arm, horizontal forces as a result of front to back loading
of frame, and the force which arise when a user pushes sideways on an arm. This side
forces which mainly tend to fail the front rail to stump joint as mentioned in the previous
discussion. The most critical joints in side frame systems are the back post to arm and the
side rail to stump and back post joints (Erdil 1998).
Back Post to Arm Joint Generally, the back post to arm joints must resist both vertical forces and horizontal forces
(Figure 2.6). Vertical forces occur, for example, when one or more people sit on an arm.
Consider the front rails-vertical (Table 2.1), for the light level of service, each joint should
resist an estimated load of 1,334 N (300 lbf), doubling that for static requirement to 2,669
N (600 lbf). This type of joint is basically flexible; thus, internal bending forces generated
under the action of vertical loading may be neglected.
The back post to arm joints must also resist front to back loading. Take Top rails-front to
back (Table 2.1) with a light duty load of 334 N (75 lbf), there are 3 acting loads, and two
side arms. Therefore, Fh = 334 x 3 /2 = 501 N (112.5 lbf) (Figure 2.8). As a first
approximation, the internal withdrawal force at the point of interest can be expressed as
57
)lbf.(N).(
*.)hh(
Fhf h 516272320346605014660
21
1 =−
=−
= (2.1)
in which f is the internal withdrawal force (pounds), h1 is height of the back post - 660.4
mm (26 in), h2 is the distance from joint center to point of loading - 203 mm(8 in), and Fh
is the horizontal front to back load on each joint - 501 N (112.5 pounds). According to this
expression the estimated withdrawal force acting on the dowels in the arm to back post
joint is 723 N (162.5 lbf) for cyclic and 1,446 N (325 lbf) for static strength requirements.
Figure 2.7 shows the side rail system under out-of plane arm outward loading which arise
when a user pushes sideways on an arm. This side forces which mainly tend to fail the
front rail to stump joint as mentioned above. Bending forces which act on arm to back post
joint due to sidethrust forces applied to the arms cannot be neglected. As a matter of fact,
high bending forces occur in this joint when a sidethrust load is applied to the arm. This
joint can be treated as a two-pin moment resisting type of joint for such a loading
condition. Figure 2.7 shows details of the arm to backpost joint under outward sidethrust
loading condition. Based on the Table 2.1, the arm-outward for light duty is taken to be
equal to 334 N (75 lbf), with an arm length of 864 mm (34 in). The ultimate bending
moment which occurs at the backpost to arm joint should be equal to 334 x 864/1000 = 288
N-m (2550 lbf-in). For static requirement, the load at this joint could be estimated at 288 x
2 = 576 N-m (5100 lbf-in).
Figure 2.6 Side rail system under vertical loading
58
Figure 2.7 The side rail system under horizontal front to back loading
Side Rails to Back Post or Stump Joints
The side rail to back post joints in a sofa frame are subjected to high in-plane bending
forces. These forces develop at the side rail to back post or side rail to stump joints when a
horizontal front to back load is applied to the top of the back post. Figure 2.8 shows the
configuration of these joints. In order to analyze these joints, the whole side system is
considered as a two dimensional frame. It may also be assumed that the arm joints in this
frame are flexible, i.e., hinged joints. Looking at Table 1.1, Top rails-front to back light
duty load of 334 N (75 lbf) with 3 loads shared by the two sides – side rail to back post
joints, the total load per joint should be equal to 334 x 3 /2 = 500 N (112.5 lbf).
Multiplying by the length of the back post – 660 mm (26 in.), the total bending moment
will be equal to 500 x 660/1000 = 330 N-m (2925 lbf-in). But as this moment is shared by
2 joints (assuming the three joints resist bending moments equally), the bending moment of
side rail to back post should be equal to 330/2 = 165 N-m (1462.5 lbf-in). Doubling that for
static loading, the proposed design moment shall be 330 N-m (2925 lbf-in).
2.3.3 Back System The back system consists of the back rail and the top rail. It is mainly subjected to
horizontal front to back shear forces, but it may also be subjected to vertical shear forces.
The top rail to back post joints are the critical joint in the back system (Erdil 1998).
59
Top Rail to Back Post Joints
In the case of vertical loading, top rails are stressed both from users sitting on the rail and
from normal sitting loads transferred to the rail. If the frame supports three people sitting
on the top rail, then it should be the same analysis as the vertical load on the front rail to
the stump. The estimated ultimate lateral shear force acting on this joint is 2002 N (450 lbf)
for light duty, double for static it will be 4003 N (900 lbf).
The back post to top rail joints (Figure 2.8) are also subjected to horizontal lateral shear
forces when users lean backward in a sofa. If we take the top rail-front to back light duty
load of 334 N (75 lbf) (Table 1.1) times the number of loads (3), and assume that this total
load is shared equally by two back posts, then each joint should support 334 x 3 /2 = 501 N
(112.5 lbf). Doubling that for static loading, each joint should be able to carry 1001 N (225
lbf).
Figure 2.8 Horizontal loads on the top rail to back post joints
2.4 Summary This chapter estimated load distribution on the joints of a full-size three-seat sofa frame
model. Structural analyses were performed on this frame using the GSA loading. Internal
forces at each joint were evaluated based on basic established structural analysis
techniques. Magnitudes and directions of internal forces at each joint in the frame were
determined based on certain assumptions related to the joints. In the later Chapter, FEM
(Finite Element Method) software (SAP 2000) was used to analyze the furniture frame and
have a better idea of the stress concentration and load distribution in every member and at
every joint in the sofa frame model.
Chapter 3 Localized density effects on fastener holding capacities in wood-based panels
61
3.1 Localized density effects on fastener holding capacities in wood-based panels. Part 1: Static tests
3.1.1 Résumé L'objectif principal de cette étude était de caractériser l’effet de la variation de densité
locale de trois types de panneaux agglomérés à base de bois sur la tenue mécanique de
différentes attaches. Des panneaux à lamelles orientées (OSB) de trois épaisseurs
différentes, des panneaux de fibres de moyenne densité (MDF) d’une épaisseur et des
panneaux de particules (PB) d’une épaisseur ont été utilisés pour évaluer la résistance à
l’arrachement de vis et agrafes sur la face et de côté. Également, nous avons évalué l’effet
sur la résistance d’enfoncement des têtes des agrafes et vis ainsi que la résistance latérale
des vis. Ensuite, les propriétés mécaniques ont été corrélées avec les variations de densité
locales des panneaux. Les résultats d'essai ont indiqué que pour les panneaux OSB, la
variation de densité a un effet significatif sur l’arrachement des vis ainsi que sur
l’enfoncement des têtes des vis et sur les résistances latérales des vis. Cependant, les effets
étaient moins évidents pour l’arrachement et l’enfoncement des têtes des agrafes. Pour les
panneaux PB, la variation de densité a eu un effet significatif sur l’arrachement et sur
l’enfoncement des têtes des vis mais les effets étaient moins prononcés pour la résistance
latérale des vis ainsi que pour l’arrachement et l’enfoncement des têtes des agrafes. Pour
les panneaux MDF, aucune corrélation significative n'a été trouvée. Ceci peut être attribué
à une faible variation de densité de ces panneaux. Les données seront employées pour
optimiser la structure des meubles et pour fournir des recommandations à l'industrie des
panneaux concernant l'utilisation des attaches en fonction de leurs produits.
3.1.2 Abstract The main objective of this study was to characterize localized density effects on some
common fasteners’ holding capacities in wood-based panels. Oriented strand board (OSB)
of three different thicknesses, medium density fiber board (MDF), and particleboard (PB)
were tested for screws and staples withdrawal from face and edge, head pull-through, and
for screw lateral resistance. The fastener holding capacities were correlated with localized
density of the panels. Test results indicated that in the OSB panels, density variation had a
62
significant effect on the screw withdrawal, head pull-through, and lateral resistances, but
the effects were less evident for the staple withdrawal and head pull-through. For PB,
density variation had a significant effect on the screw withdrawal and head pull-through
resistances, but the effects were less pronounced for screw lateral resistance, staple
withdrawal and head pull-through. For MDF, no significant correlations were found; this
could be attributed to the low density variation in these panels. The data will be used for
the optimization of furniture frames, and to provide recommendations to the panel industry
on the use of the fasteners with their products.
3.1.3 Introduction Upholstered furniture manufacturers are always looking for ways to reduce the cost of their
products through the use of new engineered materials and processes. With the development
of CNC technology, wood-based composite panels are becoming a good alternative for
solid wood. CNC technology also allows for efficient and versatile designs of frames with
fewer parts replacing redundant and bulky hardwood components (APA 1997).
Power-driven screws and staples are two of the most frequently used types of fasteners for
joining framing members in upholstered furniture due to their quick and easy installation.
A comprehensive knowledge on the performance of these fasteners in panel products is
necessary for the best use in these applications. However, the data available in technical
literature is scattered and incomplete. Performance standards for structural-use panels
(OSB and plywood) provide requirements for lateral and withdrawal capacities for nails
but not for screws or staples. Screw withdrawal capacities from face and edge of MDF and
PB have been published by Composite Panel Association (CPA 1999 and 2002). Technical
Note E830A published by APA – The Engineered Wood Association (APA 1982) provided
ultimate lateral and withdrawal loads for plywood-to-metal and plywood-to-plywood edge
connections for screws in structural applications. Based on limited number of tests, APA
(1993) issued interim recommendations for adjustment of these values for APA-
trademarked OSB.
Fastener holding capacities of different wood-based panels have been measured by several
researchers in the past (Chow et al. 1988, Williams and Nielson 1999). Table 3.1 shows
63
screw and staple holding capacities for some panel products found in the literature. Zhang
et al. (2002c, 2002d, and 2002e) and Erdil et al. (2002 and 2003a) studied the performance
of screws and staples in joints of solid wood, plywood and OSB used in furniture.
Although it is known that fastener holding capacity is related to the specific gravity of
wood or the wood-based composites, the influence of the density distribution
Table 3.1 Screw and staple holding capacities available in literature.
Screw withdrawal (N) Staple withdrawal (N)
Reference Panel Face Edge Face Edge
Staple head pull-through
ANSI
A208.2-2002
MDF 150 16 mm 1400 1200 - - -
PB MS 16mm 900 800 - - - ANSI
A208.1-1999 PB M2
16mm 1000 900 - - -
OSB-1 11mm - - 482a (40)g - 1472a (20) Chow
(1988) OSB-2
11mm - - 402a (49) - 1419a (20)
OSB 11mm 1268b 1154d 555c 861d, e -
OSB 15mm 1330b 1173d 682c 1008d, e -
Wang and Knudson (2002) OSB
18mm 1307b 1120d 864c 968d, e -
Williams and
Nielson (1999)
OSB 18mm 1516f (5) 1109f (26) - - -
MDF 19mm 1710f (3) 1410f (2)
a Staple: gauge 16, 51-mm (2-in) long, 12.7-mm (0.5-in) crown b Screw: No. 10, 38-mm (1.5-in) sheet metal screw (ThreadFast) c Staple: 51-mm (2-in), 16 gauge, 12.7mm (0.5-in) standard crown galvanized staples d Two or three panels were glued together e The penetration of the staple: 38mm f Screw: Standard one inch No. 10 gauge, flathead, low-carbon steel wood screws g Numbers in parentheses represent: coefficient of variation (%)
64
within the panels on their fastener holding capacity has not been well studied. In the
furniture industry, the question of non-uniform density distribution through the thickness
and in the plane of the panel is of high concern, because fasteners are often driven near or
in the edges. Wang and Knudson (2002) examined holding capacities of nails, screws and
staples by testing OSB from various mills and revealed significant variation between the
panels, which was mainly due to density variation among the mills and within the panels.
Fakopp Enterprise (2005) advertised a portable screw withdrawal force meter with a
correlation coefficient of 0.79 between the screw withdrawal force and density of solid
wood. Recently, Sackey et al. (2005) and Semple et al. (2005) found that face and edge
screw withdrawal resistances were strongly correlated with the internal bond of furniture
grade particleboard. However, the correlation with density was weak due to low density
variation in the panel.
In order to provide new markets or expand the existing market for OSB, MDF and
particleboard in upholstered furniture industry, comprehensive tests were conducted on
fasteners holding capacity of the wood-based panels. The key objectives of this study were
to: 1) develop data on the fasteners lateral, withdrawal and head pull-through capacities in
OSB, MDF and PB; and 2) investigate the effects of localized density distribution in panels
on the fastener holding capacities.
3.1.4 Materials and Methods A total of twenty full-size (1.22 by 2.44 m) panels were used with four replications of each
of the following products: 1) MDF: 16-mm thick, grade 150; 2) PB: 16-mm thick, grades
M2 and MS (two of each); 3) OSB: 11-mm (7/16 in.) thick; 4) OSB: 15-mm (19/32 in.)
thick; and 5) OSB: 18-mm (23/32 in.) thick. The OSB panels were grade O2 (CSA 1993),
made of aspen. Each of the four replications was obtained from a different panel
manufacturer.
At first, mapping of the horizontal (in-plane) density of panels was carried out to determine
in-plane density variation and to identify where fasteners should be located within the
plane of the panel. All panels were scanned using X-ray density scanning system
VSX9811. The panels were scanned with a 5-mm resolution, the data were further
65
processed to produce a coloured contour image of the density distribution with a final
resolution of 12.5 mm, and the final images were printed out with a 25-mm square mesh.
To determine the vertical density profiles across panel thickness, twenty-four 50-mm
square specimens were cut from each panel. These specimens were selected to cover the
entire range of horizontal density distribution within the panel. The vertical (through-
thickness) density profiles were measured using an X-ray QMS Density Profiler QDP-01X,
where X-ray beam travels parallel to the plane of the panel at a speed of 0.6 mm/s and the
average in-plane density of the 50-mm specimen is assessed with a resolution of 0.6 mm
across the thickness of the specimen.
All panels were tested in bending as received, and the moisture content (MC) was
measured following testing. Sixteen 50 x 76 mm samples were randomly cut from each
panel to determine MC according to ASTM standard D4442 (ASTM 2003c) Method B. For
each type of fastener holding capacity test, ten samples of 76 x 151 mm were cut from each
panel in such a way to cover the full range of density zones identified by colors. The
number of tests carried out in each sample varied depending on the type of test. Table 3.2
provides detailed information on the type and number of tests performed. The tests were
conducted in accordance with ASTM standards D1037 (ASTM 2003a) and D1761 (ASTM
2003b).
Table 3.2 Sampling plan to evaluate the static performance of fasteners in wood based panels.
Fastener type Property
Number of specimens per panel
Panel type a
Number of tests
per panel
Rate of loading
(mm/min) Face 10 40
Parallel to long axis 10 40 Gage 10 screw (25-mm long) Withdrawal Edge Perp. to long axis 10
D 40
15
Parallel to long axis 10 60 Lateral resistance Perp. to long axis 10 A 60 6.0 Gage10 screw
(50-mm long) Head pull-through 10 ½ of B 60 1.5
Face 15 45 Parallel to long axis 10 40 Withdrawal Edge Perp. to long axis 10
C 40
2.5 Gauge 16 staple (38-mm long, 11-mm crown)
Head pull-through 10 ½ of B 40 1.5 a A, B, C, and D indicate the four panel replicates of each material type or thickness.
66
For all tests, the thickness of panels as manufactured was used to represent the actual in-
service conditions of upholstered furniture frames. In accordance with ASTM D1037
guidelines for screw face withdrawal, screws were driven into the 18-mm OSB specimens
approximately 17 mm deep, whereas in all other panels, the screws were driven through the
full thickness of the panel. In staple face withdrawal specimens, staples were driven
through the full thickness, so that the staple crown was projected 13 mm above the face.
For edge withdrawal, screws and staples penetrated 17 and 25 mm into the specimen,
respectively. For screw withdrawal tests, lead holes were pre-drilled using a drilling bit of
3.2 mm in diameter. For head pull-through resistance tests, the fasteners were driven
through the specimen with the head or crown flush with the panel surface (the staples’
crowns were 45o to the panel edge). For lateral resistance tests, the screws were centered
on the width or length of the specimens and located 6.4 mm from the edge.
Analysis of variance (ANOVA) general linear model procedure was performed for
individual fastener holding capacities and individual types of panels on the correlation of
localized density and the ultimate holding capacity. The individual holding capacities were:
screw withdrawal, staple withdrawal, screw lateral, screw head pull-through and staple
head pull-through; and the individual types of panels were: 11-mm, 15-mm and 18-mm
OSB, 16-mm MDF and 16-mm PB. In order to classify the averages of fasteners holding
capacity of the panels, the Duncan’s multiple tests were performed on the averages.
3.1.5 Results and Discussion Panel Density and MC
Figure 3.1 shows typical images of horizontal density distribution of OSB, MDF and PB
panels. The different colors represent the density variation in the plane of panel, and each
color represents a density range of 50 kg/m3. OSB panels had high density variation: from
400 to 850 kg/m3. PB had less variation of density than OSB: from 550 to 800 kg/m3. MDF
had the lowest density variation: between 700 and 850 kg/m3.
Figure 3.2 shows average vertical density profiles from samples taken from all panels
tested. Considerable differences were found between the three groups of OSB panels. The
67
11-mm panels had the lowest face density, while the 18-mm panels had the lowest core
density. The 11-mm and the 15-mm OSB panels had similar core density. The highest
density and the least variation in density between the face and the core were observed in
MDF. The PB samples had the biggest variations between the face and the core density.
The MCs of the OSB, MDF and PB specimens were 5.7±0.3%, 7.0±0.2%, and 6.8±0.2%,
respectively.
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
S1 S6 S11
S16
S21
S26
S31
S36
S41
S46
800-850
750-800
700-750
650-700
600-650
550-600
500-550
450-500
400-450
DensityGradient(kg/m3)
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
S1 S6 S11
S16
S21
S26
S31
S36
S41
S46
900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450
DensityGradient(kg/m3)
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
S1 S6 S11
S16
S21
S26
S31
S36
S41
S46
800-850750-800700-750
650-700600-650550-600500-550
450-500400-450
DensityGradient(kg/m3)
a) b) c)
Figure 3.1 Typical images of horizontal density variation in panels: a) OSB; b) MDF; and c) PB.
Figure 3.2 Vertical density profiles of OSB, MDF and PB specimens.
68
Withdrawal Resistance of Screws
Table 3.3 and Figure 3.3 showed a summary of results of screw withdrawal tests.
Classified averages of screw withdrawal of each type of panels conducted by the Duncan’s
multiple tests are given in Table 3.3 and Figure 3.3. Table 3.3 only showed the
comparisons within each test for all types of panels, and Figure 3.3 gave the comparisons
between face and edge withdrawal in each type of panels. The face withdrawal resistance
was significantly higher than the edge withdrawal resistance for all panels (Figure 3.3).
This result was expected, as the edge withdrawal strength is controlled by panel core
density, which is significantly lower than the face density (Figure 3.2). Indeed, this is one
of the major concerns that have been identified by the furniture manufacturers using panel
products. There were no significant differences between edge parallel and perpendicular
withdrawal resistances for all panels tested.
For the OSB, it was found that the average face withdrawal resistance of the 18-mm OSB
was nearly 11% lower than that of the 15-mm OSB panels, suggesting that the withdrawal
resistance is not linearly proportional to the penetration depth, as observed by other
researchers for dowel joints (Eckelman 1969, Zhang et al. 2002a). In edge withdrawal, the
11-mm OSB panels showed the lowest resistance. Since the core density of these panels
was similar to the other panels, the low edge withdrawal resistance can be explained by the
smaller thickness and high probability of splitting. Some specimens exhibited splitting
during the insertion of screws prior to testing.
The face withdrawal resistance of MDF was similar to that of OSB; however, it was
stronger than OSB in edge withdrawal. Smaller differences were found between face and
edge withdrawal resistances of MDF due to a more uniform vertical density profile. For
PB, the face withdrawal strength was approximately 14%, 17%, and 8% less than that of
MDF, 15-mm and 18-mm OSB panels, respectively.
The average face withdrawal capacities of tested panels corresponded well with the
previously published data (Table 3.1). Both PB and MDF did meet the minimum
requirements of ANSI A208.1 (CPA 1999) and ANSI A208.2 (CPA 2002), respectively.
However, the edge withdrawal capacities of PB and OSB were lower than published
69
values. Note that Wang and Knudson (2002) glued two or three panels together for edge
withdrawal, required by ASTMD1037 standard to reduce the chance of splitting, while our
tests were performed using a single panel thickness causing high possibility of splitting.
ANOVA statistical analysis was carried out to examine the relationship between the screw
withdrawal resistance and the localized density of the panel. Results indicated significant
relationships at 95% confidence level for the screw face and edge withdrawal from OSB
and PB panels, except for the edge withdrawal parallel to the long axis of 15-mm OSB
panel, r values were found to range from 0.47 to 0.82 (Table 3.3). There was a good
correlation between screw face withdrawal resistance and localized panel density of all
OSB specimens with r = 0.54. Poor relationship was observed for MDF due to lower
variation in the horizontal density distribution of MDF in comparison with other types of
panels.
*The comparisons were performed within each group; values with the same capital letter
are not statistically different at 5% significant level.
Figure 3.3 Average screw withdrawal resistance of OSB, MDF and PB specimens.
A A
A
A
A*
B B
B B
BB
BB
B B
70
Tabl
e 3.
3 Fa
sten
er p
erfo
rman
ce w
ith lo
caliz
ed d
ensi
ty fo
r scr
ews.
Fast
ener
Pr
oper
ty
Pane
l N
omin
al
thic
knes
s (m
m)
Ave
rage
de
nsity
(k
g/m
3 ) X
Ave
rage
hol
ding
ca
paci
ty(N
) (O
bser
ved
Y)
Reg
ress
ion
equa
tion
(Pre
dict
ed Y
) r
Dif.
a
(%)
RM
SE b
11m
m
645
1087
(26.
9)c D
d y
= 2.
18x
– 32
2 0.
82*
0.3
160.
4 15
mm
67
3 14
48 (2
1.7)
A
y =
2.25
x - 6
3.7
0.47
* -0
.2
270.
3 O
SB
18m
m
588
1308
(21.
3) C
B
y =
2.13
x +
59.2
0.
52*
-0.3
23
0.9
MD
F 16
mm
78
6 13
94 (7
.4) A
B
y =
0.43
x +
1054
0.
10
0.1
101.
9 Fa
ce w
ithdr
awal
PB
16m
m
687
1206
(12.
5) C
y
= 2.
10x
- 235
0.
68*
-0.1
10
9.0
11m
m
609
712
(24.
9) D
y
= 1.
73x
- 341
0.
59*
-0.1
14
0.9
15m
m
664
953
(29.
9) B
y
= 1.
53x
- 61.
5 0.
26
-0.1
27
0.4
OSB
18
mm
58
5 94
9 (3
2.4)
B
y =
2.73
x - 6
47
0.50
* -0
.1
262.
1 M
DF
16m
m
783
1239
(6.7
) A
y =
1.17
x +
323
0.35
0
75.9
Para
llel
to
stro
ng a
xis
PB
16m
m
670
808
(10.
5) C
y
= 1.
87x
- 444
0.
80*
-0.1
50
.5
11m
m
606
801
(27.
2) C
y
= 1.
49x
- 102
0.
50*
0 18
6.7
15m
m
660
1047
(22.
4) B
y
= 2.
82x
- 817
0.
60*
0.3
185.
8 O
SB
18m
m
546
880
(30.
2) C
y
= 2.
80x
- 647
0.
51*
-0.2
22
6.2
MD
F 16
mm
78
4 11
91 (9
.8) A
y
= 0.
40x
+ 87
5 0.
10
0.2
113.
9
Scre
w
Gag
e 10
, 25
mm
lo
ng
Edge
w
ithdr
awal
Pe
rpen
dicu
lar
to
stro
ng a
xis
PB
16m
m
683
827
(11.
9) C
y
= 2.
08x
- 594
0.
69*
0 70
.0
11m
m
571
1122
(35.
3) C
y
= 3.
54x
- 899
0.
81*
0 23
3.2
15m
m
635
1842
(24.
7) B
y
= 4.
87x
- 124
7 0.
58*
-0.2
36
8.5
OSB
18
mm
58
9 22
01 (2
6.0)
A
y =
6.66
x - 1
723
0.71
* 0.
1 40
1.9
MD
F 16
mm
78
0 22
65 (7
.0) A
y
= 0.
28x
+ 20
50
0.00
-0
.1
156.
5
Para
llel
to
stro
ng a
xis
PB
16m
m
682
1154
(13.
5) C
y
= 0.
74x
+ 65
1 0.
10
-0.1
15
3.7
11m
m
568
1127
(39.
1) D
y
= 4.
10x
- 120
3 0.
77*
0.1
278.
8 15
mm
65
2 20
06 (2
7.7)
C
y =
5.13
x - 1
339
0.46
* 0
488.
3 O
SB
18m
m
591
2505
(22.
1) A
y
= 5.
81x
- 932
0.
60*
0.1
441.
7 M
DF
16m
m
790
2247
(6.7
) B
y =
-0.5
0x +
264
4 0.
00
-0.1
14
8.4
Late
ral
resi
stan
ce
Perp
endi
cula
r to
st
rong
axi
s
PB
16m
m
669
1119
(13.
2) D
y
= 2.
34x
- 447
0.
50*
0 12
6.5
11m
m
594
1491
(22.
5) C
y
= 2.
44x
+ 41
.0
0.64
* 0
254.
7 15
mm
66
0 26
77 (1
5.4)
A
y =
4.69
x - 4
23
0.73
* 0.
2 28
0.0
OSB
18
mm
59
6 24
60 (1
7.8)
B
y =
4.62
x - 2
97
0.66
* 0.
1 32
7.8
MD
F 16
mm
79
3 26
97 (7
.9) A
y
= -1
.38x
+ 3
789
0.20
0.
1 20
4.9
Scre
w
Gag
e 10
, 50
mm
lo
ng
Hea
d Pu
ll-th
roug
h
PB
16m
m
701
1587
(12.
0) C
y
= 2.
69x
- 296
0.
66*
-0.2
14
0.1
*Sig
nific
ant a
t a p
roba
bilit
y le
vel o
f 0.0
5.
Dif.
a : Diff
eren
ces b
etw
een
obse
rved
and
pre
dict
ed v
alue
s, in
per
cent
age.
RM
SE b : R
oot m
ean
squa
red
erro
r.
c Va
lues
in p
aren
thes
es a
re c
oeffi
cien
t of v
aria
tion
base
d on
all
test
spec
imen
s.
d Th
e co
mpa
riso
ns w
ere
perf
orm
ed w
ithin
eac
h te
st; va
lues
with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 5%
sign
ifica
nt le
vel.
71
Withdrawal Resistance of Staples
Results of staple withdrawal tests are presented in Table 3.4 including classified average
staple withdrawal resistances of the panels according to the Duncan’s multiple tests, but
Table 3.4 only showed the comparisons within each test. The face withdrawal resistance
was significantly higher than the edge withdrawal for all types of panels. The MDF
specimens showed the highest withdrawal values for both face and edge.
For all tested panels, the edge withdrawal resistances of 11-mm OSB panels were
approximately half as strong as the other panels because of splitting. There were no
significant differences between edge parallel and edge perpendicular withdrawal
resistances for all tested panels. The average staple face withdrawal resistance of OSB
corresponded well with the findings of Chow et al. (1988) and Wang and Knudson (2002)
(see Table 3.1). However, the edge withdrawal values were lower than those reported by
Wang and Knudson (2002) who used longer staples and two or three panels glued together.
The relationships between localized density and face withdrawal of staples were very poor
for MDF, whereas significant correlations at 95% confidence level were found for PB and
11-mm and 18-mm OSB panels (with r values ranging from 0.41 to 0.68). The correlations
for staple edge withdrawal resistance of 18-mm OSB were also significant, while the other
panels showed no or very weak relationships (see Table 3.4). The correlation was relatively
weak between staple face withdrawal resistance and localized panel density of all OSB
specimens (r = 0.38).
72
Tabl
e 3.
4 Fa
sten
er p
erfo
rman
ce w
ith lo
caliz
ed d
ensi
ty fo
r sta
ples
.
Fast
ener
Pr
oper
ty
Pane
l N
omin
al
thic
knes
s (m
m)
Ave
rage
de
nsity
(k
g/m
3 ) X
Ave
rage
hol
ding
ca
paci
ty(N
) (O
bser
ved
Y)
Reg
ress
ion
equa
tion
(Pre
dict
ed Y
) r
Dif.
a R
MSE
b
11m
m
608
482
(35.
0)c E d
y
= 1.
40x
- 367
0.
68*
-0.5
12
2.9
15m
m
653
820
(26.
8) C
y
= 0.
88x
+ 24
2 0.
28
0.4
208.
2 O
SB
18m
m
606
892
(27.
0) B
y
= 1.
37x
+ 59
.8
0.41
* 0.
2 21
7.3
MD
F
16m
m
786
976
(8.4
) A
y =
0.09
x +
906
0.00
-0
.1
81.0
Fa
ce w
ithdr
awal
PB
16m
m
741
630
(16.
6) D
y
= 2.
43x
- 116
9 0.
57*
-0.3
85
.1
11m
m
596
204
(40.
4) D
y
= 0.
27x
+ 43
.1
0.24
0
78.3
15
mm
65
2 47
9 (2
5.6)
C
y =
0.50
x +
152
0.22
0.
2 11
7.9
OSB
18
mm
60
1 56
4 (4
6.6)
AB
y
= 2.
98x-
1228
0.
79*
0.2
173.
4 M
DF
16
mm
78
0 62
8 (2
1.5)
A
y =
0.74
x +
52.3
0.
14
-0.2
13
0.8
Para
llel
to
stro
ng a
xis
PB
16m
m
749
513
(13.
5) C
B
y =
0.74
x - 3
8.9
0.37
* -0
.5
63.2
11
mm
59
2 27
7 (3
0.3)
D
y =
-0.0
5x +
304
0.
00
0.9
82.3
15
mm
66
2 54
8 (1
8.1)
B
y =
0.85
x - 1
1.7
0.44
* -0
.5
87.8
O
SB
18m
m
613
551
(27.
1) B
y
= 1.
04x-
83.8
0.
31
-0.5
16
4.6
MD
F
16m
m
783
612
(25.
6) A
y
= 0.
21x
+ 44
6 0.
00
0.3
153.
3
Edge
w
ithdr
awal
Pe
rpen
dicu
lar
to st
rong
axi
s
PB
16m
m
754
491
(11.
5) C
y
= 0.
21x
+ 33
5 0.
10
-0.5
55
.5
11m
m
594
882
(27.
9) C
y
= 2.
03x
- 322
0.
80*
-0.2
14
4.8
15m
m
644
1148
(30.
3) B
y
= -0
.20x
+ 1
275
0.00
0.
2 34
3.4
OSB
18
mm
57
8 10
71 (3
2.5)
B
y =
2.85
x - 5
74
0.65
* -0
.2
261.
1 M
DF
16
mm
77
1 13
87 (1
7.7)
A
y =
4.57
x - 2
140
0.36
0.
3 22
3.4
Stap
le
gaug
e 16
, 38
-mm
lo
ng,
11-m
m
crow
n
Hea
d Pu
ll-th
roug
h
PB
16m
m
700
842
(17.
5) C
y
= -0
.51x
+ 1
199
0.10
0
145.
1 *S
igni
fican
t at a
pro
babi
lity
leve
l of 0
.05.
D
if. a : D
iffer
ence
s bet
wee
n ob
serv
ed a
nd p
redi
cted
val
ues,
in p
erce
ntag
e.
RMSE
b : Roo
t mea
n sq
uare
d er
ror.
c Va
lues
in p
aren
thes
es a
re c
oeffi
cien
t of v
aria
tion
base
d on
all
test
spec
imen
s.
d Th
e co
mpa
riso
ns w
ere
perf
orm
ed w
ithin
eac
h te
st; va
lues
with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 5%
sign
ifica
nt le
vel.
73
Lateral Resistance of Screws
Results of screw lateral resistance tests in Table 3.3 showed that the 18-mm OSB and MDF
panels both had high resistances. The screw lateral resistances of the 11-mm OSB and PB
were about half of that of the other panels. Except for the 15-mm and 18-mm OSB, there
were no significant differences between screw lateral resistances parallel and perpendicular
to the long axis of the panels.
Significant linear relationships between localized density and the lateral resistance of
screws were found for all OSB panels in both loading directions, while the relationships
were insignificant or poor for MDF and PB (see Table 3.3). The relationship between the
screw lateral resistance and localized density for all OSB panels combined which was
found significant with r = 0.54.
Screws Head Pull-Through
Screw head pull-though resistances are shown in Table 3.3. The average resistance values
of MDF and 15-mm OSB were the highest and those of PB and 11-mm OSB were the
lowest. The 15-mm OSB showed, unexpectedly, high head pull-through resistance relative
to the other OSB panels, probably caused by high density and uniform density distribution
through the thickness of the panels.
Statistical analysis indicates that the relationships between the screw head pull-through
resistance and localized density for OSB and PB panels were significant at 95% confidence
levels, with r values ranging from 0.64 and 0.73 for PB and OSB, respectively. For MDF
panels, the correlation was not found to be statistically significant due to the low variation
of the horizontal density. In Figure 3.4, the relationship between the screw head pull-
through resistance and localized density is shown for all OSB panels combined. The
relationship was found significant with r = 0.65. Aside from isolated data points, the trend
is clearly indicative of a good linear relationship. Increasing the OSB density would
certainly improve the head pull-through resistance of screws, but that would also mean
increasing the cost of the panels.
74
Figure 3.4 Screw head pull-through resistance of OSB panels in relation to average localized density.
Staples Head Pull-Through
Staple head pull-through tests showed similar trends with those observed for screw (Table
3.4). The average resistance of the MDF was the highest while that of the 11-mm OSB and
PB panels were the lowest. The 18-mm OSB had slightly low head pull-through resistance
compared to the 15-mm OSB panels, likely due to lower density. Compared to the values
given by Chow et al. (1988) (see Table 3.1), the staple head pull-through resistance of OSB
showed considerably lower values, explained by the smaller crown and shorter staple used.
Also, it should be noted that in some tests, at load levels near failure, the gripping device
was not able to sustain the locking mechanism of the staple’s legs, and one leg slipped off,
while another remained locked. Consequently, the staple was pulled out of the panel by one
leg, and the overall failure load was lower than in those cases where slippage did not occur.
It might cause the poor correlation of the test data with the panel localized density.
The relationships between staple head pull-through resistance and localized density were
not statistically significant except for the 11-mm and 18-mm OSB (see Table 3.4). The
correlation computed for all OSB panels was relatively weak (r = 0.45).
75
3.1.6 Conclusions and Recommendations This study focused on evaluating the holding capacity of screws and staples in OSB, MDF
and PB panels. A data base of the fasteners’ face and edge withdrawal, head pull-through,
and lateral resistance under static load was developed, and correlations between fasteners
holding capacity and the localized panel density were examined. The following
conclusions and recommendations were made:
• Overall, the structure of the panel material was the most important factor for the
fastener holding capacity, but for the same type of the panel and the same type of
fastener holding capacity, localized density was an important factor.
• Among tested panels, OSB showed the highest density variation in plane and
through thickness, which was more critical to the screw than to the staple holding
capacities. The density of MDF panels varied the least, which generally led to a
more uniform fastener holding capacity.
• Generally, fasteners driven in low density zones fail at lower load levels than those
driven in high density zones. Therefore, the panels with higher density and less
density variation are beneficial for fastener performance.
The panel industry should work closely with the fasteners’ and furniture manufacturers in
order to develop new types of connectors (e.g., T-nut) that are more suited for attaching
various panel components, taking into consideration the nature and behaviour of the panel.
Such fasteners would have to be reliable, economical and easy to install. If typical panels
with traditional fasteners (i.e., screws and staples) are to be used in the upholstered
furniture frames, then new joint designs should be developed to enhance their capacity and
reduce the likelihood of premature failures due to fasteners driven in low density zones.
76
3.2 Localized density effects on fastener holding capacities in wood-based panels. Part 2: Cyclic tests
3.2.1 Résumé Pour améliorer notre compréhension de l’effet de la variation de la densité locale dans les
panneaux à base de bois sur la résistance mécanique de différents types d’attaches, nous
avons entrepris une étude approfondie incluant divers types de panneaux et attaches.
L'étude couvre des essais statiques et cycliques sur des panneaux à lamelles orientées
(OSB) de trois épaisseurs différentes, des panneaux de fibres de moyenne densité (MDF) et
des panneaux de particules (PB). La résistance à l’arrachement des vis et des agrafes sur la
face et sur la côté, la résistance latérale des vis, et la résistance d’enfoncement des têtes des
agrafes et vis ont été évaluées. Les propriétés mécaniques des attaches ont été corrélées
avec la densité locale des panneaux. Le présent article constitue la deuxième partie de cette
étude portant sur les essais cycliques, la première partie portant sur les essais statiques a
déjà été publiée dans un autre article. Similairement aux résultats des essais statiques, les
essais cycliques ont indiqué que dans le cas des panneaux OSB la variation de densité a un
effet significatif sur la résistance à l’arrachement des vis, sur l’enfoncement des têtes et sur
les résistances latérales des vis. Cependant, les effets étaient moins évidents avec la
résistance à l’arrachement et l’enfoncement des têtes des agrafes. Pour les panneaux PB, la
variation de densité a eu un effet significatif sur la résistance à l’arrachement de face et sur
la résistance à l’enfoncement des têtes des vis et des agrafes mais les effets étaient moins
prononcés pour la résistance à l’arrachement sur la côté des vis et agrafes et pour la
résistance latérale des vis. Pour les panneaux MDF, aucune corrélation significative n'a été
trouvée, ceci peut être attribué à la faible variation de densité de ces panneaux. Les
données seront employées pour optimiser la structure des meubles et pour fournir des
recommandations à l'industrie des panneaux sur l'utilisation des attaches pour leurs
produits.
3.2.2 Abstract To improve our understanding of localized density effects in wood-based panels on holding
capacities of fasteners commonly used in furniture, a comprehensive study was conducted
77
using static and cyclic tests of withdrawal and head pull-through of screws and staples, and
lateral resistance of screws in oriented strand board (OSB), medium density fiber board
(MDF), and particleboard (PB). This article presents results of cyclic tests, and
comparisons are made with the static test results reported in Part 1. Similar to static tests,
cyclic test data indicated that density variation in OSB panels had a significant effect on
the screw withdrawal, head pull-through, and lateral resistances, but the effects were less
evident with the staple withdrawal and head pull-through. For PB, density variation had a
significant effect on the screw and staple face withdrawal and head pull-through
resistances, but the effects were less pronounced for screw and staple edge withdrawal, and
screw lateral resistances. For MDF, no significant correlations were found, likely due to the
low density variation in these panels. The data will be used to provide recommendations to
the panel industry on the use of fasteners with their products and to optimize furniture
frames.
3.2.3 Introduction To reduce the cost of framing components, upholstered furniture manufacturers are always
on the look for alternative materials that are less expensive, but as strong and reliable as the
traditional ones. With the development of CNC technology, composite panels have a good
potential to replace solid wood in upholstered furniture frames. However, the suitability
and performance of traditional fasteners used in panel products for such applications is not
well studied yet. One of the concerns is the variation and non-uniformity in the density
distribution across the thickness and in the plane of the panel, and how it could affect the
holding capacity of fasteners. Available reference values are based on static tests, while
limited information is found about the density effects on fastener holding capacities in
wood-based panels under cyclic loading conditions.
Few studies were conducted on the performance of wood or wood-based material
assemblies under cyclic or fatigue tests using different test protocols. For example,
reversed and non-reversed cyclic loading (Hayashi et al. 1980) were used to evaluate the
fatigue properties of wood butt joints with metal-plate connectors (MPC) in timber. Moura
et al. (1995) used a non-reversed cyclic load schedule (varying tension) followed by a
78
sinusoidal function to examine the influence of wood density on the mechanical behavior
of MPC joints.
Upholstered furniture frames are subjected in service to a wide range of loads, which act as
repetitive events of loading and unloading. Typically, in the furniture industry, long-term
fatigue loading is carried out using a large number of non-reversed loading cycles (25,000
cycles on each load level depending on the performance acceptance level) with an average
rate of twenty cycles per minute (GSA 1998). This performance test regime is based on a
zero-to-maximum (one sided or non-reversed) cyclic stepped fatigue load method rather
than a static or constant amplitude cycling load method (Eckelman 1988b). For instance,
Zhang et al. (2006) studied bending fatigue life of MPC joints in furniture-grade pine
plywood by subjecting the joints to one-sided stepped cyclic bending loads.
This study is part of a broader research program to examine the localized density effects on
fastener holding capacities in wood-based panels. This paper presents cyclic test data and it
complements the static test results reported by Wang et al. (2007a). The key objective of
this study is to evaluate the holding capacity of screws and staples in commercial wood-
based panels under cyclic loading in comparison with the static loading. The paper also
discusses the correlation between the fastener holding capacity and the density distribution
in panels. Technical information generated in this study will be used to provide
recommendations to the panel industry on the use of fasteners with their products and to
optimize furniture frame construction.
3.2.4 Materials and Methods The specimens for cyclic tests were prepared using the same materials and mapping and
cutting techniques as described in the previous paper (Wang et al. 2007a). Table 3.5
provides detailed information on the type and number of tests performed.
ASTM D1037 and D1761 testing procedures were used to carry out the static tests at a
constant rate of loading head displacement. However, for cyclic loading, the jigs were
modified to allow for loading and unloading cycles without slack and a constant rate of
loading was applied (load-controlled test). Set-ups used for the static and cyclic screw
79
lateral resistance tests are shown in Figure 3.5. Fasteners were driven in panel specimens
following the same techniques as described in Wang et al. 2007a.
Prior to cyclic testing, specimens were subjected to static monotonic loading, and results
were reported in paper Wang et al. (2007a). The ultimate reference load (Pref) for each
specific test (see Table 3.6) determined from the static tests was used to calculate the load
levels needed for the cyclic stepped loading. The cyclic loading was applied in three steps
with thirty cycles at each load level: 15%, 35% and 70% Pref, after which the specimens
were loaded to failure (Figure 3.6). Note that for the staple edge withdrawal tests, the load
levels in the first step, instead of 15%, were 30% and 25% Pref for parallel and
perpendicular orientations, respectively (see Table 3.6.2). A preload of 40 N was applied to
eliminate the slack in the system during the cycling. The load rate was adjusted to produce
15 cycles per minute, in order to finish 90 cycles in six minutes to meet average static tests.
The cyclic loading regime used in this study is referred to as a short-term fatigue to
distinguish it from a typical fatigue type of loading which is usually carried out with a large
number of loading and unloading cycles until failure occurs. Due to the long time needed
to perform a single test following the General Service Administration (GSA 1998)
procedure, it was decided to carry out the short-term cyclic test that lasts approximately six
minutes. This allowed for testing sufficient number of specimens from various panel types
and thicknesses.
Table 3.5 Sampling plan to evaluate the cyclic performance of fasteners in wood based panels.
Fastener type Property
Number of specimens per panel
Panel type a
Number of tests
per panel
Rate of loading
(cycles/min)
Face 10 20 Parallel to long axis 10 20 Gage 10 screw
(25-mm long) Withdrawal Edge Perp. to long axis 10
D 20
15
Parallel to long axis 10 20 Lateral resistance Perp. to long axis 10
A 20
15 Gage10 screw (50-mm long)
Head pull-through 10 ½ of B 20 15 Face 10 20
Parallel to long axis 10 20 Withdrawal Edge Perp. to long axis 10
20 20
15 Gauge 16
staple (38-mm long, 11-mm
crown) Head pull-through 10 ½ of B 20 15 a A, B, C, and D indicate the four panel replicates of each material type or thickness.
80
Figure 3.5 A test set-up for carrying out static (left) and cyclic (right) lateral loading resistance of screws
Table 3.6 Reference load levels for cyclic loading
Table 3.6.1 Reference load levels for screw withdrawal resistance both on face and edge (N)
Panel type Face Edge (Parallel) Edge (Perpendicular)
15% 163 15% 107 15% 120 35% 380 35% 249 35% 280
OSB 11mm (7/16")
1086.7
70% 761
712.1
70% 498
800.9
70% 561 15% 217 15% 143 15% 157 35% 507 35% 334 35% 366
OSB 15mm
(19/32")
1448.2
70% 1014
953.1
70% 667
1046.5
70% 733 15% 196 15% 142 15% 132 35% 458 35% 332 35% 308
OSB 18mm
(23/32")
1307.8
70% 915
949.3
70% 665
880.3
70% 616 15% 209 15% 186 15% 179 35% 488 35% 434 35% 417 MDF
(16mm)
1394 70% 976
1239
70% 867
1191
70% 834 15% 181 15% 121 15% 124 35% 422 35% 283 35% 289 PB
(16mm)
1206 70% 844
808
70% 566
827
70% 579
81
Table 3.6.2 Reference load levels for staple withdrawal resistance both on face and edge (N)
Panel type Face Edge (Parallel) Edge (Perpendicular)
15% 72 30% 61 25% 69 35% 169 35% 71 35% 97 OSB 11mm
(7/16") 482.2 70% 338
203.5 70% 142
276.6 70% 194
15% 118 15% 72 15% 82 35% 275 35% 168 35% 192 OSB 15mm
(19/32") 785.19
70% 550
479.4
70% 336
548
70% 384 15% 130 15% 85 15% 83 35% 304 35% 198 35% 193 OSB 18mm
(23/32") 869.95 70% 609
564.5 70% 395
551 70% 386
15% 146 15% 94 15% 92 35% 342 35% 220 35% 214 MDF
(16mm)
976 70% 683
628
70% 440
612
70% 428 15% 97 517 15% 78 15% 74 35% 225 35% 181 35% 172 PB
(16mm)
644 70% 451 70% 362
492
70% 344 Table 3.6.3 Reference load levels for screw lateral resistance (N)
Panel type (Parallel) (Perpendicular)
15% 168 15% 169 35% 393 35% 394 OSB 11mm (7/16") 1122.2 70% 786
1127.2 70% 789
15% 276 15% 301 35% 645 35% 703 OSB 15mm (19/32") 1841.9 70% 1289
2007.7 70% 1405
15% 330 15% 376 35% 770 35% 877 OSB 18mm (23/32") 2201 70% 1540
2505.2 70% 1755
15% 340 15% 337 35% 793 35% 786 MDF
(16mm) 2265 70% 1586
2247 70% 1573
15% 172 15% 168 35% 402 35% 392 PB
(16mm) 1148 70% 804
1119 70% 783
82
Table 3.6.4 Reference load levels for screw and staple head pull-through (N)
Panel type Screw Staple
15% 224 15% 132 35% 522 35% 309 11mm (7/16") 1491.470% 1044
882.1 70% 617
15% 402 15% 172 35% 937 35% 402 15mm (19/32") 2676.970% 1874
1148.3 70% 804
15% 369 15% 161 35% 861 35% 375 18mm (23/32") 2459.970% 1722
1071 70% 750
15% 404 15% 205 35% 943 35% 479 MDF
(16mm) 2694 70% 1886
1369 70% 958
15% 238 15% 126 35% 555 35% 295 PB
(16mm) 1587 70% 1111
842 70% 589
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250 300 350 400
Time (s)
Load
(N)
30 Cycles
30 Cycles
30 Cycles
Loading to failure
Figure 3.6 An example of typical cyclic loading regime for fastener holding capacity tests of screw face withdrawal on 11-mm OSB panels.
83
Analysis of variance (ANOVA) general linear model procedure was performed on
individual fastener holding capacities for all types of panels to examine the correlation
between localized density and the ultimate holding capacity. The following holding
capacities were analyzed: screw withdrawal, staple withdrawal, screw lateral, screw head
pull-through and staple head pull-through. The following panels were tested: 11-mm, 15-
mm and 18-mm OSB, 16-mm MDF and 16-mm PB. In order to classify the averages of
fasteners holding capacity of the panels, the Duncan’s multiple tests were performed on the
averages.
3.2.5 Results and Discussion Analysis results including comparisons between the static and cyclic loading are given in
Tables 3.7 to 3.9. An example of typical load-displacement curves of the cyclic and
corresponding static tests of screw head pull-through on 15-mm OSB panels is shown in
Figure 3.7.
Withdrawal Resistance of Screws
Table 3.7 and Figure 3.8 show a summary of test results of the withdrawal resistance of
screws from face and edge under cyclic loading. Classified averages of screw withdrawal
for each type of panels conducted with the Duncan’s multiple tests are also given in Table
3.7. But Table 3.7 only showed the comparisons within each test for all types of panels,
and Figure 3.8 gave the comparisons between face and edge withdrawal in each type of
panels. The face withdrawal strength was significantly higher than the edge withdrawal
strength with the exception of the 11-mm and 18-mm OSB panels, where the values were
not significantly different (Figure 3.8). The differences could be attributed to the
orientation of the strands and the way the testing is done for face withdrawal as strands get
usually peeled off with the repeated cycles of loading and unloading. There were no
significant differences between the edge strength in withdrawal parallel and perpendicular
to the panel long axis for all panels tested.
The average face withdrawal resistance of the 15-mm OSB was the highest and that of the
11-mm OSB was the lowest among the tested panels. MDF showed capacities similar to
84
Tabl
e 3.
7 Te
st re
sults
for s
crew
per
form
ance
in c
yclic
load
ing
Fast
ener
Pr
oper
ty
Pane
l N
omin
al
thic
knes
s (m
m)
Ave
rage
de
nsity
(k
g/m
3 ) X
Ave
rage
hol
ding
ca
paci
ty (N
) (O
bser
ved
Y)
Reg
ress
ion
equa
tion
(Pre
dict
ed Y
) r
Dif.
a
(%)
RM
SE b
11m
m
586
898
(37.
4)c C
d y
= 2.
58x
- 613
0.
83*
-0.1
18
2 15
mm
61
6 14
48 (2
0.2)
A
y =
2.00
x +
218
0.53
* -0
.1
243
OSB
18
mm
58
5 12
10 (2
5.8)
B
y =
1.76
x +
179
0.47
* 0.
1 27
1 M
DF
16m
m
788
1394
(7.4
) A
y =
-0.2
7x +
160
9 0.
06
-0.2
10
1 Fa
ce w
ithdr
awal
PB
16m
m
688
1183
(9.5
) B
y =
2.66
x - 6
51
0.59
* 0.
3 89
.1
11m
m
568
813
(23.
8) B
y
= 1.
28x
+ 88
.5
0.51
* -0
.3
162
15m
m
665
1136
(16.
4) A
y
= 0.
12x
+ 10
56
0.04
0
182
OSB
18
mm
59
6 11
53 (2
3.0)
A
y =
3.08
x - 6
82
0.76
* -0
.1
167
MD
F 16
mm
78
2 11
94 (1
1.5)
A
y =
1.54
x - 1
0.9
0.24
0.
1 13
2
Para
llel t
o st
rong
axi
s
PB
16m
m
703
833
(10.
8) B
y
= 1.
58x
- 277
0.
42
-0.1
79
.1
11m
m
554
871
(18.
2) B
y
= 1.
18x
+ 21
8 0.
46*
-0.1
13
7 15
mm
67
6 11
21 (1
8.8)
A
y =
2.01
x - 2
38
0.59
* 0
165
OSB
18
mm
59
3 11
73 (2
5.7)
A
y =
2.91
x - 5
53
0.45
* 0
262
MD
F 16
mm
79
1 12
06 (9
.3) A
y
= 0.
67x
+ 67
3 0.
20
0.3
108
Scre
w
Gag
e 10
, 25
mm
lo
ng
Edge
w
ithdr
awal
Perp
endi
cula
r to
long
axi
s
PB
16m
m
683
810
(12.
5) B
y
= 0.
29x
+ 61
5 0.
09
-0.4
98
.5
11m
m
568
953
(35.
5) C
y
= 3.
17x
- 845
0.
70*
-0.3
23
8.6
15m
m
655
1829
(27.
0) B
y
= 4.
00x
– 78
8 0.
68*
-0.2
35
5 O
SB
18m
m
615
2162
(26.
2) A
y
= 6.
99x
- 213
6 0.
79*
0 34
0 M
DF
16m
m
784
2114
(9.6
) A
y =
0.89
x +
1413
0.
11
0.2
196
Para
llel t
o st
rong
axi
s
PB
16m
m
688
1037
(17.
8) C
y
= -0
.56x
+ 1
426
0.08
-0
.4
181
11m
m
583
1225
(22.
4) B
y
= 2.
35x
- 147
0.
56*
0.2
222
15m
m
645
1971
(25.
9) A
y
= 4.
31x
– 80
7 0.
57*
-0.1
40
8 O
SB
18m
m
562
2026
(24.
0) A
y
= 3.
29x
+ 17
8 0.
33
0 44
9 M
DF
16m
m
793
2162
(15.
4) A
y
= 4.
23x
– 11
92
0.34
0
305
Late
ral
resi
stan
ce
Perp
endi
cula
r to
stro
ng a
xis
PB
16m
m
675
966
(14.
8) C
y
= 1.
61x
- 123
0.
34
0.2
131
11m
m
613
1764
(25.
7) B
y
= 3.
13x
– 15
6 0.
78*
0.1
278
15m
m
675
2918
(14.
6) A
y
= 2.
42x
+ 12
83
0.43
* 0.
1 37
8 O
SB
18m
m
582
2904
(23.
4) A
y
= 6.
61x
– 94
1 0.
80*
-0.1
40
4 M
DF
16m
m
779
3008
(3.7
) A
y =
1.80
x +
1603
0.
33
0.1
101
Scre
w
Gag
e 10
, 50
mm
lo
ng
Hea
d Pu
ll-th
roug
h
PB
16m
m
685
1921
(8.3
) B
y =
3.71
x - 6
16
0.71
* -0
.2
110
* Si
gnifi
cant
at a
pro
babi
lity
leve
l of 0
.05
Dif.
a : Diff
eren
ces b
etw
een
obse
rved
and
pre
dict
ed v
alue
s, in
per
cent
age.
RM
SE b : R
oot m
ean
squa
red
erro
r.
c Va
lues
in p
aren
thes
es a
re c
oeffi
cien
t of v
aria
tion
base
d on
all
test
spec
imen
s.
d Th
e co
mpa
riso
ns w
ere
perf
orm
ed w
ithin
eac
h te
st; v
alue
s with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 5%
sign
ifica
nt le
vel.
85
Tabl
e 3.
8 Te
st re
sults
for s
tapl
e pe
rfor
man
ce in
cyc
lic lo
adin
g.
Fast
ener
Pr
oper
ty
Pane
l N
omin
al
thic
knes
s (m
m)
Ave
rage
de
nsity
(k
g/m
3 ) X
Ave
rage
hol
ding
ca
paci
ty (N
) (O
bser
ved
Y)
Reg
ress
ion
equa
tion
(Pre
dict
ed Y
) r
Dif.
a R
MSE
b
11m
m
599
377
(44.
7)c D
d y
= 1.
28x
- 387
0.
82*
-0.7
94
.3
15m
m
649
752
(29.
0) B
y
= 1.
74x
- 378
0.
57*
0.1
176
OSB
18
mm
58
8 82
5 (2
1.9)
B
y =
1.65
x - 1
45
0.65
* 0
134
MD
F
16m
m
791
1029
(10.
2) A
y
= 0.
21x
+ 85
9 0.
05
0.4
102
Face
with
draw
al
PB
16m
m
762
649
(19.
8) C
y
= 1.
53x
- 516
0.
55*
-0.1
10
6 11
mm
58
0 20
9 (4
7.2)
D
y =
1.04
x –
393
0.79
* -0
.6
59.4
15
mm
65
0 38
8 (3
4.4)
C
y =
1.55
x - 6
16
0.53
* -0
.9
111
OSB
18
mm
60
5 46
1 (2
1.8)
B
y =
0.74
x +
16.2
0.
53*
-0.6
83
.6
MD
F
16m
m
776
543
(14.
7) A
y
= -1
.55x
+ 1
746
0.35
0
73.2
Para
llel t
o st
rong
axi
s
PB
16m
m
741
474
(20.
7) B
y
= -0
.68x
+ 9
79
0.20
-0
.2
94.3
11
mm
59
8 23
8 (3
6.1)
C
y =
-0.0
4x +
259
0.
002
1.2
83.9
15
mm
60
8 45
9 (2
7.9)
B
y =
1.49
x - 4
45
0.50
* -0
.4
108
OSB
18
mm
60
9 46
3 (3
5.4)
B
y =
2.03
x –
774
0.64
* 0.
2 12
4 M
DF
16
mm
77
5 60
4 (1
3.6)
A
y =
1.46
x - 5
32
0.48
* 0.
8 70
.8
Ed
ge
with
draw
al
Perp
endi
cula
r to
stro
ng a
xis
PB
16m
m
760
483
(10.
9) B
y
= 0.
59x
+ 35
0.
39
-0.1
47
.4
11m
m
566
824
(22.
6) C
y
= 1.
24x
+ 12
3 0.
49*
-0.1
15
9 15
mm
68
8 14
38 (2
8.3)
A
y =
4.20
x - 1
447
0.47
* -0
.3
351
OSB
18
mm
58
9 11
59 (1
8.1)
B
y =
1.49
x +
280
0.53
* 0.
1 17
3 M
DF
16
mm
77
8 13
46 (9
.2) A
y
= -0
.79x
+ 1
959
0.14
0.
1 12
0
Stap
le
gaug
e 16
, 38
-mm
lo
ng,
11-m
m
crow
n
Hea
d Pu
ll-th
roug
h
PB
16m
m
702
1101
(13.
1) B
y
= 1.
97x
- 282
0.
54*
0 11
8 *
Sign
ifica
nt a
t a p
roba
bilit
y le
vel o
f 0.0
5 D
if. a : D
iffer
ence
s bet
wee
n ob
serv
ed a
nd p
redi
cted
val
ues,
in p
erce
ntag
e.
RMAE
b : Roo
t mea
n sq
uare
d er
ror.
c Va
lues
in p
aren
thes
es a
re c
oeffi
cien
t of v
aria
tion
base
d on
sam
e te
st sp
ecim
ens.
d Th
e co
mpa
riso
ns w
ere
perf
orm
ed w
ithin
eac
h te
st; v
alue
s with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 5%
sign
ifica
nt le
vel.
86
Tabl
e 3.
9 C
ompa
rison
s for
scre
w a
nd st
aple
per
form
ance
s in
stat
ic a
nd c
yclic
load
ings
Sc
rew
ave
rage
hol
ding
cap
acity
(N)
(Obs
erve
d Y
)
Stap
le a
vera
ge h
oldi
ng c
apac
ity (N
) (O
bser
ved
Y)
Fa
sten
er
Prop
erty
Pa
nel
Nom
inal
th
ickn
ess
(mm
) St
atic
C
yclic
St
atic
C
yclic
11m
m
1087
(26.
9) a
Ab
898
(37.
4) A
48
2 (3
5.0)
A
377
(44.
7) B
15
mm
14
48 (2
1.7)
A
1448
(20.
2) A
82
0 (2
6.8)
A
752
(29.
0) A
O
SB
18m
m
1308
(21.
3) A
12
10 (2
5.8)
A
892
(27.
0) A
82
5 (2
1.9)
A
MD
F
16m
m
1394
(7.4
) A
1394
(7.4
) A
976
(8.4
) B
1029
(10.
2) A
Fa
ce w
ithdr
awal
PB
16m
m
1206
(12.
5) A
11
83 (9
.5) A
63
0 (1
6.6)
A
649
(19.
8) A
11
mm
71
2 (2
4.9)
B
813
(23.
8) A
20
4 (4
0.4)
A
209
(47.
2) A
15
mm
95
3 (2
9.9)
B
1136
(16.
4) A
47
9 (2
5.6)
A
388
(34.
4) B
O
SB
18m
m
949
(32.
4) B
11
53 (2
3.0)
A
564
(46.
6) A
46
1 (2
1.8)
A
MD
F
16m
m
1239
(6.7
) A
1194
(11.
5) A
62
8 (2
1.5)
A
543
(14.
7) B
Para
llel t
o st
rong
axi
s
PB
16m
m
808
(10.
5) A
83
3 (1
0.8)
A
513
(13.
5) A
47
4 (2
0.7)
A
11m
m
801
(27.
2) A
87
1 (1
8.2)
A
277
(30.
3) A
23
8 (3
6.1)
A
15m
m
1047
(22.
4) A
11
21 (1
8.8)
A
548
(18.
1) A
45
9 (2
7.9)
B
OSB
18
mm
88
0 (3
0.2)
B
1173
(25.
7) A
55
1 (2
7.1)
A
463
(35.
4) A
M
DF
16m
m
1191
(9.8
) A
1206
(9.3
) A
612
(25.
6) A
60
4 (1
3.6)
A
Scre
w
Gag
e 10
, 25
mm
lo
ng
Edge
w
ithdr
awal
Pe
rpen
dicu
lar
to st
rong
axi
s
PB
16m
m
827
(11.
9) A
81
0 (1
2.5)
A
491
(11.
5) A
48
3 (1
0.9)
A
11m
m
1122
(35.
3) A
95
3 (3
5.5)
A
15m
m
1842
(24.
7) A
18
29 (2
7.0)
A
OSB
18
mm
22
01 (2
6.0)
A
2162
(26.
2) A
M
DF
16
mm
22
65 (7
.0) A
21
14 (9
.6) B
Para
llel t
o st
rong
axi
s
PB
16m
m
1154
(13.
5) A
10
37 (1
7.8)
B
11m
m
1127
(39.
1) A
12
25 (2
2.4)
A
15m
m
2006
(27.
7) A
19
71 (2
5.9)
A
OSB
18
mm
25
05 (2
2.1)
A
2026
(24.
0) B
M
DF
16
mm
22
47 (6
.7) A
21
62 (1
5.4)
A
Late
ral
resi
stan
ce
Perp
endi
cula
r to
stro
ng a
xis
PB
16m
m
1119
(13.
2) A
96
6 (1
4.8)
B
11m
m
1491
(22.
5) B
17
64 (2
5.7)
A
882
(27.
9) A
82
4 (2
2.6)
A
15m
m
2677
(15.
4) B
29
18 (1
4.6)
A
1148
(30.
3) B
14
38 (2
8.3)
A
OSB
18
mm
24
60 (1
7.8)
B
2904
(23.
4) A
10
71 (3
2.5)
A
1159
(18.
1) A
M
DF
16
mm
26
97 (7
.9) B
30
08 (3
.7) A
13
87 (1
7.7)
A
1346
(9.2
) A
Scre
w
Gag
e 10
, 50
mm
lo
ng
Hea
d Pu
ll-th
roug
h
PB
16m
m
1587
(12.
0) B
19
21 (8
.3) A
84
2 (1
7.5)
B
1101
(13.
1) A
a Va
lues
in p
aren
thes
es a
re c
oeffi
cien
t of v
aria
tion
base
d on
sam
e te
st sp
ecim
ens.
b Th
e co
mpa
riso
ns w
ere
perf
orm
ed b
etw
een
stai
c an
d cy
clic
test
s; v
alue
s with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 5%
sign
ifica
nt
leve
l.
87
Figure 3.7 Example of load-displacement curves of static and cyclic tests of screw head pull-through on 15-mm OSB panels.
0
200
400
600
800
1000
1200
1400
1600
OSB 11mm OSB 15mm OSB 18mm MDF 16mm PB 16mm
Panel type
Scre
w w
ithdr
awal
str
engt
h (N
) FaceEdge PEdge Pe
* The comparisons were performed within each group; values with the same capital letter are not statistically different at 5% significant level Figure 3.8 Average cyclic withdrawal resistance of screws in OSB, MDF and PB panels.
0
300
600
900
1200
1500
1800
2100
2400
2700
15 17 19 21 23 25Deplacement (mm)
Load
(N)
CyclicStatic1Static2
Deflection (mm)
A* A
A
A
B BA
AA
BB
A
B B
A
88
the 15-mm OSB. PB was similar with the 18-mm OSB. In edge withdrawal, the 11-mm
OSB and 16-mm PB panels showed the lowest resistances, which can be explained by the
low core density of PB and the smaller thickness and therefore, the high probability of
splitting of the 11-mm OSB. Some specimens exhibited splitting during the insertion of
screws prior to testing. There were no significant differences between the edge withdrawal
of 15-mm and 18-mm OSB and the 16-mm MDF.
As can be seen in Table 3.9, generally, no significant differences were found between static
and cyclic screw face withdrawal resistances for all the panels. There are some significant
between static and cyclic screw edge withdrawal for OSB panels. In fact, for screw edge
withdrawal resistance in both parallel and perpendicular to the strong axis of the panel, the
cyclic edge withdrawal was higher than that of the static edge withdrawal for all OSB
panels. This could be related to the densification of the wood strands due to the repeated
cycles of loading and unloading. Or this cyclic load used in the tests which had not
produced fatigue damage. More research is needed in this area with an increased number of
cycles to determine if the effect persists.
The ultimate fastener holding capacity has been used as an indicator in this study.
However, other parameters associated with the load-displacement relationship could be
established to identify the difference between the static and cyclic behavior of fasteners, for
example, the initial stiffness, the slip or fastener movement in the panel specimen at a
certain load level or at ultimate load.
ANOVA was carried out to verify if a relationship exists between the screw face and edge
withdrawal resistances and the localized density of the panel. Results indicated that for the
cyclic face withdrawal in all OSB and PB panels, the relationship was significant at 95%
confidence level; r-values were found to range from 0.47 to 0.83 (Table 3.7). However,
poor relationship was observed for MDF. This could be attributed to the uniformity in the
MDF localized density as less variation is usually found in the horizontal density
distribution of MDF in comparison to OSB or PB panels. For edge withdrawal of screws
under cyclic load, the relationship was found to be significant for all OSB panel specimens
perpendicular to the long axis of the panel, while for the parallel direction, the relationship
89
was only significant for 11-mm and 18-mm OSB (Table 3.7). However, relationships were
poor for both MDF and PB panels. There was a relatively good correlation between screw
face withdrawal resistance and localized panel density of all OSB specimens (r = 0.59).
Withdrawal Resistance of Staples
Table 3.8 presents the results of cyclic staple withdrawal tests including classified average
values according to the Duncan’s multiple test. But Table 3.8 only showed the comparisons
within each test for all types of panels. Face withdrawal resistance was significantly higher
than the edge withdrawal for all types of panels. For both face and edge withdrawal, MDF
specimens showed the highest resistance, while 11-mm OSB demonstrated the lowest for
all panel types. The edge withdrawal resistance of 11-mm OSB was less than half that of
the other panels which can be explained by the splitting associated with stapling due to the
small thickness. In fact the split was visible in some specimens before the test. There were
no significant differences between the edge withdrawal resistances parallel and
perpendicular to the long side of the panel for all tested materials except MDF.
From Table 3.9, generally, lower withdrawal resistances were observed following cyclic
loading in comparison to static loading for OSB panels. It could be explained by OSB
might have more gap between the chips and less wood contact. Therefore, it could be
concluded that staple face and edge withdrawal resistance in OSB is more sensitive to
cyclic loading than in other panel products tested.
Examining interactions between the localized density and the face withdrawal of the
staples under the cyclic load, it was evident that the relationships are significant for OSB
and PB panels, but not for MDF, at 95% confidence level as can be seen in Table 3.8. The
r-values ranged from 0.55 to 0.82. For staple edge withdrawal resistance parallel to the
long panel axis, the relationships were significant for OSB panels but not for MDF and PB.
However, for perpendicular direction, the correlation was only significant for the 15-mm
and 18-mm OSB and MDF panels. PB specimens did not exhibit any significant
relationship between the two parameters (Table 3.8). The correlation was good between
staple face withdrawal resistance and localized panel density of all OSB specimens (r =
0.61).
90
Lateral Resistance of Screws
Test results in Table 3.7 indicate that the 18-mm OSB and MDF panels demonstrated the
highest resistances among the tested panels. The resistances of the 11-mm OSB and PB
were the lowest. Except for the 11-mm OSB, there were no significant differences between
screw lateral resistances in the direction parallel and perpendicular to the long axis of the
panels.
As showed in Table 3.9, some cyclic lateral resistances of screws appeared to be lower
than those determined from static tests; the rests were not significantly different.
Significant linear relationships between localized density and the lateral resistance of
screws were found for OSB panels in both loading directions, except for the 18-mm OSB
panels with screws loaded perpendicular to the long axis of the panel. However, the
relationships were found insignificant for MDF and PB (see Table 3.7). The relationship
between the screw lateral resistance and localized density of OSB panels combined was
found to be significant (r = 0.51).
Screw Head Pull-Through
Screw head pull-though resistance values are shown in Table 3.7. The average resistance
value of MDF panels was the highest and that of the 11-mm OSB was the lowest. The 15-
mm OSB exhibited similar resistance to the 18-mm OSB and the 16-mm MDF panels,
probably due to high density and uniform density distribution through the thickness of the
panels.
The average cyclic screw head pull-through resistance was higher than the static resistance
for all tested panels (Table 3.9). One possible explanation is that this cyclic load used in the
tests which had not produced fatigue damage. Another explanation could be the repeated
cycles of loading and unloading lead to a densification of the wood fiber underneath the
screw head, which does not occur in static test. In practice, such densification is only
possible if the head pull-through resistance of screws does not exceed the withdrawal
resistance of the screw shank from the main member. Otherwise, the screws will withdraw
completely from the other component before the full head pull-through resistance is
developed.
Statistical analysis indicates that the relationships between the screw head pull-through
resistance and localized density for OSB and PB panels were significant at 95% confidence
levels, with r-values ranging from 0.43 to 0.80 for OSB and PB, respectively. For MDF
panels, the correlation could not be proven statistically significant due to the low variation
of the horizontal density. The relationship between the screw head pull-through resistance
and localized density for OSB panels combined was relatively weak (r = 0.48).
Staple Head Pull-Through
Staple head pull-though resistances are presented in Table 3.8. The average resistance of
the 15-mm OSB was the highest while that of the 11-mm OSB was the lowest. The 18-mm
OSB showed a lower resistance than the 15-mm OSB panels, likely due to lower density.
The average resistance of MDF panels was in the same order as that of 15-mm OSB
panels, likely due to the high face and core density of the panels.
It should be noted that in some tests, at load levels near failure, the gripping device was not
able to sustain the locking mechanism of the staple’s legs, and one leg slipped off, while
the other remained locked. Consequently, the staple was pulled out of the panel by one leg,
and the overall failure load was lower than in those cases where the slippage did not occur.
The slippage was observed more often during static tests. This phenomenon might have
caused the poor correlation of the test data with the localized density of the panel.
Examining the cyclic staple head pull-through resistance of the 15-mm OSB and PB
specimens, it was evident that the resistance under cyclic loading was higher than that of
the static one. No significant differences were observed for the other panels. One could
assume that the potential increase in the staple head pull-through could be attributed to the
localized densification of the wood fibers underneath the staple crown that occurred due to
repetitive loading and unloading. We could not find any explanation as to why such
phenomenon was associated with the 15-mm thick OSB and PB but not other OSB or MDF
panels.
92
The relationship between staple head pull-through resistance and localized density was
statistically significant except for the MDF (see Table 3.8). The small r-value (0.47 to 0.54)
associated with the relationship might be attributed to the small number of samples tested.
The relationship between staple head pull-through resistance and localized density showed
a good correlation for OSB panels combined, and it was found significant with r-value =
0.64 (Figure 3.9). Aside from isolated data points, the trend is clearly indicative of a good
linear relationship. Increasing the OSB density would certainly improve the staple head
pull-through resistance, but that would probably mean increasing the cost of the panels.
y = 2.85x - 622R2 = 0.403
r = 0.64
400
800
1200
1600
2000
2400
400 450 500 550 600 650 700 750 800
Averaged localized density (kg/m3)
Cyc
lic s
tapl
e he
ad p
ull-t
hrou
gh
resi
stan
ce (
N)
Figure 3.9 Cyclic head pull-through resistance of staples in OSB panels in relation to average localized density.
93
3.2.6 Conclusions and Recommendations Generally, cyclic tests of fastener holding capacities in wood-based panels showed similar
results to the corresponding static tests. For the cyclic loading regimes used in this study
(90 cycles at different load levels), no significant differences were observed between static
and cyclic behavior in terms of ultimate fasteners holding capacity with few exceptions.
Localized densification of wood fibers could be attributed to increasing fasteners capacities
for certain panels and fasteners combinations following repeated events of loading and
unloading. Lower values of cyclic capacity for other combinations could be associated with
the fatigue effect. In order to better understand the fatigue response, different loading
regimes with increased number of loading cycles are needed. Further analysis of the load-
deformation relationships including initial stiffness and deformation at a certain load level
can be used to better characterize the cyclic behavior of the fasteners.
Increasing panel density would improve the fastener holding capacity. However, reducing
the variation in localized density by producing panels with more consistent and uniform
density distribution for use in the upholstered furniture industry could be more effective
and possibly more economical for improving the fastener holding design values of the
panels.
Chapter 4 Gusset-plate joints
95
4.1 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1: Static load
4.1.1 Résumé Afin d’obtenir une rapidité et une la facilité d’installation, des agrafeuses électriques sont
généralement employées pour assembler les différents constituants structuraux des meubles
rembourrés. Pour introduire avec succès les panneaux à lamelles orientées (OSB) comme
élément de structure dans l’industrie du meuble rembourré, il est nécessaire d’acquérir des
connaissances concernant la résistance mécanique en flexion de joints de type goussets
agrafés construits avec de l'OSB. Dans cette étude, la résistance mécanique statique en
flexion de joints en forme de T abouté avec deux goussets a été évaluée expérimentalement
et analytiquement pour des goussets de différentes longueurs (4, 6, 8, 10 et 12-po) (102,
152, 203, 254 et 305-mm) attachés avec des agrafes de 1.0 pouce (25-mm) et 1.5 pouce
(38-mm), avec et sans adhésif. La résistance mécanique en flexion du joint a augmenté
proportionnellement avec la longueur du gousset jusqu'à ce que la force du gousset excède
celle du joint principal. La prévision analytique de la résistance mécanique en flexion des
joints agrafés a été satisfaisante. L'application d’un adhésif sur la surface de connexion a
changé les modes de rupture des joints et a augmenté leur résistance mécanique en flexion.
4.1.2 Abstract Power-driven staples are commonly used to join framing members in upholstered furniture
construction due to their quick and easy installation. To successfully introduce oriented
strandboard (OSB) into upholstered furniture as frame stock, moment capacity data for
stapled gusset-plate joints constructed of OSB is needed. In this study, the static moment
capacity of T-shaped, end-to-side joints with two gusset-plates was determined
experimentally and analytically for gusset-plates of different lengths (4, 6, 8, 10 and 12-in)
(102, 152, 203, 254 and 305-mm) attached with 1.0-in (25-mm) and 1.5-in (38-mm) long
staples with and without adhesive. The moment capacity of the joint increased in
proportion with the length of the gusset-plate until the strength of the gusset exceeded that
of the main joint member. Analytical prediction of the moment capacity of an unglued
96
stapled joint was found satisfactory. Application of glue to the connection surface changed
the failure modes of the joints and increased their moment resistance capacity.
4.1.3 Introduction Today, seventy-five percent of homes built in North America utilize OSB panels for floor,
wall, and roof sheathing (SBA 2004). OSB producers continue to supply the market with
large quantities of panels. However, OSB consumption by the housing industry has
matured and offers limited growth potential; therefore, the OSB manufacturers should seek
new markets with the furniture industry being a candidate. In today’s competition with
foreign manufacturers, the furniture industry needs innovative products more than ever. In
general, OSB panels cost less than plywood or solid wood; therefore, the use of OSB in
upholstered furniture frames can reduce the cost of production and allow for more profits.
Modification of a product or designing a new one requires reliable information about the
performance of materials and joints which are going to replace traditional ones in order to
maintain the quality and to meet the consumer’s expectations. In order to encourage the
furniture industry to consider OSB as a new material for their products, technical
information on the performance of OSB as a framing member must be made available to
the industry.
Due to their quick and easy installation, power-driven staples are the most commonly used
fasteners to join framing members and to attach fabric to the frame in upholstered
furniture. Generally, it is believed that staples have limited holding strength in withdrawal.
When staples are used to attach two members by gusset-plates, the joint may develop
considerable strength, as the staples resist shear load rather than withdrawal (Zhang and
Maupin 2004). Therefore, the gusset-plate joints could be used for critical joints, such as
back bottom rail - back post and bottom side rail - back post joints in upholstered furniture
frame as shown in Figure 4.1, since these joints are highly stressed and difficult to
reinforce.
Limited information is available about the moment capacities of gusset-plate joints
constructed of wood composites. Eckelman (1971c) and Zhang et al. (2001b) studied the
97
performance of T-shaped, end-to-side joints with glued-on plywood gusset-plates of
different configurations. Eckelman (1971c), using Douglas-fir plywood as joint members,
showed that the strength of the joints was limited by the properties of gusset-plate
materials, specifically, by rolling shear strength and in-plane shear strength. Zhang et al.
(2001b) expanded on Eckelman’s research by using southern yellow pine plywood, aspen
Timberstrand, and aspen Engineered Strand Lumber (ESL) as joint members and gusset-
plates made of southern yellow pine plywood attached with glue and staples. It was
reported that the material of the joint member and the number of staples did not influence
the joint strength, since all failures occurred in gusset-plates. Performance of OSB as a
frame member or a gusset-plate in a T-shaped joint has not been studied.
In North America, design values for stapled connections are based on empirical data, and
not on mechanics-based models. In this paper, the European Yield Model (EYM) equations
from Eurocode 5 (2004) and geometry considerations are used for analysis of the
connection capacity. The equations used in the EYM are based upon a theory first
developed by Johansen (1949). The equations predict the ultimate strength of a dowel-type
joint due to either a bearing failure of the joint members or the simultaneous development
of a bearing failure of the joint members and plastic hinge formation in the fastener. In
deriving Johansen's ultimate load equations it is assumed that both the fastener and the
timber are ideal rigid-plastic materials. The mode of failure and the ultimate shear strength
for a single fastener are determined by the thickness and the embedding strength of the
main and side members and by the fastener diameter and yield moment.
Side rail to back post joint
28 in.
72 in.
Side rail
Side rail
Top rail
Back
pos
t
34 in. Front rail
Back rail
Back rail to back post joint
Bac
k po
st
Figure 4.1 Schematic of a three-seat sofa frame (Critical joints—Side rail to back post joint & Back rail to back post joint).
98
The primary objective of this research was to develop basic technical data on static
moment capacities of stapled and glued-stapled, T-shaped, end-to-side gusset-plate joints
constructed of OSB. The specific objectives were to 1) understand how gusset-plate length,
number and size of staples affect the moment capacity of T-shaped joints, 2) compare
moment capacities of gusset-plate joints with and without glue application, and 3) verify
analytical equations of the EYM for prediction of load capacity of stapled gusset-plate
joints. The data will be further used for fatigue testing of joints and for optimization of
upholstered furniture frame design.
4.1.4 Materials and Methods The T-shaped, end-to-side stapled gusset-plate joint specimens comprised two principal
members, a post and a rail, joined by two gusset-plates symmetrically attached on both
sides of the joint as shown in Figure 4.2. The joints were constructed of OSB produced by
Norbord (Canada). The principal members were 23/32-in. (18-mm) thick, 6-in. (152-mm)
wide, 16-in. (406-mm) long, and the gussets were 7/16-in. (11-mm) thick, 6-in. (152-mm)
wide and five different lengths: 4, 6, 8, 10 and 12-in. (102, 152, 203, 254 and 305-mm).
The width of the principal members was taken based on recommendations by Chen (2003).
The number of staples per side and their length varied with the length of the gusset plate as
is shown in Table 4.1. Figure 4.2 shows the staple placement pattern for glued joints, and
Figure 4.3 shows the placement of staples in gusset-plates of unglued joints. The staples,
commonly used in furniture production, were SENCO N17 16-gage galvanized chisel-end-
point type with a crown width of 7/16-in. (11-mm) and leg lengths of 1.0 and 1.5-in. (25
and 38-mm) with leg cross-section of 0.062 x 0.055-in. (1.57 x 1.40-mm). The staples were
coated with Sencote coating, a nitro-cellulose based plastic. The staples were power-driven
flush into specimens with a pressure of 55 psi (380 kPa). Five series of tests were
conducted with the glued-on gusset-plates. A PVA adhesive with solid content of 47%,
typically used in furniture manufacturing, was supplied by ADHESIFS ADHPRO INC.
To prepare the components, 4 by 8-ft (1.22 by 2.44-m) panels were cut into 6-in. (152-mm)
strips along the 8-ft (2.44-m) direction, then cut to length, and randomized. Static tests on
99
the glued joints were conducted at least 48 hours after the application of glue to allow for
curing. Density, moisture content, internal bond strength and flat and edgewise bending
properties of OSB were determined using the matching specimens. The mechanical
properties were evaluated in accordance with ASTM D 1037 (ASTM 2005a).
355P
-
-
152
406
51
406
20
3030
20 20 20
12.7 D.15
2Rail
Post
* All dimensions in mm.
Figure 4.2 Configuration of a typical staple-glued gusset-plate joint.
100
Tabl
e 4.
1 D
escr
iptio
n of
the
spec
imen
s, lo
ad c
apac
ities
, and
failu
re m
odes
of g
usse
t-pla
te jo
ints
con
stru
cted
of O
SB.
G
usse
t-pl
ate
leng
th
Stap
le
leng
th
Num
ber
of
stap
les
Num
ber
of
spec
imen
s
Pred
icte
d ul
timat
e lo
ad
Mea
n ul
timat
e lo
ad
CO
V
Ref
eren
ce
resi
stan
ce a
Dif.
b M
ode
of fa
ilure
c Jo
int
conf
igur
atio
n (in
) (in
)
(K
ip)
(Kip
) (%
) (K
ip)
(%)
a
4 1.
5 20
10
0.
694
0.67
Ad
4.8
0.64
6 -7
W
40%
, W+S
10%
, SO
50%
b 6
1.5
20
10
0.72
9 0.
85 B
7.
6 0.
825
13
W 3
0%, W
+S 1
0%,
W+S
O 2
0%, W
+GR
10%
, G
R+S
O 2
0%, G
R 1
0%
c 8
1.5
20
10
0.85
7 1.
01 C
5.
3 0.
973
14
W 4
0%, W
+GR
20%
, W
+GR
+S 2
0%, S
O 2
0%
d 10
1.
5 20
10
0.
937
1.02
C
5.3
0.98
0 5
W 6
0%, W
+GR
10%
, GR
10%
, M
R 1
0%, S
O 1
0%
e 12
1.
5 20
10
1.
032
0.98
C
6.3
0.94
7 -8
W
70%
, W+G
R 2
0%, M
R 1
0%
f 10
1.
0 32
10
0.
786
0.87
B
7.8
0.84
1 7
W 7
0%, W
+GR
20%
, W+S
10%
g 10
1.
0 32
10
0.
756
0.87
B
7.0
0.84
2 11
W
70%
, W+G
R 1
0%, W
+S 2
0%h
10
1.0
36
10
0.81
1 0.
97 C
9.
4 0.
942
16
W 5
0%, W
+GR
30%
, W+S
20%
Ung
lued
i 8
1.0
40
10
0.79
9 0.
92 B
, C
8.4
0.89
5 12
W
10%
, W+G
R 1
0%,
W+S
O 2
0%, W
+S 4
0%,
GR
+S 1
0%, G
R 1
0%
4 1.
0 8
10
0.
68 A
7.
0 0.
661
S
100%
6
1.0
8 10
0.92
B, C
6.
9 0.
890
M
R 1
0%, G
R+S
30%
, S 6
0%
8 1.
0 8
10
1.
15 D
8.
7 1.
116
M
R 3
0%, G
R+S
60%
, S 1
0%
10
1.0
8 10
1.27
E
11.6
1.
250
M
R 4
0%, G
R 6
0%
Glu
ed
12
1.0
8 10
1.24
D, E
11
.8
1.21
6
GR
100
%
a Ref
eren
ce re
sist
ance
com
pute
d us
ing
expe
rim
enta
l dat
a an
d AS
TM D
5457
pro
cedu
re (K
R = 1
). b D
iffer
ence
bet
wee
n pr
edic
ted
peak
load
and
refe
renc
e re
sist
ance
. c W
= st
aple
with
draw
al; S
= in
-pla
ne sh
ear f
ailu
re o
f OSB
; SO
= S
hear
-out
of O
SB; M
R =
mem
ber r
uptu
re; G
R =
gus
set-p
late
rupt
ure.
d Va
lues
with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t the
95%
sign
ifica
nce
leve
l.
1in
= 2
5.4
mm
; 1K
ip =
100
0 lbf =
4.4
48 k
N.
101
1717
1751
262526 252525152
313031 3030152
2018
1820
76
314531 45152
2120
2020
102
21
314531 45152
2625
2525
127
26
314531 45152
3130
3030
152
31
(
a)
(b)
(c
)
(d
)
(e)
313031 30152
1818
1818
127
1918
18
30
313031 30152
2221
2121
127
2121
30
313031 30
152
2221
2121
127
2121
30
313031 30152
1717
1717
102
1717
30
(f
)
(g
)
(h)
(i)
* Al
l dim
ensi
ons i
n m
m.
Figu
re 4
.3 P
lace
men
t of s
tapl
es in
gus
set-p
late
s of u
nglu
ed jo
ints
(Con
figur
atio
ns a
-i).
102
In order to conform to durability performance test standards such as the General Service
Administration (GSA) test regimen FNAE-80-214A (GSA 1998), strength design of
upholstered furniture frame requires information about the performance of each joint in a
sofa frame. According to the GSA, the bending moment acting on the back rail to back post
joint is considered very high. For a 72-in. (1.83-m) long three-seat sofa of medium-duty
category, three concentrated vertical loads of 300 lbf (1334N) are applied to the back-rail
with a total of 900 lbf (4003 N) (Table 4.2). If the back-rail has two rigid joints with back
posts, each joint carries a bending moment of 300×72/8+300×12×(72-12)/72=5700 lbf-in
(644 N-m) in fatigue test (Figure 4.4). To estimate the static load capacity, the load is
doubled resulting in a static moment capacity of 11400 lbf-in (1288 N-m). To comply with
the GSA requirements, the target static load on the joint with a 14-in. (356-mm) long arm
used in the tests is approximately 11400/14 = 814 lbf (3621 N).
All specimens were tested using a Tinius-Olsen universal testing machine. The post of the
joint was bolted to the test fixture with 2/3-in. (17-mm) aluminium spacers so that the
gusset-plates could deform freely during the test. Vertical upward load was applied to the
rail at a rate of 0.2 in./min (5.1mm/min) (Zhang et al. 2001b), and the load at failure was
recorded using a load cell with the accuracy of 0.2%.
Table 4.2 Performance-acceptance levels of upholstered furniture referencing to GSA (1998).
Cyclic Vertical Load
Test
Initial Loads
Load Increments
Number of Loads
Light-service
Acceptance Level
Medium-service
Acceptance Level
Heavy-service
Acceptance Level
(lbf) (lbf) (lbf) (lbf) (lbf)
On Front Rail 100 100 3 300 400 600
On Back Rail 100 100 3 200 300 500 1.000 lbf = 4.448 N
103
28 in.
72 in.
Side rail
Side rail
Top rail Back post
300 lbf.300 lbf. 300 lbf.
Back rail
Back rail to back post joint
Back rail to back post joint
Front rail
24 in.24 in.12 in. 12 in.Bac
k po
st
Figure 4.4 GSA load applied on the back rail of a three-seat sofa frame (back rail to back post joint).
Predicted Ultimate Load
To predict the load capacity of the moment resisting connection, the analysis of a single
dowel-type fastener (staple) was combined with the analysis of its performance in the joint
of a given geometry. To ensure the design performance of the joint, the location of the
fasteners with respect to the end and the edge of the members should conform to the
assumptions of Eurocode 5 (EYM 2004). However, the design is not always controlled by
the load-carrying capacity of the single fastener. It depends on the configuration of the
connection that may induce supplementary moment couple and shear stresses in the joint
due to eccentricity.
(1) Analysis of a single staple:
To estimate the load capacity of a single staple, R, the following properties were assumed:
embedding strength of OSB = 9,120 psi (63 MPa), tensile strength of the staple = 87,020
psi (600 MPa) from Eurocode 5 (EYM 2004), and the cross-section of the staple leg 0.062
x 0.055 in. (1.57 x 1.40 mm). Calculations for staples using EYM equations (see page 110)
showed that in the joint of a given configuration, staples yield in bending at two plastic-
hinge points per shear plane, with limited localized crushing of OSB near the shear planes
in the side members. The characteristic resistance values were estimated at 190 lbf (860 N)
and 150 lbf (670 N) for the 1.5-in. and 1.0-in. staples, respectively.
104
(2) Performance of the staple in the moment resisting connection.
To derive the design equations, the mechanical behaviour of the moment resisting
connection is examined. To counteract the applied moment, each fastener is loaded at a
different angle depending on the layout of the joint. The assumption is made that the
eccentric load P can be replaced by an equivalent force and an eccentric moment of
magnitude M=P×e acting at the centroid C of the fastener group as shown in Figure 4.5.
The eccentricity e is a function of the geometry of the joint. For a symmetric fastener
pattern, the centroid is found at the geometrical center of the group and the maximum
resultant shear force in the most-stressed fastener is determined for the fastener located
furthermost from the centroid using the following procedure.
For any fastener with coordinates (xi, yi) at a radial distance ri from the centroid of a group
of n fasteners under the load P, the resultant force Ri can be presented by its components
Rxi and Ryi, as shown in Figure 4.6. For the most-stressed fastener at the point with
coordinates (xa, ya), the resultant force is calculated from:
222yaxaa RRR += (4.1)
where:
∑
= 2)(
i
axa r
yMR
(4.2)
∑+= 2
)(
i
aya r
xMnPR
(4.3)
222 ∑∑∑ += iii yxr
(4.4)
The connection design is adequate if Ra is less than the ultimate shear strength R of a single
fastener. Equations (1) to (4) can be used to estimate the load-carrying capacity P of the
moment resisting joint when R is known.
105
e
P
c
Figure 4.5 Schematic of a moment-resisting connection.
P
rA
ri
x
y
MC
i
A
Rxi
RyiRi
Figure 4.6 Forces in fasteners of a moment-resisting connection.
4.1.5 Results and discussion Mechanical and physical properties of OSB
Table 4.3 shows the mechanical and physical properties of OSB panels used in the tests.
For each property shown in the Table, between 22 and 44 specimens were tested.
ra
106
Table 4.3 Average values (COV%) of physical and mechanical properties of joint members and gusset-plates.
MOE (GPa) MOR (MPa) Materials Density
(kg/m3)
Moisture content
(%)
Internal Bond (MPa) Flatwise Edgewise Flatwise Edgewise
Joint member: 23/32 in. (18mm)
OSB
594 (6.8)
6.8 (7.7)
0.426 (18.2)
6.33 (8.2)
4.74 (5.4)
32.2 (12.1)
22.4 (11.7)
Gusset-plate:
7/16 in. (11mm)
OSB
590 (6.8)
6.2 (7.0)
0.417 (17.5)
6.66 (15.7)
5.18 (9.1)
37.1 (16.7)
23.1 (16.4)
Failure Modes
In the tested samples, six failure modes were observed: staple withdrawal, OSB shear-out,
in-plane shear failure of OSB rail member, in-plane shear failure of OSB gusset-plate
gusset-plate rupture and rail member rupture as shown in Figure 4.7 and Table 4.1. In the
joints with intermediate gusset-plates (6, 8 and 10-in) (152, 203 and 254-mm), a mixture of
failure modes was observed. Note, however, that in unglued stapled joints shear-out was
the dominant failure mode in short (4-in) (102-mm) gusset-plates whereas staple
withdrawal was most often observed in the joints with long (12-in) (305-mm) gusset-
plates. Differences in performance of the short and long gusset plates became more
obvious in the glued joints. All 4-in (102-mm) gusset-plates failed in shear in plane of the
panel (Figure 4.7f), while all 12-in (305-mm) gusset-plates failed in gusset plate rupture
(Figure 4.7c). These results indicate that the 4-in (102-mm) gusset-plate was not
adequately sized for the optimum capacity and the 12-in (305-mm) gusset-plate was
oversized. The discussion of load capacities presented below confirms this conclusion.
Load capacity
Mean values and coefficients of variation (COV) of ultimate load capacity of the tested
joints are summarized in Table 4.1. Statistical comparisons of results were performed using
ANOVA general linear model and the Tukey’s multiple comparison tests.
107
(a) OSB shear-out (b) Staple withdrawal
(c) Gusset-plate rupture (d) Member rupture
(e) in-plane shear of rail member (f) Shear in plane of gusset-plate
Figure 4.7 Typical failure modes of gusset-plate joints.
108
In unglued joints with twenty 1.5-in (38-mm) long staples, an increase of gusset-plate
length from 4 to 6-in (102 to 152-mm) and from 6 to 8-in (152 to 203-mm) significantly
increased the peak load by 27% and 19%, respectively. Further increase of gusset-plate
length did not increase the load capacity of the joints as can be seen in Figure 4.8.
Therefore, for this particular joint geometry, the 8-in (203-mm) gusset-plate presented the
optimum design. Note that to achieve similar load levels, about twice as many 1.0-in (25-
mm) long staples were needed (Figures 4.3h and 4.3i). Comparison of configurations f and
g (Figures 4.3f and 4.3g) shows that changing positions of staples in gusset-plates did not
influence the ultimate load significantly.
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14
Gusset-plate length (in.)
Ref
eren
ce re
sist
ance
(lbf
.)
Glued joints (experimental)
Stapled unglued joints (experimental)
Stapled unglued joints (predicted)
Figure 4.8 Experimental reference resistance vs. predicted peak loads of stapled gusset-plate joint assemblies with/without glue.
109
Based on the experimental data, the reference resistance values were calculated as the
lower 5-th percentile with a 75% confidence using the procedure described in ASTM
D5457 (ASTM 2005b)., assuming two-parameter Weibull distribution and a reliability
normalisation factor KR = 1. Table 4.1 and Figure 4.8 show a comparison between the
experimental reference resistance values and the predicted ultimate loads of stapled joints
calculated using the EYM equations and the connection geometry. The experimental values
for stapled joints were 5 to 16% higher than the predicted loads with two exceptions. The
loads carried by 4-in (102-mm) and 12-in (305-mm) gusset-plates were 7% to 8% less than
predicted. This can be explained by the analysis of the failure modes observed during the
tests. The 4-in (102-mm) gusset-plates were inadequately short, and the densely placed
staples often caused shear-out failure in the post before the fasteners developed their full
capacity (Figure 4.7a). On the other hand, the 12-in (305-mm) gusset-plates were
excessively large for this joint; most staples did not reach their shear capacity and failed in
withdrawal due to lateral instability of the rail. These results warrant caution when
applying the principles of the EYM to the joint design where the sizes of the members and
placement of fasteners may not be adequate to develop plastic hinges as assumed in the
theory.
In spite of the satisfactory prediction of stapled gusset-plate joints static strength , the use
of so many staples to construct the joint is not desirable for furniture makers. The use of
glue to attach gusset-plates is much more efficient and requires the minimum number of
staples to fabricate a joint of the same size with the same or higher load capacity.
Experimental results showed that the load capacity of glued joints increased in proportion
with the size of the gusset-plates up to the length of 10 in (254-mm) (Figure 4.8). Further
increase in length of the gusset-plate did not lead to any significant improvement due to the
fact that the strength of the glue bond exceeded the strength of the gusset-plate material
(see Figure 4.7c). In comparison with unglued joints with 20 staples, the mean ultimate
load capacities of joints with 6, 8, 10 and 12-in (152, 203, 254 and 305-mm) gusset-plates
were increased by 8%, 14%, 25% and 27%, respectively.
110
4.1.6 Conclusion Effects of gusset-plate length, number and length of staples, placement of staples, and glue
application on the static load capacity of T-shape OSB gusset-plate joints were
investigated. Application of glue was the most important factor affecting the performance
of the joints, which allowed for strength increase up to 27%. An increase in length of
gusset-plate from 4 to 8-in (102 to 203-mm) boosted peak load for both glued and unglued
joints, but further increase of gusset-plate length did not enhance the strength of the joints.
Twice as many 1.0-in (25-mm) long staples had to be used to achieve similar load levels
with 1.5-in (38-mm) long staples for unglued gusset-plate joints. Changing positions of the
staples in gusset-plates did not affect the strength of the joints of tested configurations.
Failure modes depended on the size of the gusset-plates. Predicted and experimental
reference resistance values for stapled joints were in satisfactory agreement; however, there
is a limit to the application of the yield theory when the geometry of the joint prevents the
development of the full shear capacity. It is advisable to verify extreme cases by tests.
4.1.7 APPENDIX Formulas for characteristic strength of staples:
( ) ( )
( ) ( )
⎪⎪⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪⎪⎪
⎨
⎧
++
+⎥⎥⎦
⎤
⎢⎢⎣
⎡−
+++
+
+⎥⎥⎦
⎤
⎢⎢⎣
⎡−
+++
+
+⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛+++
+
=
42
1215.1
4214
1221
05.1
424
122
05.1
4112
1
.min
,,1,,
,22,1,
,22,1,
,21,1,
,1,1,
,
1
2
2
1
232
1
2
1
221,1,
2,2,
1,1,
,
RkaxkhRky
Rkax
kh
Rkykh
Rkax
kh
Rkykh
Rkaxkh
kh
kh
Rkv
FdfM
Fdtf
Mdtf
Fdtf
Mdtf
Ftt
tt
tt
ttdtf
dtfdtf
F
ββ
βββ
βββ
βββ
βββ
βββββ
111
where: RkvF , = characteristic load-carrying capacity per shear plane per fastener, N;
it = panel thickness or penetration depth, with i = 1 or 2, mm;
kihf ,, = 1.07.065 itd − , characteristic embedment strength in ith member, N/mm2;
d = 48.140.157.1 =× , fastener diameter, mm;
RkyM , = 6.245.0 dfu , characteristic fastener yield moment, Nmm; where uf = 600, tensile strength of the wire, N/mm2;
β =kh
kh
ff
,1,
,2, , ratio between the embedment strength of the members;
RkaxF , = penkax dtf , , characteristic axial withdrawal capacity of the fastener, N;
where 26, 1020 kkaxf ρ−×= , characteristic pointside withdrawal strength, N/mm2;
kρ = 500, characteristic panel density, kg/m3; Notes:
1) 1.5-in. long staples were considered in single shear, because pent = 9 mm = 6d is not sufficient to develop the second shear plane.
2) For 1-in. long staples, pent = 14.3 mm ≤ 14 d , therefore a factor of 69.07.20/3.1414/ ==dt pen was applied.
The Figures A1 and A2 show 1.5-in (38-mm) and 1-in (25-mm) long staples in the panels:
t1=11.1mm
t2=18.3mm
OSB 11.1mm
OSB 18.3mm
OSB 11.1mm t3 = 8.6mm
t1=11.1mm
t2=14.3mm
OSB 11.1mm
OSB 18.3mm
OSB 11.1mm
(A1) (A2)
Figure A-- Schematic of 1.5-in (38-mm) (A1) and 1-in (25-mm) (A2) long staples penetration in the panels.
112
4.2 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 2: Fatigue load
4.2.1 Résumé Pour obtenir le rapport entre la résistance mécanique en flexion statique et la fatigue, la
performance à la fatigue de joints en forme de T aboutés avec deux goussets construit en
panneaux à lamelles orientés (OSB), a été étudiée. Au total, 108 joints agrafés et agrafés-
collés avec des goussets des différentes longueurs (6, 8 et 10 po) (152, 203 et 254-mm) ont
été soumis à des charges échelonnées de flexion cyclique sur un seul côté. Les résultats
d'essai ont montré que les assemblages avec des goussets d'OSB parviennent à la rupture
en moins de 25 000 cycles lorsqu’un niveau de chargement échelonné a excédé 63
pourcent de leur résistance en flexion statique. Le ratio de dépassement pour le test statique
à la fatigue était en moyenne de 2.1 avec un coefficient de variation de 12 pour cent. Dans
les joints agrafés, les ratios les plus élevés étaient associés à l’arrachement d'agrafe comme
mode de rupture dominant. Dans les joints agrafé-collé, les ratios bas étaient associés au
cisaillement dans le plan et les ratios élevés, avec la rupture des panneaux OSB.
4.2.2 Abstract In order to obtain the ratios of static-to-fatigue moment capacity, the fatigue performance
of T-shaped, end-to-side gusset-plate joints made of oriented strandboard (OSB) was
investigated. A total of 108 stapled and glued-stapled joints with gusset-plates of different
lengths (6, 8 and 10 in) (152, 203 and 254-mm) were subjected to one-side cyclic stepped
bending loads. Test results showed that assemblies with OSB gusset-plates would fail
within 25,000 cycles when a stepped load level exceeded 63 percent of their static moment
capacity. The passing static-to-fatigue ratio averaged 2.1 with the coefficient of variation of
12 percent. In the stapled joints, the higher ratios were associated with the staple
withdrawal as dominating failure mode. In the glued-stapled joints lower ratios were
associated with in-plane shear and the higher ratios – with the rupture of the OSB panels.
113
4.2.3 Introduction The furniture manufacturing, including upholstered furniture, is a dynamic industry with
many opportunities to diversify their products using various materials and designs. The use
of panel products, such as plywood and oriented strand board (OSB), to substitute solid
hardwood in upholstered furniture frames, is gaining popularity. Gusset-plates are used to
join back rail to back post and side rail to back post and other highly stressed joints, which
are difficult to reinforce by other means (Zhang et al. 2001b). For OSB to access the
upholstered furniture industry, technical data on the performance of connections made with
OSB must be provided to ensure that it is well-suited for such application. This is the
second paper in a series that deals with this topic (Wang et al. 2007b), which will focus on
the fatigue performance of joints made with OSB framing members and gusset-plates
assembled with staples with and without glue.
In engineering, the term of fatigue is defined as the progressive damage that occurs in
materials subjected to cyclic loading (USDA 1999). By contrast to common belief, fatigue
is the main cause of failure in wooden furniture; therefore, special attention must be paid to
the fatigue resistance of a wood frame (Eckelman and Zhang 1995), which is controlled, in
principle, by the fatigue life of its critical joints. The furniture performance test standards
such as GSA test regimen FNAE-80-214A (GSA 1998), requires information on the joint
fatigue performance, particularly fatigue failure load and fatigue life, i.e. the number of
load cycles survived until failure. The standard performance test regime is based on a zero-
to-maximum non-reversed cyclic stepped fatigue load method rather than static or constant
amplitude cycling load method (Eckelman 1988b).
Multi-cycle fatigue tests are expensive as they require specialized equipment and
considerable testing time in comparison with static tests. Therefore, it would be useful to
correlate the static and fatigue performance to characterize various types of joints in the
future. Several studies were focused on correlating the static and fatigue moment resistance
of wood joints with various fasteners. Zhang et al. (2003) investigated the fatigue life of T-
shaped, end-to-side assemblies using two-pin dowel joints by subjecting them to one-side
constant and stepped cyclic bending loading. A mathematical representation was developed
114
to correlate the applied moment to the number of cycles to failure. Zhang et al. (2006)
studied the bending fatigue life of metal-plate-connected joints in furniture grade pine
plywood subjected to one-side cyclic stepped bending loads. They reported that there was a
strong relationship between the static moment capacity and the load level causing failure in
a fatigue test. The passing fatigue moment level was 46% of the static moment capacity.
No information has been found in literature on the fatigue resistance of gusset-plate joints
made of OSB. The main objective of this study was to evaluate the fatigue resistance of
OSB gusset-plate joints and determine the ratio of the static moment capacities to their
fatigue moment capacities for design purposes. The second objective was to gather the
information on the failure modes of such assemblies under stepped fatigue loads.
4.2.4 Materials and Methods Each test specimen consisted of post and rail made of structural 23/32-in (18-mm) OSB
joined with a pair of 7/16-in (11-mm) OSB gusset-plates symmetrically attached on both
sides of the joint with staples with or without glue. Basic material properties, fabrication
procedures, and configuration details of the joints tested statically were reported in Wang
et al. (2007b). For fatigue tests, the panel materials from the same batch were used and the
joints of the same configurations were constructed using the same procedures with the
exception of the length of the rail and the gusset-plates. The rail length was increased from
16-in (406-mm) to 23-in (584-mm) to accommodate the capacity of the pneumatic
cylinders used in the test setup. The gusset-plates used in fatigue tests were 6, 8 and 10-in
(152, 203 and 254-mm) long, because the static tests (Wang et al. 2007b) showed that
shorter and longer gusset-plates were not efficient in these joints. Columns 1 through 7 of
Tables 4.4 and 4.5 provide the information on the tested configurations including the
number of replicates and the average static moment capacity as reported by Wang et al.
(2007b).
Joint assemblies were subjected to two loading schedules, representing 1) the backrest
frame and 2) seat load foundation test for a 72-in (1.83-m) long three-seat sofa frame
without middle upright on the back (Figure 4.9). To determine the loads for the first
115
Tabl
e 4.
4 Te
st sp
ecim
en c
onfig
urat
ions
and
resu
lts fo
r GSA
bac
kres
t fra
me
sche
dule
.
Fatig
ue
Rat
io o
f st
atic
/fatig
ue
Gusset-plate
length
Staple length
Number of staple
Number of specimens
Stat
ic
peak
lo
ad
(Ave
.)
Stat
ic
mom
ent
(Ave
.) Pa
ssed
m
omen
t Fa
iled
mom
ent
Cum
ulat
ive
No.
of
cycl
es to
failu
re
Pass
ed
Faile
d M
ode
of fa
ilure
a
Type of joint
(in)
(Kip
) (K
ip-in
)
1
2 3
4 5
6 7
8 9
10
11
12
13
6 1.
5 20
9
0.86
(8
.1)
12.1
6.
77
(8)b
7.82
(7
) 10
0,00
0+19
,479
Ac
(10)
1.
78
1.54
WR
+GR
2/9
W
R+G
R+S
3/9
, W
R+S
3/9
, W
R 1
/9
8 1.
5 20
9
1.01
(5
.3)
14.1
6.
42
(5)
7.47
(5)
100,
000+
14,1
45 A
(8
) 2.
20
1.89
W
R 5
/9,
WR
+GR
+S 4
/9
Stapled
10
1.5
20
9 1.
04
(4.7
) 14
.5
7.23
(5
) 8.
28
(4)
125,
000+
7,89
7 B
(5
) 2.
00
1.75
W
R 4
/9,
WR
+GR
3/9
, W
R+G
R+S
2/9
6 1
8 9
0.92
(6
.9)
12.9
7.
82
(10)
8.
87
(9)
150,
000+
237
C
(10)
1.
65
1.45
M
R 5
/9, S
4/9
8 1
8 9
1.15
(8
.7)
16.1
9.
10
(12)
10
.2
(10)
15
0,00
0+23
,864
D
(14)
1.
77
1.59
M
R 4
/9,
GR
+S 4
/9,
S 1/
9
Glued
10
1 8
9 1.
28
(11.
2)
17.9
8.
98
(8)
10.0
(8)
150,
000+
23,1
93 D
(9
) 1.
99
1.78
M
R 6
/9, G
R 3
/9
a Mod
e of
failu
re: W
R =
stap
le w
ithdr
awal
and
rupt
ure;
S =
in-p
lane
shea
r fai
lure
of O
SB; M
R =
mem
ber r
uptu
re; G
R =
gus
set-p
late
ru
ptur
e.
b Valu
es in
par
enth
eses
are
the
coef
ficie
nt o
f var
iatio
n (%
).
c Valu
es w
ith th
e sa
me
capi
tal l
ette
r are
not
stat
istic
ally
diff
eren
t at t
he 9
5% si
gnifi
canc
e le
vel.
1in
= 2
5.4
mm
; 1K
ip =
100
0 lbf =
4.4
48 k
N; 1
Kip
-in=
113
N-m
.
116
Tabl
e 4.
5 Te
st sp
ecim
en c
onfig
urat
ions
and
resu
lts fo
r GSA
seat
load
foun
datio
n sc
hedu
le.
Fatig
ue
Rat
io o
f st
atic
/fatig
ue
Gusset-plate length
Staple length
Number of staple
Number of specimens
Stat
ic
peak
lo
ad
(Ave
.)
Stat
ic
mom
ent
(Ave
.) Pa
ssed
m
omen
t Fa
iled
mom
ent
Cum
ulat
ive
No.
of
cycl
es to
failu
re
Pass
ed
Faile
d
Mod
e of
failu
rea
Type of joint
(in)
(Kip
) (K
ip-in
)
1
2 3
4 5
6 7
8 9
10
11
12
13
6 1.
5 20
9
0.86
(8
.1)
12.1
6.
00
(0)b
9.00
(0
) 50
,000
+402
Ac
(1)
2.01
1.
34
W 6
/9,
W+G
R 2
/9,
W+S
1/9
8 1.
5 20
9
1.01
(5
.3)
14.1
6.
00
(0)
9.00
(0
) 50
,000
+365
A
(0)
2.36
1.
57
W 6
/9, W
+S 3
/9
Stapled
10
1.5
20
9 1.
04
(4.7
) 14
.5
6.00
(0
) 9.
00
(0)
50,0
00+2
,624
C
(2)
2.42
1.
61
W 9
/9
6 1
8 9
0.92
(6
.9)
12.9
6.
00
(0)
9.00
(0
) 50
,000
+1,6
04 B
(4
) 2.
15
1.43
G
R+S
5/9
, S 4
/9
8 1
8 9
1.15
(8
.7)
16.1
7.
33
(22)
1.
03
(15)
50
,000
+21,
577
D
(8)
2.19
1.
56
MR
4/9
, G
R+S
4/9
, S
1/9
Glued
10
1 8
9 1.
28
(11.
2)
17.9
8.
00
(19)
1.
10
(14)
50
,000
+22,
467
D
(11)
2.
24
1.63
M
R 6
/9, G
R 2
/9,
GR
+S 1
/9
a Mod
e of
failu
re: W
= st
aple
with
draw
al; S
= sh
ear i
n pl
ane
of O
SB; M
R =
mem
ber r
uptu
re; G
R =
gus
set-p
late
rupt
ure.
b Va
lues
in p
aren
thes
es a
re th
e co
effic
ient
of v
aria
tion
(%).
c Valu
es w
ith th
e sa
me
capi
tal l
ette
r are
not
stat
istic
ally
diff
eren
t at t
he 9
5% si
gnifi
canc
e le
vel.
1in
= 2
5.4
mm
; 1K
ip =
100
0 lbf =
4.4
48 k
N; 1
Kip
-in =
113
N-m
.
Side rail to back post joint
Side rail to back post joint
100 lbf.100 lbf.
28 in.
72 in.
Side rail
Side rail
100 lbf.
Top rail Back post
Bac
k po
st
34 in. Front rail
Back rail
(a)
28 in.
72 in.
Side rail
Side rail
Top rail Back post
100 lbf.100 lbf. 100 lbf.
Back rail
Back rail to back post joint
Back rail to back post joint
Front rail
24 in.24 in.12 in. 12 in.Back
pos
t
(b)
Figure 4.9 Schematic of a three-seat sofa frame: a) side rail to back post joint; b) back rail to back post joint.
schedule (Table 4.6), it was assumed that three equidistant point loads shown in Figure
4.9(a) were applied horizontally at the top back rail connected to the top ends of two back
posts. The magnitude of these loads at each load step is shown in column 1 (Table 4.6).
These forces deliver loads acting on each of two back posts with the magnitude equal half
of the total load as is shown in column 2 (Table 4.6). Assuming that the height of the back
post in real sofa is 28-in (711-mm), the loads produce moment couples shown in column 3
(Table 4.6). To create the same moments during the tests with the arm of 21-in (533-mm),
the forces shown in column 4 (Table 4.6) were applied to the rail. Similarly, for the second
schedule (Table 4.7), three equidistant point loads applied vertically to the bottom back rail
were assumed as shown in Figure 4.9 (b) and column 1 (Table 4.7). Therefore, the end post
was subjected to a moment couple shown in column 2 (Table 4.7), under the load shown in
column 3 applied at the 20-in (508-mm) arm.
118
Table 4.6 Cyclic stepped load schedule using GSA backrest frame testing schedule.
Backrest frame test
(moment arm = 28 in) Joint test (moment arm = 21 in)
Rail loads Reaction forces
Applied moments Loads
(lbf) (lbf) (Kip-in) (lbf)
Cumulative cycles
3 x 75 112.5 3.15 150 25,000 3 x 100 150 4.20 200 50,000 3 x 125 187.5 5.25 250 75,000 3 x 150 225 6.30 300 100,000
Extended test 3 x 175 262.5 7.35 350 125,000 3 x 200 300 8.40 400 150,000 3 x 225 337.5 9.45 450 175,000 3 x 250 375 10.50 500 200,000
1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.
Table 4.7 Cyclic stepped load schedule for testing using GSA seat load foundation testing schedule.
Joint test (moment arm = 20 in) Seat load foundation
test loads
Applied moments Loads
(lbf) (Kip-in) (lbf) Cumulative
cycles 3 x 100 3.00 150 25,000 3 x 200 6.00 300 50,000 3 x 300 9.00 450 75,000 3 x 400 12.00 600 100,000 3 x 500 15.00 750 125,000
1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.
The fatigue tests were conducted using pneumatic cylinders built-in a specially designed
supporting frame illustrated in Figure 4.10, which allowed testing nine specimens
simultaneously. In both backrest frame and seat load foundation tests, 25,000 load cycles
were applied at a rate of 20 cycles/min at each load level according to the schedules shown
in Tables 4.6 and 4.7, respectively (GSA 1998). After 25,000 cycles, the load was
increased to the next level and load cycling continued. Limit switches were installed on
each cylinder to stop the test of a specimen which suffered a major damage. When backrest
frame joint assemblies passed all levels in the main load schedule the tests continued on to
the extended load schedule shown in Table 4.6 until all the specimens failed. The highest
119
load level sustained by a specimen for 25,000 cycles without failure was used to calculate
the “passed” moment. The number of cycles sustained by the specimen at the next load
level was included into the cumulative number of cycles and the load level at failure was
used to calculate the “failed” moment. Failure modes were determined for each specimen.
4.2.5 Results and Discussion Test results of backrest frame and seat foundation joints are summarized in Tables 4.4 and
4.5, respectively. Columns 8 to 10 show the average values and coefficients of variation of
the passed and failed moments and the cumulative number of cycles to failure. ANOVA
general linear model procedure was performed for different sizes of gusset-plates with or
without glue applications on the fatigue passed load, fatigue failed load, fatigue passed
moment, fatigue failed moment, and fatigue cumulative No. of cycles to failure. Tukey’s
multiple tests were also performed for the classification of the average fatigue cumulative
No. of cycles to failure (Column 10). The average values of passed and failed moments and
Figure 4.10 Setup for the fatigue test of gusset-plate connected joint assemblies.
120
the corresponding average static moment capacities (column 7) were used to calculate,
respectively, the passed and failed static-to-fatigue moment capacity ratios shown in
columns 11 and 12. Higher static-to-fatigue ratios indicate a larger gap between the fatigue
moment capacity of the joint and its capacity determined in static tests; i.e., for a given
fatigue resistance the joint would be required a higher static strength. The last column in
Tables 4.4 and 4.5 lists all observed failure modes and their relative frequency within the
group.
As was expected from the static tests, the glued-stapled joints (Table 4.4) showed
significantly higher failure loads and fatigue life in comparison with the unglued stapled
joints. Unglued stapled joints with 6-in (152-mm) and 8-in (203-mm) gusset-plates
demonstrated no significant difference of fatigue failure loads. Therefore, the static-to-
fatigue ratio of the joints with 6-in (152-mm) gusset-plates appeared to be lower
considering their lower static strength. The stapled joints with 10-in (254-mm) gusset-
plates demonstrated statistically higher fatigue resistance and, accordingly, higher fatigue
life; however, their static-to-fatigue ratios were similar to those with 8-in (203-mm) gusset-
plates. Analysis of the failure modes suggests contribution of OSB panel failures generally
associated with the lower static-to-fatigue ratios, while the higher ratios were associated
with withdrawal of staples.
Similar correlations were found for the glued-stapled joints. The joints with 6-in. gusset-
plates with statistically lower fatigue capacity and fatigue life demonstrated lower static-to-
fatigue capacity ratios; whereas the joints with larger gusset-plates (8 and 10-in) (203 and
254-mm) showed no significant difference of fatigue performance with higher static-to-
fatigue ratios for the 10-in (254-mm) plates. Analysis of failure modes shows that
approximately half of the glued joints with 6-in (152-mm) and 8-in (203-mm) gusset-plates
failed from in-plane shear, while all glued joints with 10-in (254-mm) plates failed in
rupture of one of the joint members, indicating that in the latter case the strength of the
glued area exceeded the strength of the joint members.
It can be noted in Table 4.5 that due to larger load increments in the seat load foundation
test schedule, there were fewer differences observed between pass-fail loads of joints with
121
different gusset-plates, i.e., the load schedule was less sensitive to the differences in the
joint configurations. Therefore, in spite of a slightly longer fatigue life, the static-to-fatigue
ratios of the joints with larger gusset-plates turned out to be higher for both unglued and
glued joint assemblies because of their higher static resistance.
Static to fatigue moment capacity ratio
The ratio of the static to failed fatigue moment varied from 1.34 to 1.89 for stapled joints
and from 1.43 to 1.78 for the glued-stapled joints. The corresponding ratio for the passed
fatigue moment varied from 1.78 to 2.42 and from 1.65 to 2.24 for the stapled and glued-
stapled joints, respectively, with the lower values obtained for the joints with smaller
gusset-plates. The average ratio of static moment to fatigue failed moment for 12 tested
groups subjected to two different schedules was 1.60 with a coefficient of variation (COV)
of 10 percent. In other words, the average OSB gusset-plate joint failed under a load level
of 63 percent of its static moment capacity after being subjected to a series of cyclic
stepped loads. Respectively, the average ratio of static to fatigue passed moment was 2.06
with a COV of 12 percent.
Previously, the average static to fatigue passed moment capacity ratio of 2.2 with a COV of
13 percent was reported for two-pin dowel joints (Zhang et al. 2003) and 2.5 with a COV
of 11 percent for metal-plate connected joints in furniture grade pine plywood (Zhang et al.
2006). Comparison with these studies shows that the average ratio of static to fatigue
moment capacity of upholstered furniture frame joints varies from one fastening system to
another. Based on this information, it is suggested that to pass the fatigue test, an average
ratio of 2.2 for wooden dowels, 2.5 for the metal-plate connectors, and 2.1 for OSB gusset-
plates could be used for upholstered furniture design.
4.2.6 Conclusions Cyclic load fatigue tests on stapled and glued-stapled OSB joints with gusset-plates of
three different sizes were performed and compared with their static moment resistance to
determine the influence of the gusset-plate size, material and fastening system on the static-
to-fatigue moment capacity ratio and on failure modes of the joints. Results showed that
122
despite differences in failure modes, both stapled and glued-stapled joints had similar
static-to-fatigue moment capacity ratios. In the stapled joints, the higher ratios were
associated with the staple withdrawal as the dominating failure mode. In the glued-stapled
joints lower ratios were associated with in-plane shear, and the higher ratios – with the
rupture of the OSB panels. Statistical analysis and comparison with previous studies
showed that the average value of 2.1 can be used as the passing static-to-fatigue ratio for
design of upholstered furniture frames with OSB gusset-plate joints. In other words, it is
advised to design gusset-plate joints so that they will not be loaded to more than 48 percent
of their static moment capacity.
4.2.7 Practicality Information obtained in this study of joint assemblies subjected to cyclic stepped loads
provides designers with technical data assisting in rational and optimum designs of
upholstered furniture frames to meet certain desired performance requirements.
Chapter 5 Metal-plate connected joints
124
5.1 Static bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames
5.1.1 Résumé Des connecteurs de plaque métallique sont généralement utilisés pour relier les joints
critiques dans les structures des meubles rembourrés à cause de leur résistance mécanique
élevée, leur assemblage rapide et le raccordement facile des membres d’épaisseur
uniforme. Pour faciliter l’introduction de panneaux à lamelles orientés (OSB) dans les
structures de meubles rembourrés, des données de base pour les connecteurs métalliques
construits avec de l’OSB sont nécessaires. Dans cette étude, la résistance statique en
flexion de joints en forme de T avec des plaques métalliques a été déterminée
expérimentalement pour différentes configurations. La résistance des joints avec une paire
de plaques métalliques a augmenté proportionnellement avec la largeur de la plaque
métallique et cela jusqu'à 6-po (152-mm). Lorsque les plaques métalliques étaient égales à
la largeur de la pièce d'OSB, la quantité et la concentration de dents ont affaibli
l’assemblage. Les joints avec deux paires de plaques métalliques étaient environ 50% plus
forts que ceux avec une seule paire pour une même couverture. Les mêmes observations
ont été trouvées pour la rigidité.
5.1.2 Abstract Metal-plate connectors are commonly used to connect critical joints in upholstered
furniture frames due to their high load resistance, rapid assembly, and easy connection of
members with uniform thickness. To successfully introduce oriented strand board (OSB)
into furniture frames, basic data for metal-plate connected joints constructed of OSB is
needed. In this study, the static moment capacity of T-shaped joints with metal-plates was
determined experimentally for different configurations. The moment capacity of the joint
with one pair of metal-plates increased in proportion with the width of the metal-plate up to
6-in (152-mm). When the metal-plate was equal the full width of the OSB member, too
many teeth cut into it, making the assembly weaker. Metal-plated joints with two pairs of
125
plates were about 50% stronger than those with a single pair of metal-plates covering the
same area. The same trends were found for the stiffness of metal-plated joints.
5.1.3 Introduction Metal plate connectors (MPC), commonly called “truss plates”, are widely used for joining
wood members, and especially in trussed rafters and joists. Introduced by A. Carroll
Sanford in 1952, MPC changed the wood construction industry. Prefabricated wooden roof
and floor trusses, most of which use MPC, are used in 80% of light commercial and
residential construction in the United States and Canada. The MPC are typically fabricated
from rolled metal sheets of 20, 18 or 16-gauge steel. The sheet metal is cut into a variety of
sizes. The size of MPC depends on the geometry of the joint intended to be held in
equilibrium. Requiring little time for joint fabrication and enhancing the strength and
stiffness of trusses of almost any shape, MPC reduces fabrication cost and time, and
develops a degree of efficiency and architectural flexibility which was not possible before.
The furniture industry is a relatively new area for the MPC. Although originally designed
for use in construction applications, MPC has gained popularity as a connector for critical
joints such as front post-front rail and side rail-back post joint in upholstered furniture
frame construction (Zhang et al. 2005). As a connector in upholstered furniture, MPC
provides high load resistance, rapid joint assembly and easy connection of members with
uniform thickness.
The furniture industry continues to use more and more wood-based panels, but limited
information is available on the moment capacities of metal-plate connected joints
constructed of wood composites. The moment capacities of metal-plated and gusset-plated
joints constructed of plywood and OSB have been addressed by a few researchers. Tables
5.1 and 5.2 show the moment capacities of metal-plated and gusset-plated joints for
plywood and OSB found in the literature. Eckelman (1980) studied the performance of T-
shaped, end to side-grain joints constructed of red oak, yellow-poplar, soft maple, and
Douglas-fir with 18- and 20-gage metal plates of various shapes. Zhang et al. (2005, 2006)
expanded Eckelman’s research by using furniture grade 3/4-in (19-mm) thick 7-ply
southern yellow pine plywood as material. They reported that metal-plate and rail widths
126
affected the moment capacity of MPC plywood joints significantly. Generally, there is very
little research on connections in OSB furniture frames. Wang et al. (2007b, 2007c)
evaluated the feasibility of using OSB as a material for gusset-plated joints in upholstered
furniture. The results showed that the moment capacity of the joint increased in proportion
to the length of the gusset-plate until the strength of the gusset exceeded that of the main
member; application of glue changed the failure modes of the joints and increased their
strength significantly. The performance of OSB as a frame member in a T-shaped metal-
plated joint has not been studied before.
The primary objective of this research was to develop basic data on the static bending
resistance of T-shaped, metal-plate connected joints constructed of OSB. The specific
objectives were 1) to understand how metal-plate width, number and configurations affect
moment resistance of T-shaped joints; 2) to determine the stiffness of metal-plate joints
constructed of OSB; 3) to understand the behavior of the joints through their failure modes;
and 4) to determine an optimum configuration for the bending capacity of metal-plated
joints. The data will be further used for fatigue testing of the joints and for optimization of
upholstered furniture frame designs.
Table 5.1 Moment capacities of metal-plated joints constructed of plywood available in literature (Zhang et al. 2005).
Rail width Metal-plate length Metal-plate width Moment capacity b Panel
(in) (in) (in) (kip-in)
1.6 6.12 (11) 2.4 7.53 (7) 4.5 3.2 9.83 (8) 1.6 5.98 (9) 2.4 7.73 (5)
Plywooda
6.0
6.0 3.2 9.57 (6)
a Furniture grade 3/4-in (19-mm) thick seven-ply southern yellow pine plywood. b Mean value (COV%) 1in = 25.4 mm; 1kip-in = 113 N-m.
127
Table 5.2 Moment capacities of gusset-plate joints constructed of OSB available in literature (Wang et al. 2007b).
Rail width
Gusset-plate width
Gusset-plate
length
Staple length
Number of
staples
Mean ultimate
load COV Moment
capacityJoint configuration Panel
(in) (in) (in) (in) (in) (kip) (%) (kip-in) a 4.0 1.5 20 0.67 Ab 4.8 9.38 b 6.0 1.5 20 0.85 B 7.6 11.9 f 10.0 1.0 32 0.87 B 7.8 12.2
Unglued
g 10.0 1.0 32 0.87 B 7.0 12.2 4.0 1.0 8 0.68 A 7.0 9.52 Glued
OSB a 6.0 6.0
6.0 1.0 8 0.92 B 6.9 12.9 a 23/32-in (18-mm) thick OSB produced by Norbord (Canada). b Values with the same letter are not statistically different at the 95% significance level. 1in = 25.4 mm; 1kip = 1000 lbf = 4.448 kN; 1kip-in = 113 N-m.
5.1.4 Materials and Methods The T-shaped, end-to-side, metal-plate joint specimens were comprised of two principal
members, a post and a rail, joined by one or two pairs of metal-plates symmetrically
attached on both sides of the joint, i.e., an equal number of teeth were pressed into both the
rail and post, as shown in Figure 5.1. For the configurations with two pairs of metal-plates
on each side (series G1 and G3), a distance of 0.5-in (12.7-mm) was left between edges of
the rails and that of the plates. The two structural members were positioned in such a way
that the long side center of the post was perfectly aligned with the short side center of the
rail. The joints were constructed of OSB conforming to CSA 0325 (CSA 2003) produced
by Norbord (Canada). The OSB members were 23/32-in (18-mm) thick, 6-in (152-mm)
wide, 16-in (406-mm) long; and the metal-plates were 2x6-in (51x152-mm) or 4x6-in
(102x152-mm), SK-20 manufactured and provided by Jager Building Systems Inc. For
configurations involving metal-plates of 1.0-in or 3.0-in (25-mm or 76-mm) wide, the
metal-plates were cut from either the 2x6-in (51x152-mm) or 4x6-in (102x152-mm) plates.
Care was taken during cutting to ensure symmetric plates with the same number of teeth
were produced.
128
Figure 5.1 An example of metal-plated joint with two LVDTs’ points A and B.
To prepare the OSB components, 4 by 8-ft (1.22 by 2.44-m) OSB panels were cut into 6-in
(152-mm) strips along the 8-ft (2.44-m) direction, then crosscut into 16-in (406-mm) long
blanks and randomized. The metal-plates were installed with a hydraulic press, using a
pressure of 70 psi (483 kPa). To ensure rail end and post side tight contact, two staples
were used to pre-align the joint. To hold metal-plates and members in alignment, the two
opposite corners of each metal-plate were hammered into the two members. Metal-plates
were pressed one at a time to full uniform contact between plate and OSB. Six series of
tests were conducted with metal-plates. The configuration of the T-shaped, end-to-side
MPC joint specimens for this study are shown in Figure 5.2. Density, moisture content,
internal bond strength and flat and edgewise bending properties of the OSB were
determined before testing the assemblies. The mechanical properties were evaluated in
accordance with ASTM D1037 (ASTM 2005a).
In order to conform to durability performance test standards such as GSA test regimen
FNAE-80-214A (GSA 1998), design strength of upholstered furniture frames requires
information about the performance of each joint in a typical sofa frame. According to the
GSA, the bending moment acting on the back rail to back post joint is considered very
high. For a 72-in (1.83-m) long three-seat sofa of light-duty category, three concentrated
A
B
129
vertical loads of 200 lbf (890 N) are applied to the back-rail with a total of 600 lbf (2669
N) (Table 5.3). If the back-rail has two rigid joints with back posts, each joint carries a
bending moment of 200×72/8+200×12×(72-12)/72=3800 lbf-in (429.4 N-m) in fatigue test.
To estimate the static load capacity, the load is doubled resulting in a static moment
capacity of 7600 lbf-in (858.8 N-m) With a 14-in (356-mm) long arm used in the tests, the
target static load on the joint is approximately 7600/14 = 543 lbf (2415 N).
All specimens were tested using a Tinius-Olsen universal testing machine. The post of the
joint was bolted to the test fixture with 0.67-in (17-mm) aluminium spacers so that the
metal-plates could deform freely during the test. Vertical upward load was applied to the
rail at a rate of 0.2 in/min (5 mm/min) (Zhang et al. 2005), and the load at failure was
recorded using a load cell with accuracy of 0.2%. As can be seen in Figure 5.1, joint
slippages at top and bottom between two points (A and B) were measured using two linear
variable differential transducers (LVDTs).
Calculation of the rotational stiffness of the joint
As shown in Figure 5.3, the two points of LVDTs were originally located at A and B at a
distance of 8.78 in (223 mm) from each other, which remained constant. During the test,
the LVDT at point A contracted the distance AA’ = a; the LVDT at point B retracted the
distance CB’ = b. Therefore, angle of rotation, α, of the arm can be expressed from:
xb
xatg
−==
223α (5.1)
It can be derived as a function of displacements a and b as follows:
223batg +=α (5.2)
Moment-rotation curves (as shown in Figure 5.4) were used to calculate the rotational
stiffness of the joints as a slope between 10-lbf (44.5-N) and 40% of ultimate load
(Gebremedhin et al. 1992).
130
Configuration G1: Configuration G2:
1 in
1 in
3 in16 in
6 in 16 in
6 in
2 in16 in
6 in 16 in
6 in
(a) (b) Configuration G3: Configuration G4:
2 in
2 in
1 in16 in
6 in 16 in
6 in
3 in16 in
6 in 16 in
6 in
(c) (d) Configuration G5: Configuration G6:
4 in16 in
6 in 16 in
6 in
6 in16 in
6 in 16 in
6 in
(e) (f)
* 1 in = 25.4 mm
Figure 5.2 Configurations of metal-plated joints.
131
Table 5.3 Acceptance performance level of upholstered furniture in accordance with GSA (1998).
Test Initial Loads
Load Increments
Number of
Loads
Light-service
Acceptance Level
Medium-service
Acceptance Level
Heavy-service
Acceptance Level
(lbf) (lbf) (lbf) (lbf) (lbf) Cyclic Vertical Load Test on -- Front Rail 100 100
3
300
400 600
-- Back Rail 100 100
3
200
300 500 1.000 lbf = 4.448 N
Figure 5.3 Measurement of the angle of rotation, α.
132
0
1
2
3
4
5
6
7
8
9
10
0 0.005 0.01 0.015 0.02 0.025 0.03
Angle of rotation (rad.)
Mom
ent (
Kip
-in.)
G1-1G1-2G1-3G1-4G1-5G1-7G1-8G1-9G1-10
Figure 5.4 Typical moment-rotation curves of metal-plated joints.
5.1.5 Results and Discussion Physical and mechanical properties of OSB
Table 5.4 shows the physical and mechanical properties of OSB panels used in the tested
specimens.
Failure Modes
In tested assemblies, five types of failure modes were observed (Figure 5.5 and Table 5.5):
metal-plate yield in tension, metal-plate tooth pull-out, OSB crushing on the top corner of
rail member, in-plane shear of OSB, and OSB member rupture. In the test assemblies with
two pairs of metal-plates (G1-2 by 1x6-in (25x152-mm) and G3-2 by 2x6-in (51x152-
mm)), mixed failure modes were observed. However, metal-plate yielding in tension
(Figure 5.5a) was the dominant failure mode in narrower metal-plates (G1-2 by 1x6-in
(25x152-mm), G2-1 by 2x6-in (51x152-mm), and G4-1 by 3x6-in (76x152-mm)). Metal-
plate tooth pull-out (Figure 5.5b) was most often observed in the joints with wider metal-
133
plates (G5-1 by 4x6-in (102x152-mm), and G3-2 by 2x6-in (51x152-mm)). In test
assemblies with the widest metal-plate (G6-1 by 6x6-in (152x152-mm)), OSB member
rupture on the tension side (Figure 5.5e) was evident, since too many teeth cut into the
OSB, weakening the member. The discussion of bending strength presented below
confirms this conclusion.
Table 5.4 Physical & mechanical properties of OSB.
Property Mean (COV%) Modulus of elasticity flatwise MOE, GPa 6.33 (8.2) Modulus of elasticity edgewise MOE, GPa 4.74 (5.4) Modulus of rupture flatwise MOR, MPa 32.2 (12.1) Modulus of rupture edgewise MOR, MPa 22.4 (11.7) Density, kg/m3 594 (6.8) Moisture content, % 6.8 (7.7) Internal bond, MPa 0.426 (18.2)
Table 5.5 Ultimate load capacity and failure modes of metal-plated joints constructed of OSB.
Metal-plate size
Pair of metal-plates
Number of
specimens
Mean ultimate
load COV Moment
capacity Mode of failure a Joint configuration
(in) (lbf) (%) (kip-in)
G1 1x6 2 10 575 Cb 7.7 8.05 50% PY,
20% PY+TP, 10% TP, 20% CR
G2 2x6 1 10 384 D 9.1 5.38 100% PY
G3 2x6 2 10 798 A 8.3 11.2 50% TP,
30% TP+S, 10% CR, 10% MR
G4 3x6 1 10 542 C 6.0 7.59 90% PY, 10% TP G5 4x6 1 10 697 B 5.8 9.76 100% TP G6 6x6 1 10 780 A 9.3 10.9 90% MR, 10% TP
a PY = Metal-plate yield in tension; TP = Metal-plate tooth pull-out; CR = OSB crushed on the top corner of rail member; S =In-plane shear of OSB; MR = OSB member rupture. b Values with the same letter are not statistically different at the 95% significance level. 1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.
134
(a) Metal-plate yield in tension (b) Metal-plate tooth pull-out
(c) OSB crushed on the top of rail (d) Shear in plane of OSB
(e) OSB member rupture
Figure 5.5 Typical failure modes of metal-plated joints.
135
Load and moment capacity
Mean values and coefficients of variation (COV) of ultimate load capacity of OSB metal-
plated assemblies are summarized in Table 5.5. Statistical comparisons of results were
performed using an ANOVA general linear model and Tukey’s multiple comparison tests.
In joints with one pair of metal-plates, an increase of metal-plate width from 2 to 3-in (51
to 76-mm), 3 to 4-in (76 to 102-mm), and 4 to 6-in (102 to 152-mm) significantly increased
the mean ultimate load by 41%, 29% and 12%, respectively. In assemblies with two pairs
of metal-plate joints, significant differences were found. The mean ultimate load of two
pairs of 2 by 6-in (51 by 152-mm) metal-plates (G3) was 39% higher than assemblies with
two pairs of 1 by 6-in (25 by 152-mm) metal-plates (G1). Assemblies made with two pairs
of 1 by 6-in (25 by 152-mm) (G1) were, on average, 50% stronger than those made with
one pair of 2 by 6-in (51 by 152-mm) (G2) and 6% stronger than those with one pair of 3
by 6-in (76 by 152-mm) (G4) metal-plates. The mean ultimate load of assemblies with two
pairs of 2 by 6-in (51 by 152-mm) (G3) was 14% higher than that of assemblies with one
pair of 4 by 6-in (102 to 152-mm) (G5) and no significant difference than that of
assemblies with one pair of 6 by 6-in (152 by 152-mm) plates (G6). This again can be
explained by the fact that there were too many teeth cutting into the OSB members which
made it weaker. The assembly with two pairs of 2 by 6-in (51 by 152-mm) (G3) metal-
plates had the highest bending strength of all configurations as can be seen in Table 5.5 and
Figure 5.6. Therefore, it can be concluded that for this particular joint geometry and size,
the two pairs of 2 by 6-in (51 by 152-mm) (G3) metal-plates were the optimum design.
Comparisons were made for the moment capacities of tested assemblies (Table 5.5) with
the previously published data (Wang et al. 2007b) on plywood assemblies with metal-
plates and OSB with gusset-plates (Tables 5.1 and 5.2). The moment capacity (5.38 kip-in
(608 N-m)) of the OSB joint with one pair of 2 by 6-in (51 by 152-mm) (G2) plates was
lower than that of the plywood joint with one pair of 1.6 by 6-in (41 by 152-mm) plates
(5.98 kip-in (676 N-m)) from Table 5.1. The moment capacity (7.59 kip-in (858 N-m)) of
the OSB joint with one pair of 3 by 6-in (76 by 152-mm) (G4) plates was also lower than
that of a plywood joint with one pair of 2.4 by 6-in (61 by 152-mm) plates (7.73 kip-in
(873 N-m)) from Table 5.1. In OSB assemblies with two pairs of 1 by 6-in (25 by 152-mm)
136
0
100
200
300
400
500
600
700
800
900
G2 G4 G5 G6 G1 G3
Metal-plate configuration
Mea
n ul
timat
e lo
ad (l
bf.)
Figure 5.6 Experimental mean ultimate loads of metal-plated joints.
(G1) plates, the moment capacity (8.05 kip-in (910 N-m)) was somewhat higher than that
of the plywood joint with one pair of 2.4 by 6-in (61 by 152-mm) plates (7.73 kip-in (873
N-m)) from Table 5.1. However, the moment capacity of the OSB joints with two pairs of
2 by 6-in (51 by 152-mm) (G3) metal plates (11.2 kip-in (1,266 N-m)) was quite similar to
those with one pair of 6 by 6-in (152 by 152-mm) stapled gusset-plate unglued joint of
OSB (11.9 kip-in (1,345 N-m)) from Table 5.2, and higher than one pair of 4 by 6-in (102
to 152-mm) gusset-plate in both glued and unglued joints (9.52 and 9.38 kip-in (1,076 and
1,060 N-m), respectively).
Rotational stiffness of metal-plate joints
Moment-rotation curves in Figure 5.4 demonstrate a nonlinear relationship, but the lower
half portion of the curves can reasonably be characterized as linear. Therefore, in this
study, the slope of the curve between 10-lbf (44.5-N) to 40% of ultimate load was used to
calculate the rotational stiffness of joints. Generally, the stiffness value of the joints with
one pair of metal-plates was much lower than that of the joints with two pairs of metal-
plates, as shown in Figure 5.7. Assemblies with two pairs of 1 by 6-in (25 by 152-mm)
(G1) metal-plates were even stiffer than those with one pair of 6 by 6-in (152 by 152-mm)
137
(G6) metal-plates. Among the joints with one pair of metal plates, the 1 by 4x6-in
(102x152-mm) (G5) was much stiffer than 1 by 3x6-in (76x152-mm) (G4), as shown in
Table 5.6 and Figure 5.7.
Table 5.6 Stiffness of six configurations of metal-plate joints.
Metal-plate size Rotational stiffness COV Joint
configuration (in)
Number of metal-plates (kip-in/rad) (%)
G1 1x6 2 1677 A a 29
G2 2x6 1 252 D 31
G3 2x6 2 1852 A 35
G4 3x6 1 558 C 34
G5 4x6 1 1295 B 10
G6 6x6 1 1391 B 8 a Values with the same letter are not statistically different at the 95% significance level. 1in = 25.4 mm; 1kip-in = 113 N-m.
0
400
800
1200
1600
2000
G2 G4 G5 G6 G1 G3
Metal-plate configurations
Stiff
ness
(Kip
-in./r
ad)
Figure 5.7 Rotational stiffness of metal-plated joints.
138
5.1.6 Conclusion The effect of metal-plate width and number of metal-plates on the static bending resistance
of T-shaped OSB metal-plated joints was investigated. For the same width of metal-plates,
the use of two pairs of metal-plates was the most critical factor affecting the performance
of the joints, allowing for strength increase up to 50% in comparison with one pair of
metal-plates. An increase in the width of metal-plates from 2 to 4-in (51 to 102-mm)
boosted the mean ultimate load considerably for both one and two pairs of metal-plated
joints. In assemblies with one pair of 6 by 6-in (152 by 152-mm) metal-plates, the mean
ultimate load was slightly lower than that of assemblies with two pairs of 2 by 6-in (51 by
152-mm) This can be explained by the weakening of the OSB section due to the large
number of teeth cutting through the member. The stiffness values for the joints with one
pair of metal-plates were lower than those for joints with two pairs of metal-plates. The
failure modes observed depended on the size and configuration of the metal-plates. Among
the tested configurations, the joint with two pairs of 2 by 6-in (51 by 152-mm) plates was
the strongest and showed the highest stiffness.
139
5.2 Fatigue bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames
5.2.1 Résumé Cette étude a permis d’évaluer la performance à la fatigue de joints en forme de T en
panneaux à lamelles orientés (OSB) connectés avec deux plaques métalliques. Cette étude
a permis d’obtenir les ratios de résistance en flexion statique versus fatigue. Au total, 80
joints avec des plaques en métal de différentes configurations ont été soumis à des charges
échelonnées de flexion cyclique sur un seul côté. Les résultats d'essai ont prouvé que ces
assemblages atteignent la rupture après moins de 25.000 cycles lorsqu’un niveau de
chargement échelonné excède 63 pour cent de leur résistance statique de flexion. Les ratios
de dépassement de statique versus fatigue étaient en moyenne de 2,5 avec un coefficient de
variation de 22 pour cent. Dans tous les joints de plaques métallique, le mode de rupture
dominant était la rupture de la plaque métallique, le reste était du cisaillement en
arrachement de l’OSB.
5.2.2 Abstract This study evaluated the fatigue performance of T-shaped, end-to-side, metal-plate
connected joints made of oriented strandboard (OSB) to obtain the static-to-fatigue
moment capacity ratios. A total of 80 joints with metal plates of different configurations
were subjected to one-side cyclic stepped bending loads. Test results showed that
assemblies with OSB metal-plates would fail within 25,000 cycles when a stepped load
level exceeded 63 percent of their static moment capacity. The passing static-to-fatigue
ratios averaged 2.5 with a coefficient of variation of 22 percent. In all metal-plated joints,
the dominating failure mode was metal-plate yield; the rest was shear-out of OSB.
5.2.3 Introduction Upholstered furniture generally refers to seating furniture, such as sofas, chairs, and stools,
which are padded for comfort and covered with fabric or leather. The framework of
140
upholstered furniture is usually made of wood or wood based products. The growth of the
industry is influenced by the rate of new home construction and the number of existing
homes being remodelled.
High quality products, made possible by the availability of technical information on the
materials and joints connecting the various components, are important to the upholstered
furniture industry. Such information will help the industry to develop and produce well-
designed and durable furniture. Wood and wood based products are used widely in
furniture production and are rapidly gaining popularity. Oriented strand board (OSB) is one
of these wood based panels which has experienced high growth and is expected to continue
on this trend. For OSB to access the upholstered furniture market, technical data on the
performance of connections made with OSB must be provided to ensure that it is well-
designed and well-suited for such applications.
The behaviour of joints under load is a function of the fasteners and materials that are used
to construct the joints. Different types of connections are used to make joints in the
upholstered furniture. A connector or a fastener is a mechanical device (e.g., staple, screw,
nail, bolt, etc.) or a mechanical assembly (e.g., shear plate, nailed or toothed metal plate,
etc.), or an adhesive used to hold together two or more pieces of wood or wood based
products.
Metal-plate connectors (MPC) are made of sheet steel with punched teeth. The teeth are
integral metal projections of the plate formed perpendicular to the plate during the
stamping process. When pressed into the fibre of wood, these teeth can transmit lateral
loads.
In engineering, the term fatigue is defined as the progressive damage that occurs in
materials subjected to cyclic loading (USDA 1999) and it has been much less studied in the
past than the static loading. In daily use, upholstered furniture is exposed to repeated loads,
which may cause fatigue failure. The response of the furniture or more specifically of the
joints to repeated loads determines the quality of the joints and subsequently of the
furniture. In order to support the use of OSB in the furniture, relevant technical information
is needed. This paper is focused on the fatigue performance of joints made with OSB
141
framing members and metal-plates, and it is one of a series of publications dealing with
introduction of OSB in upholstered furniture frames (Wang et al. 2007a, 2007b, 2007c, and
2007d).
Multi-cycle fatigue tests are expensive as they require specialized equipment and
considerable testing time in comparison with static tests. Therefore, it would be useful to
correlate static and fatigue performance to characterize various types of joints. Several
previous studies have focused on correlating the static and fatigue moment resistance of
wood joints with various fasteners. Zhang et al. (2003) investigated the fatigue life of T-
shaped, end-to-side assemblies using two-pin dowel joints by subjecting them to one-sided
constant and stepped cyclic bending loading. A mathematical representation was developed
to correlate the applied moment to the number of cycles to failure. Zhang et al. (2006)
studied the bending fatigue life of metal-plate-connected joints in furniture grade pine
plywood subjected to one-sided cyclic stepped bending loads. They reported that there was
a strong relationship between static moment capacity and the load level causing failure in a
fatigue test. The passing fatigue moment level achieved just prior to failure was 46% of the
static moment capacity. Wang et al. (2007c) evaluated the moment capacity of OSB
gusset-plate joints for upholstered furniture under fatigue load. Test results showed that
assemblies with OSB gusset-plates would fail within 25,000 cycles when a stepped load
level exceeded 63 percent of their static moment capacity. The passing static-to-fatigue
capacity ratio averaged 2.1 with a coefficient of variation of 12 percent.
The literature review has shown that no technical information is available on the fatigue
performance of metal-plate connected joints constructed of OSB. The main objective of
this study was to evaluate the fatigue resistance of OSB metal-plate connected joints and
determine the ratio of the static to their fatigue moment capacities for design purposes. The
second objective was to gather the information on the failure modes of such assemblies
under stepped fatigue loads.
5.2.4 Materials and Methods Each test specimen consisted of a post and a rail made of structural 23/32-in (18-mm) OSB
joined with one pair or two pairs of metal-plates symmetrically attached on both sides of
142
the joint. Basic material properties, fabrication procedures, and configuration details of the
joints tested statically are reported in a previous paper by the authors (Wang et al. 2007d).
For fatigue tests, the panel materials from the same batch were used and joints of the same
configurations were constructed using the same procedures with the exception of the length
of the rail. The rail length was increased from 16 in (406 mm) to 23 in (584 mm) to
accommodate the load capacity of the pneumatic cylinders used in the test setup. The
metal-plated series used in fatigue tests were G1, G5, G3 and G4. Series G2 and G6 were
not tested in fatigue because static tests showed that G2 and G6 metal-plates were not
efficient (Wang et al. 2007d). The configuration of the T-shaped, end-to-side MPC joint
specimens for this study are shown in Figure 5.8. Table 5.7 provides the information on the
tested configurations and the number of replicates.
Joints were subjected to two loading schedules from GSA test regimen FNAE-80-214A
(GSA 1998), representing 1) the backrest frame, and 2) seat load foundation test for a 72-in
(1.83-m) long three-seat sofa frame without middle upright on the back (Figure 5.9). To
determine the loads for the first schedule (Table 5.8), it was assumed that three equidistant
point loads shown in Figure 5.9(a) were applied horizontally at the top back rail connected
to the top ends of two back posts. The magnitude of these loads at each load step is shown
in column 1 of Table 5.8. These forces deliver loads acting on each of the two back posts
with a magnitude equal to one half of the total load as is shown in column 2 of Table 5.8.
Assuming that the height of the back post in a real sofa is 28-in (711-mm), the loads
produce moment couples shown in column 3 of Table 5.8. To produce the same moment
magnitude during the tests with a moment arm of 21-in (533-mm), test loads were
calculated and applied to the rail (as given in column 4 of Table 5.8). Similarly, for the
second schedule (Table 5.9), three equidistant point loads applied vertically to the bottom
back rail were assumed as shown in Figure 5.9(b) and column 1 of Table 5.9. Therefore,
the end post was subjected to a moment couple shown in column 2 of Table 5.9, which
produced a test load values as given in column 3 of Table 5.9 applied at a 20-in (508-mm)
arm.
143
Configuration G1:
1 in
1 in
3 in16 in
6 in 16 in
6 in
(a) Configuration G3: Configuration G4:
2 in
2 in
1 in16 in
6 in 16 in
6 in
3 in16 in
6 in 16 in
6 in
(b) (c) Configuration G5:
4 in16 in
6 in 16 in
6 in
(d)
* 1in = 25.4 mm
Figure 5.8 Configurations of metal-plated joints for fatigue tests.
144
Table 5.7 Test specimen configurations.
Metal-plate dimensions Pair of metal-plates Number of replicates (in)
G1 1x6 2 10 G5 4x6 1 10 G3 2x6 2 10 G4 3x6 1 10
Note: 1 in = 25.4 mm
Side rail to back post joint
Side rail to back post joint
100 lbf.100 lbf.
28 in.
72 in.
Side rail
Side rail
100 lbf.
Top rail Back post
Bac
k po
st
34 in. Front rail
Back rail
(a)
28 in.
72 in.
Side rail
Side rail
Top rail Back post
100 lbf.100 lbf. 100 lbf.
Back rail
Back rail to back post joint
Back rail to back post joint
Front rail
24 in.24 in.12 in. 12 in.Bac
k po
st
(b)
Figure 5.9 Schematic of a three-seat sofa frame. a) side rail to back post joint; b) back rail to back post joint.
145
Table 5.8 Cyclic stepped load levels using GSA backrest frame testing schedule.
Backrest frame test
(moment arm = 28 in) Joint test (moment arm = 21 in)
Rail loads Reaction forces
Applied moments Test loads
(lbf) (lbf) (kip-in) (lbf)
Cumulative No. of cycles
3 x 75 113 3.15 150 25,000 3 x 100 150 4.20 200 50,000 3 x 125 188 5.25 250 75,000 3 x 150 225 6.30 300 100,000
Extended test 3 x 175 263 7.35 350 125,000 3 x 200 300 8.40 400 150,000 3 x 225 338 9.45 450 175,000 3 x 250 375 10.5 500 200,000
Note: 1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.
The fatigue tests were conducted using specially designed testing bench made of pneumatic
cylinders attached to a supporting frame as illustrated in Figure 5.10, which allowed testing
of ten specimens simultaneously. In both backrest frame and seat load foundation tests,
25,000 load cycles were applied at a rate of 20 cycles/min at each load level according to
the schedules shown in Tables 5.8 and 5.9, respectively. After 25,000 cycles, the load was
increased to the next level and load cycling continued. Limit switches were installed on
each cylinder to stop testing of individual specimens which suffered major damage. When
backrest frame joints passed all levels in the main load schedule the tests continued on to
the extended load schedule shown in Table 5.8 until all the specimens failed. The highest
load level sustained by a specimen after 25,000 load cycles without failure was used to
calculate the “passed” moment. The number of cycles sustained by the specimen at the
next load level was included into the cumulative number of cycles and the load level at
failure was used to calculate the “failed” moment. Failure modes were determined for each
specimen.
146
Table 5.9 Cyclic stepped load levels using GSA seat load foundation testing schedule.
Joint test (moment arm = 20 in) Seat load foundation test
loads Applied moments
Test loads (lbf) (kip-in) (lbf)
Cumulative No. of cycles
3 x 100 3.00 150 25,000 3 x 200 6.00 300 50,000 3 x 300 9.00 450 75,000 3 x 400 12.0 600 100,000 3 x 500 15.0 750 125,000
Note: 1 in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.
Figure 5.10 Setup for fatigue test of metal-plate connected joints.
5.2.5 Results and Discussion Test results of backrest frame and seat foundation joints are summarized in Tables 5.10 and
5.11. Columns 4 to 6 of both tables show the average values and coefficients of variation of
the passed and failed moments and the cumulative number of cycles to failure. ANOVA
general linear model procedure was performed for different configurations of metal-plates
on the fatigue passed load, fatigue failed load, fatigue passed moment, fatigue failed
147
moment, and fatigue cumulative number of cycles to failure. Tukey’s multiple tests were
also performed for the classification of the average fatigue cumulative number of cycles to
failure (Column 6). The average values of passed and failed moments and the
corresponding average static moment capacities (column 3) were used to calculate,
respectively, the passed and failed static-to-fatigue moment capacity ratios shown in
columns 7 and 8. Higher static-to-fatigue ratios indicate a larger gap between the fatigue
moment capacity of the joint and its capacity determined in static tests. The last column in
Tables 5.10 and 5.11 lists the observed failure modes and their relative frequency of
occurrence within the test group.
As was expected from the static tests, the series with two pairs of metal-plate joints (Table
5.10) showed significantly higher failure loads and fatigue life in comparison with those
where one pair of the same or similar width of metal-plate joints were used. The joints with
two pairs of 1 by 6-in (25 by 152-mm) plates (G1) demonstrated no significant difference
of fatigue failure loads of joints with one pair of 4 by 6-in (102 by 152-mm) plates (G5).
Joints with two pairs of 2 by 6-in (51 by 152-mm) plates (G3) demonstrated statistically
highest fatigue resistance and, accordingly, higher fatigue life; however, their static-to-
fatigue ratio was similar to that of joints with two pairs of 1 by 6-in (25 by 152-mm) plates
(G1). Analysis of the failure modes indicated that mixed metal-plate yield with shear-out
of OSB failure modes were generally associated with the higher fatigue life joints, while
the joints with lower fatigue life mostly associated with metal-plate yield.
Similar correlations are shown in Table 5.11. The joints with two pairs of plates showed
significantly higher failure loads and fatigue life in comparison with the joints with one
pair of plates of the same or similar width. The joints with two pairs of 2 by 6-in (51 by
152-mm) plates (G3) demonstrated the highest fatigue resistance. However, their static-to-
fatigue ratio was the lowest due to the high static moment capacity. Analysis of failure
modes showed that all specimens in series G4 with the lowest fatigue life failed due to
metal-plate yield, while the higher fatigue life series (G1, G5 and G3) failed in a mixed
metal-plate yield and shear-out-of-OSB failure modes.
148
Tabl
e 5.
10 T
est r
esul
ts u
sing
GSA
bac
kres
t fra
me
sche
dule
.
Fa
tigue
R
atio
St
atic
pe
ak
load
(A
ve.)
Stat
ic
mom
ent
(Ave
.) Pa
ssed
m
omen
t Fa
iled
mom
ent
Cum
ulat
ive
No.
of
cycl
es to
failu
re
Stat
ic/
pass
ed
Stat
ic/
faile
d
M
ode
of fa
ilure
a
(lbf)
(k
ip-in
)
G1
575
(7.7
) b
8.04
4.
20
(0)
5.25
(0)
50,0
00+7
,801
(7) B
c 1.
92
1.53
20
% M
-P Y
, 80%
M-P
Y +
SP
G5
697
(5
.8)
9.76
4.
52
(11)
5.
57
(9)
50,0
00+1
5,00
6 (1
7) B
2.
16
1.75
10
0% M
-P Y
+ S
P
G3
798
(8.3
) 11
.2
5.67
(1
0)
6.72
(8)
75,0
00+1
6,96
7 (1
4) A
1.
97
1.66
30
% M
-P Y
, 70%
M-P
Y +
SP
G4
542
(6.0
) 7.
58
2.52
(5
2)
3.99
(11)
25
,000
+4,6
74 (2
4) C
3.
01
1.90
90
% M
-P Y
, 10%
M-P
Y +
SP
a Mod
e of
failu
re: M
-P Y
= M
etal
-pla
te y
ield
; SP
= S
hear
- out
of O
SB.
b Valu
es in
par
enth
eses
are
the
coef
ficie
nt o
f var
iatio
n (%
).
c Valu
es w
ith th
e sa
me
lette
r are
not
stat
istic
ally
diff
eren
t at t
he 9
5% si
gnifi
canc
e le
vel.
1lbf
= 4
.448
N; 1
kip-
in =
113
N-m
.
149
Tabl
e 5.
11 T
est r
esul
ts u
sing
GSA
seat
load
foun
datio
n sc
hedu
le.
Fa
tigue
R
atio
St
atic
pe
ak
load
(A
ve.)
Stat
ic
mom
ent
(Ave
.) Pa
ssed
m
omen
t Fa
iled
mom
ent
Cum
ulat
ive
No.
of
cycl
es to
failu
re
Stat
ic/
pass
ed
Stat
ic/
faile
d
M
ode
of fa
ilure
a
(lbf)
(k
ip-in
)
G1
575
(7.7
) b
8.04
3.
00
(0)
6.00
(0)
25,0
00+2
,182
(3) C
c 2.
68
1.34
40
% M
-P Y
, 60%
M-P
Y +
SP
G5
697
(5
.8)
9.76
3.
00
(0)
6.00
(0)
25,0
00+1
2,62
9 (1
0) B
3.
25
1.63
30
% M
-P Y
, 70%
M-P
Y +
SP
G3
798
(8.3
) 11
.2
6.00
(0
) 9.
00
(0)
50,0
00+1
,618
(3) A
1.
86
1.24
10
% M
-P Y
, 10%
SP,
80
% M
-P Y
+ S
P
G4
542
(6.0
) 7.
58
2.70
(3
5)
5.70
(1
7)
25,0
00+1
92 (9
) D
2.81
1.
33
100%
M-P
Y
a Mod
e of
failu
re: M
-P Y
= M
etal
-pla
te y
ield
; SP
= S
hear
-out
of O
SB.
b Valu
es in
par
enth
eses
are
the
coef
ficie
nt o
f var
iatio
n (%
).
c Valu
es w
ith th
e sa
me
lette
r are
not
stat
istic
ally
diff
eren
t at t
he 9
5% si
gnifi
canc
e le
vel.
1lbf
= 4
.448
N; 1
kip-
in =
113
N-m
.
Static to fatigue moment capacity ratio
The ratio of static to failed fatigue moment varied from 1.24 to 1.66 for joints with two
pairs of plates and from 1.33 to 1.90 for joints with one pair of plates. The corresponding
ratio for the passed fatigue moment varied from 1.86 to 2.68 and from 2.16 to 3.25 for the
joints with two pairs and one pair of plates, respectively. The overall average ratio of static
moment to fatigue failed moment for all eight test series subjected to two different loading
schedules was 1.59 with a coefficient of variation (COV) of 20 percent. In other words, the
average OSB metal-plated joint failed under a load level of 63 percent of its static moment
capacity after being subjected to a series of cyclic stepped loads. The results are similar to
those obtained with OSB gusset-plate (Wang et al. 2007c). Under stepped loads with a
maximum magnitude of 63 percent of static moment capacity, the fatigue moment
resistance of metal-plated connected joints was mostly governed by failure in the OSB
material, rather than metal tooth rupture.
The average ratio of static to fatigue passed moment was 2.5 with a COV of 22 percent.
Previously, an average static to fatigue passed moment capacity ratio of 2.2 with a COV of
13 percent was reported for two-pin dowel joints (Zhang et al. 2003), 2.5 with a COV of 11
percent for metal-plated connected joints in furniture grade pine plywood (Zhang et al.
2006), and 2.1 with a COV of 12 percent for OSB gusset-plated joints (Wang et al. 2007c).
Comparison with these studies shows that the average ratio of static to fatigue moment
capacity of upholstered furniture frame joints varies from one fastening system to another.
However, based on this information and for simplification purposes, it could be suggested
that an approximate ratio of 2.5 for the metal-plate connectors with plywood or OSB could
be adopted for upholstered furniture designs.
5.2.6 Conclusions Cyclic load fatigue tests on OSB joints with metal-plates of four configurations were
performed and compared with their static moment resistance to determine the influence of
the metal-plate configuration, material and fastening system on the static-to-fatigue
moment capacity ratio and on failure modes of the joints. Results showed that despite
differences in failure modes, joints with either one pair or two pairs of metal connector
151
plates had similar static-to-fatigue moment capacity ratios. In joints with two pairs of
plates, a mixture of metal-plate yield and shear-out of OSB was the dominant failure mode.
In joints with one pair of plates, lower fatigue life was associated with essentially metal-
plate yield. Statistical analysis and comparison with previous studies showed that a static-
to-fatigue ratio of 2.5 can be adopted as the passing ratio for design of upholstered
furniture frames. In other words, it is advised to design metal-plated joints so that they will
not be loaded to more than 40 percent of their static moment capacity.
5.2.7 Practicality Information obtained in this study of joint assemblies subjected to cyclic stepped loads
provides designers with technical data that can be used to develop rational and optimum
designs of upholstered furniture frames to meet desired performance requirements.
Chapter 6 Out-of-plane static bending resistance of gusset-plate and metal-plate joints constructed of
oriented strand board for upholstered furniture frames
153
6.1 Résumé Les connecteurs avec goussets et avec plaques métalliques sont généralement utilisés pour
les joints critiques dans les structures des meubles rembourrés à cause de leur résistance
mécanique élevée. Pour introduire avec succès des panneaux à lamelles orientés (OSB)
dans les structures des meubles rembourrés, nous avons évalué des joint de type gousset en
OSB ainsi que des joints de type plaques métallique. Dans cette étude, la résistance statique
en flexion en dehors du plan des joints en forme de T avec des goussets et des plaques
métallique a été déterminée expérimentalement pour différentes configurations. La
comparaison avec les résistances en flexion dans le plan a été faite également. La
résistance en flexion dans le plan était beaucoup plus grande que la résistance en flexion en
dehors du plan pour les joints métal-plaqué et gousset-plaqué. Le joint avec deux paires de
2 par 6-po (51 par 152-mm)de plaque métallique est la configuration optimum qui a montré
la charge unitaire maximale la plus élevée parmi tous les joints à plaque métallique
examinés. Pour les joints à gousset, une augmentation de longueur de gousset-plat de 4 à
8-po (102 à 203-mm) a résulté en une charge maximale amplifiée pour les joints collé et
sans colle, mais un accroissement ultérieur de la longueur du gousset-plat, ne résulta pas en
une augmentation significative de la peformance, on peut en conclure que pour cette
géométrie, le gousset-plat 8-po (203-mm) présente la conception optimum. Les joints de
plaque métallique et de gousset d’OSB sans colle ont montré les valeurs semblables de
rigidité, mais les joints de gousset collés ont eu une rigidité beaucoup plus grande que les
joints gousset sans colle. Les joints gousset ont présenté environ 80% de résistance
supplémentaires en flexion hors du plan par rapport à la moyenne que des joints avec
plaque métallique.
6.2 Abstract Gusset-plate and metal-plate connectors are commonly used to connect critical joints in
upholstered furniture frames due to their high load resistance. To successfully introduce
oriented strand board (OSB) into furniture frames, basic data on the performance of gusset-
plate and metal-plate joints constructed of OSB is needed. In this study, out-of-plane static
moment capacity of T-shaped joints with gusset-plates and metal-plates were determined
experimentally for different configurations and comparison with in-plane moment
154
capacities were made. In-plane moment capacities were found to be 4 to 6 times higher
than out-of-plane moment capacities for both metal-plate and gusset-plate joints. Joints
with two pairs of 2 by 6-in (51 by 152-mm) metal-plates, which showed the highest
ultimate unit load, appeared to be the optimum configuration among all the metal-plate
joint configurations tested. For gusset-plate joints, an increase in length of gusset-plate
from 4 to 8-in (102 to 203-mm), boosted the peak load for both glued and unglued joints,
but a further increase of the length did not result in any significant increase in the peak
load. It can be concluded that for this particular joint geometry, the 8-in (203-mm) gusset-
plate presented the optimum design. Metal-plate and unglued gusset-plate joints
demonstrated similar stiffness values; however, glued gusset-plate joints had much higher
stiffness than unglued gusset-plate joints. On average, gusset-plate joints exhibited about
80% higher out-of-plane static moment capacity than metal-plate joints.
6.3 Introduction The wood-based panel industry has experienced increasing growth since its inception and it
is predicted to increase its production capacity further by economizing the utilization of
raw materials. OSB capacity in Canada increased from 3.21 to 10.30 million m3 during last
decade (1994 to 2004) and it is expected to reach 13.13 million m3 by 2008 (RISI 2004).
To date, OSB has captured about 75 percent of the residential construction market as a
sheathing material. But there is a limit for OSB volumes that can be supplied to
construction applications because the demand varies with the price of structural panels. As
a result, OSB manufactures are looking for new markets for their product in order to
maintain their increasing production capacity. The upholstered furniture sector is one
market where there is a potential for expansion (APA 1997, Tabarasi 2002). The recent
development in the Computer Numeric Control (CNC) technology and machinery
encourages upholstered furniture producers to think of alternative ways of minimizing the
cost of raw material and speeding up the production process. However, such new markets
require technical information about the performance of the wood-based panels and joints in
terms of design and manufacturing processes for upholstered furniture to suit their end-use
applications.
155
Metal plate connectors (MPC) have been used in light-frame constructions in North
America since 1950s. The MPC requires little time for joint fabrication and enhances the
strength and stiffness of trusses of almost any shape. However, the use of MPC in the
furniture industry is relatively new, especially in frames made with OSB. MPC and gusset-
plates provide high load resistance, rapid joint assembly and easy connection of members.
They are already used for critical joints such as front post-front rail and side rail-back post
joint in upholstered furniture frame construction (Zhang et al. 2001b and 2005).
Some information is available on the in-plane moment capacities of metal-plate and gusset-
plate joints constructed of plywood and OSB. Eckelman (1971c) and Zhang et al. (2001b)
studied the performance of T-shaped, end-to-side joints with glued-on plywood gusset-
plates of different configurations. Eckelman (1980) studied the performance of T-shaped,
end to side-grain joints constructed of red oak, yellow-poplar, soft maple, and Douglas-fir
with 18- and 20-gauge metal plates of various shapes. Zhang et al. (2005) expanded
Eckelman’s research by using furniture grade 3/4-in (19-mm) thick 7-ply southern yellow
pine plywood as material. They reported that metal-plate and rail widths affected the
moment capacity of MPC plywood joints significantly. Generally, there is limited research
on connections in OSB furniture frames. Wang et al. (2007b, 2007c, 2007d, and 2007e)
evaluated the feasibility of using OSB as a material for gusset-plate and metal-plate joints
in upholstered furniture. The results show that the in-plane moment capacity of the joint
increased in proportion to the length of the gusset-plate until the capacity of the gusset
plate exceeded that of the main member. Application of glue, generally, altered the failure
modes of the joints and increased significantly their strength.
Although, proper designs of frames will attempt to avoid out-of-plane loading, certain
upholstered furniture designs with panels will require that joints be subjected to out-of-
plane loads. For example loads acting on the sofa seat springs apply out-of-plane bending
to the front rail. Tables 6.1 and 6.2 show in-plane moment capacities of metal-plate and
gusset-plate joints for OSB determined previously by Wang et al. 2007d and 2007b.
The primary objective of this research was to develop basic data on the out-of-plane static
bending resistance of T-shaped, gusset-plate and metal-plate joints constructed of OSB.
156
The specific objectives were 1) to understand how plate configurations affect out-of-plane
moment resistance of T-shape joints; 2) to determine the stiffness of joints constructed of
OSB; 3) to understand the behavior of joints based on their failure modes; and 4) to
determine an optimum configuration for the bending capacity of metal-plate and gusset-
plate joints. The data will further be used for the optimization of upholstered furniture
frame designs.
6.4 Materials and Methods Each test specimen consisted of a post and a rail (T-shaped) made of structural 23/32-in
(18-mm) OSB joined with one pair of gusset-plates or one pair or two pairs of metal-plates
symmetrically attached on both sides of the joint. Basic material properties, fabrication
procedures, and configuration details of the joints tested statically were reported in a
previous paper by the authors (Wang et al. 2007b, 2007d). For this study, panel materials
from the same batch were used and joints of the same configurations were constructed
using the same procedures. The configurations of the T-shaped, end-to-side gusset-plate
and MPC joint specimens for this study are shown in Figures 6.1 to 6.3. Tables 6.3 and 6.4
provide the information on the tested configurations and the number of replicates. Density,
moisture content, internal bond, flat and edgewise bending properties of the OSB were
determined before testing the assemblies. The mechanical properties were evaluated in
accordance with ASTM D 1037 standard (ASTM 2005a).
In order to conform to durability performance test standards such as the GSA test regime
FNAE-80-214A (GSA 1998), structural design of upholstered furniture frames requires
information on the performance of each joint in a typical sofa frame. According to the
GSA, for a 72-in (1.83-m) long three-seat sofa of light-duty category, three concentrated
vertical loads of 300 lbf (1,334 N) are applied to the front-rail for a total of 900 lbf (4,003
N) (Table 6.5). Fifteen springs are installed along the sofa to carry the entire load with 5
springs per seat to carry the horizontal loads distributed as shown in Table 6.6. If the front-
rail is assumed to have two rigid joints with front posts, each joint will carry an out-of-
plane bending moment of 61×4+76×8+81×12/2=1338 lbf-in (151 N-m) in fatigue test, as
shown in Figure 6.4. To estimate the static load capacity, the load is doubled resulting in a
157
static moment capacity of 2676 lbf-in (302 N-m). With a 14-in. (356-mm) long arm used in
the tests, the target static load on the joint is approximately 2676/14 = 191 lbf (850 N).
All specimens were tested using a Tinius-Olsen universal testing machine. The post
member of the specimen was clamped to the test fixture. Vertical upward load was applied
to the rail at a rate of 0.2 in./min (5 mm/min) (Zhang et al. 2001b), and the load at failure
was recorded using a load cell with an accuracy of 0.2%. As shown in Figure 6.5, the
displacement of the joint was measured using a Linear Variable Differential Transducer
(LVDT) at the bottom point A located at a distance of 6.5 in (165 mm) from the juncture of
the post and rail. As can be seen in Figure 6.6, during the test, the LVDT at point A
retracted the distance AA’ = a; Therefore, the angle of rotation, α, of the arm can be
expressed as a function of displacement a:
165atg =α (6.1)
Moment-rotation graphs (Figure 6.7) were used to calculate the rotational stiffness of the
joints expressed as the slope of the straight line between 10-lbf (44.5-N) and 40% of
ultimate load (Gebremedhin et al. 1992).
158
Tabl
e 6.
1 In
-pla
ne m
omen
t cap
aciti
es o
f met
al-p
late
d jo
ints
con
stru
cted
of O
SB a
vaila
ble
in li
tera
ture
(Wan
g et
al.
2007
d).
M
etal
-pl
ate
size
Pair
of
met
al-
plat
es
Num
ber
of
spec
imen
s
Mea
n ul
timat
e lo
ad
CO
VM
omen
t ca
paci
ty
Stiff
ness
C
OV
M
ode
of fa
ilure
a Jo
int
conf
igur
atio
n (in
)
(lb
f)
(%)
(kip
-in)
(kip
-in/ra
d)
(%)
G1
1x6
2 10
57
5 C
b 7.
7 8.
05
1677
Ab
29
50%
PY
, 20
% P
Y+T
P,
10%
TP,
20%
CR
G
2 2x
6 1
10
384
D
9.1
5.38
25
2 D
31
10
0% P
Y
G3
2x6
2 10
79
8 A
8.
3 11
.2
1852
A
35
50%
TP,
30
% T
P+S,
10
% C
R, 1
0% M
R
G4
3x6
1 10
54
2 C
6.
0 7.
59
558
C
34
90%
PY
, 10%
TP
G5
4x6
1 10
69
7 B
5.
8 9.
76
1295
B
10
100%
TP
G6
6x6
1 10
78
0 A
9.
3 10
.9
1391
B
8 90
% M
R, 1
0% T
P a P
Y =
Met
al-p
late
yie
ld in
tens
ion;
TP
= M
etal
-pla
te to
oth
pull-
out;
CR
= O
SB c
rush
ed o
n th
e to
p co
rner
of r
ail m
embe
r; S
=In
-pl
ane
shea
r of O
SB; M
R =
OSB
mem
ber r
uptu
re.
b Va
lues
with
the
sam
e le
tter a
re n
ot st
atis
tical
ly d
iffer
ent a
t the
95%
sign
ifica
nce
leve
l.
1in
= 2
5.4
mm
; 1 lb
f = 4
.448
kN
; 1ki
p-in
= 1
13 N
-m.
159
Tabl
e 6.
2 In
-pla
ne m
omen
t cap
aciti
es o
f gus
set-p
late
join
ts c
onst
ruct
ed o
f OSB
ava
ilabl
e in
lite
ratu
re (W
ang
et a
l. 20
07b)
.
G
usse
t-pl
ate
leng
th
Stap
le
leng
th
Num
ber
of
stap
les
Num
ber
of
spec
imen
s
Pred
icte
d ul
timat
e lo
ad
Mea
n ul
timat
e lo
ad
CO
V
Ref
eren
ce
resi
stan
ce a
Dif.
b M
ode
of fa
ilure
c Jo
int
conf
igur
atio
n (in
) (in
)
(k
ip)
(kip
) (%
) (k
ip)
(%)
a
4 1.
5 20
10
0.
694
0.67
Ad
4.8
0.64
6 -7
W
40%
, W+S
10%
, SO
50%
b 6
1.5
20
10
0.72
9 0.
85 B
7.
6 0.
825
13
W 3
0%, W
+S 1
0%,
W+S
O 2
0%, W
+GR
10%
, G
R+S
O 2
0%, G
R 1
0%
c 8
1.5
20
10
0.85
7 1.
01 C
5.
3 0.
973
14
W 4
0%, W
+GR
20%
, W
+GR
+S 2
0%, S
O 2
0%
d 10
1.
5 20
10
0.
937
1.02
C
5.3
0.98
0 5
W 6
0%, W
+GR
10%
, GR
10%
, M
R 1
0%, S
O 1
0%
e 12
1.
5 20
10
1.
032
0.98
C
6.3
0.94
7 -8
W
70%
, W+G
R 2
0%, M
R 1
0%
f 10
1.
0 32
10
0.
786
0.87
B
7.8
0.84
1 7
W 7
0%, W
+GR
20%
, W+S
10%
g 10
1.
0 32
10
0.
756
0.87
B
7.0
0.84
2 11
W
70%
, W+G
R 1
0%, W
+S 2
0%h
10
1.0
36
10
0.81
1 0.
97 C
9.
4 0.
942
16
W 5
0%, W
+GR
30%
, W+S
20%
Ung
lued
i 8
1.0
40
10
0.79
9 0.
92 B
, C
8.4
0.89
5 12
W
10%
, W+G
R 1
0%,
W+S
O 2
0%, W
+S 4
0%,
GR
+S 1
0%, G
R 1
0%
4 1.
0 8
10
0.
68 A
7.
0 0.
661
S
100%
6
1.0
8 10
0.92
B, C
6.
9 0.
890
M
R 1
0%, G
R+S
30%
, S 6
0%
8 1.
0 8
10
1.
15 D
8.
7 1.
116
M
R 3
0%, G
R+S
60%
, S 1
0%
10
1.0
8 10
1.27
E
11.6
1.
250
M
R 4
0%, G
R 6
0%
Glu
ed
12
1.0
8 10
1.24
D, E
11
.8
1.21
6
GR
100
%
a Ref
eren
ce re
sist
ance
com
pute
d us
ing
expe
rim
enta
l dat
a an
d AS
TM D
5457
pro
cedu
re (K
R = 1
). b D
iffer
ence
bet
wee
n pr
edic
ted
peak
load
and
refe
renc
e re
sist
ance
. c W
= st
aple
with
draw
al; S
= in
-pla
ne sh
ear f
ailu
re o
f OSB
; SO
= S
hear
-out
of O
SB; M
R =
mem
ber r
uptu
re; G
R =
gus
set-p
late
rupt
ure.
d Va
lues
with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 95%
sign
ifica
nce
leve
l.
1in
= 2
5.4
mm
; 1ki
p =
100
0 lbf =
4.4
48 k
N.
160
Configuration G1: Configuration G2:
1 in
1 in
3 in16 in
6 in 16 in
6 in
2 in16 in
6 in 16 in
6 in
(a) (b) Configuration G3: Configuration G4:
2 in
2 in
1 in16 in
6 in 16 in
6 in
3 in16 in
6 in 16 in
6 in
(c) (d) Configuration G5: Configuration G6:
4 in16 in
6 in 16 in
6 in
6 in16 in
6 in 16 in
6 in
(e) (f) * 1in = 25.4 mm
Figure 6.1 Configurations of metal-plate joints for out-of-plane moment tests.
161
355P
-
-
15240
651
406
20
3030
20 20 20
12.7 D.
152Rail
Post
* All dimensions are in mm.
Figure 6.2 Configuration of a typical staple-glued gusset-plate joint for out-of-plane moment tests.
162
1717
1751
262526 252525152
313031 3030152
2018
1820
76
314531 45152
2120
2020
102
21
314531 45152
2625
2525
127
26
314531 45152
3130
3030
152
31
(
a)
(b)
(c
)
(d
)
(e)
313031 30152
1818
1818
127
1918
18
30
313031 30152
2221
2121
127
2121
30
313031 30
152
2221
2121
127
2121
30
313031 30152
1717
1717
102
1717
30
(f
)
(g
)
(h)
(i)
* Al
l dim
ensi
ons a
re in
mm
. Fi
gure
6.3
Pla
cem
ent o
f sta
ples
in g
usse
t-pla
tes o
f ung
lued
join
ts (C
onfig
urat
ions
a-i)
for o
ut-o
f-pl
ane
mom
ent t
ests
.
163
Tabl
e 6.
3 O
ut-o
f-pl
ane
mom
ent c
apac
ities
and
stiff
ness
of m
etal
-pla
te jo
ints
con
stru
cted
of O
SB.
M
etal
-pl
ate
size
Pair
of
met
al-
plat
es
Num
ber
of
spec
imen
s
Mea
n ul
timat
e lo
ad
CO
VM
omen
t ca
paci
ty
Stiff
ness
C
OV
M
ode
of fa
ilure
a Jo
int
conf
igur
atio
n (in
)
(lb
f)
(%)
(kip
-in)
(lbf-
in/ra
d)
(%)
G1
1x6
2 5
113.
3 B
b 12
.6
1.59
19
584
C
5.7
PY+T
P+M
B 2
0%,
TP+M
B 2
0%,
MB
40%
, G
2 2x
6 1
5 99
.0 C
12
.0
1.39
15
688
D
5.4
100%
TP
G3
2x6
2 5
132.
9 A
3.
7 1.
86
2425
8 A
7.
3 10
0% T
P+S
G4
3x6
1 5
101.
0 C
13
.0
1.41
18
330
C
2.8
100%
TP+
S G
5 4x
6 1
5 12
2.4
A, B
5.
6 1.
71
2212
2 B
4.
5 10
0% T
P+S
G6
6x6
1 5
133.
9 A
5.
4 1.
87
2497
6 A
8.
1 10
0% T
P+S
a PY
= M
etal
-pla
te y
ield
in te
nsio
n; T
P =
Met
al-p
late
toot
h pu
ll-ou
t; M
B =
Met
al-p
late
ben
d; S
=In
-pla
ne sh
ear o
f OSB
mem
ber.
b Va
lues
with
the
sam
e le
tter i
ndex
are
not
stat
istic
ally
diff
eren
t at 9
5% si
gnifi
canc
e le
vel.
1i
n =
25.
4 m
m; 1
lbf =
4.4
48 N
; 1ki
p-in
= 1
13 N
-m; 1
lbf-i
n =
113
N-m
m.
164
Tabl
e 6.
4 O
ut-o
f-pl
ane
mom
ent c
apac
ities
and
stiff
ness
of g
usse
t-pla
te jo
ints
con
stru
cted
of O
SB.
G
usse
t-pl
ate
leng
th
Stap
le
leng
th
Num
ber
of
stap
les
Num
ber
of
spec
imen
s
Mea
n ul
timat
e lo
ad
CO
V
Mea
n ul
timat
e m
omen
t
St
iffne
ss
C
OV
Mod
e of
failu
re a
Join
t co
nfig
urat
ion
(in)
(in)
(lbf)
(%
) (lb
f-in
) (lb
f-in
/rad)
(%
)
a 4
1.5
20
5 11
2.8
Gb
15.4
15
79
1557
1 H
5.
8 G
W+S
100
%
b 6
1.5
20
5 16
1.3
E, F
6.
1 22
58
1998
6 G
12
.8
GW
+S 1
00%
c 8
1.5
20
5 20
0.7
B, C
5.
3 28
10
2229
7 F
4.7
GW
+S 8
0%,
GR
+S 2
0%
d 10
1.
5 20
5
203.
1 A
, B
7.4
2844
26
065
E 9.
9
GR
20%
, M
R 2
0%,
GW
+S 2
0%,
S 40
%
e 12
1.
5 20
5
208.
7 A
, B
15.0
29
21
2692
0 E
4.8
S 80
%,
S+G
R 2
0%
f 10
1.
0 32
5
183.
3 C
, D
13.8
25
67
2715
6 E
7.1
S 60
%, M
R 4
0%
g 10
1.
0 32
5
221.
8 A
5.
1 31
05
2728
4 E
5.8
S 40
%, M
R 6
0%
h 10
1.
0 36
5
198.
8 B
, C, D
6.
3 27
84
2588
1 E
5.2
S 80
%, M
R 2
0%
Ung
lued
i 8
1.0
40
5 18
0.1
D, E
10
.5
2521
21
894
F, G
6.
0 S
20%
, GR
20%
, M
R60
%
4 1.
0 8
5 11
7.6
G
8.4
1646
22
588
F 3.
3 S
100%
6
1.0
8 5
160.
2 F
5.7
2243
30
864
D
4.8
S 10
0%
8 1.
0 8
5 19
4.8
B, C
, D
3.9
2727
40
449
C
3.1
S 80
%, M
R 2
0%
10
1.0
8 5
209.
9 A
, B
4.6
2939
46
888
B
5.8
S 10
0%
Glu
ed
12
1.0
8 5
221
A
10.7
30
94
5022
4 A
4.
1 S
100%
a G
W =
Gus
set-p
late
stap
le w
ithdr
awal
; S =
In-p
lane
shea
r fai
lure
of O
SB m
embe
r; M
R =
mem
ber r
uptu
re; G
R =
gus
set-p
late
ru
ptur
e.
b Va
lues
with
the
sam
e ca
pita
l let
ter a
re n
ot st
atis
tical
ly d
iffer
ent a
t 95%
sign
ifica
nce
leve
l.
1in
= 2
5.4
mm
; 1lb
f = 4
.448
N; 1
lbf-i
n =
113
N-m
m.
165
Table 6.5 Acceptance performance level of upholstered furniture in accordance with GSA (1998).
Test Initial Loads
Load Increments
Number of Loads
Light-service
Acceptance Level
Medium-service
Acceptance Level
Heavy-service
Acceptance Level
(lbf) (lbf) (lbf) (lbf) (lbf)
Cyclic Vertical Load Test on -- Front Rail 100 100
3
300
400 600
-- Back Rail 100 100
3
200
300 500 1.000 lbf = 4.448 N. Table 6.6 Distributed loads applied on each springs per seat of sofa (from Tackett and Zhang 2007).
Load distribution Spring 1 Spring 2 Spring 3 Spring 4 Spring 5
(lbf)
Horizontal 61 76 81 76 61
Vertical 30 60 65 60 30
1.000 lbf = 4.448 N.
61 lbf
61 lbf
76 lbf
76 lbf
81 lbf
12 in.
8 in.
4 in.
Figure 6.4 Schematic of the out-of-plane bending carried by the front rail.
166
Figure 6.5 An example of out-of-plane bending test joint with a LVDT point A.
Figure 6.6 Measurement of the angle of rotation, α.
167
0
500
1000
1500
2000
2500
3000
3500
0 0,05 0,1 0,15 0,2 0,25
Angle of rotation (rad.)
Out
-of-p
lane
mom
ent (
lbf-i
n.)
C8-1C8-2C8-3C8-4C8-5
(a)
0
500
1000
1500
2000
2500
0 0,05 0,1 0,15 0,2 0,25
Angle of rotation (rad.)
Out
-of-p
lane
mom
ent (
lbf-i
n.)
G3-1G3-2G3-3G3-4G3-5
(b)
Figure 6.7 Typical out-of-plane moment-rotation curves: (a) gusset-plate, and (b) metal-plate joints.
168
6.5 Results and Discussion Table 6.7 shows the physical and mechanical properties of OSB panels from which the test
specimens were fabricated.
Failure Modes
In tested assemblies, seven types of failure modes were observed as shown in Figure 6.8
and Tables 6.3 and 6.4. For metal-plate joints, assemblies with two pairs of narrow metal-
plates (G1-2 by 1x6-in (25x152-mm)) experienced mixed failure modes, including metal-
plate yield in tension (Figure 6.8d), metal-plate tooth pull-out (Figure 6.8c), and metal-
plate bend (Figure 6.8e). Metal-plate tooth pull-out was the dominant failure mode in the
narrowest metal-plate joints (G2-1 by 2x6-in (51x152-mm)). Metal-plate tooth pull-out
mixed with in-plane shear of OSB member (Figure 6.8a or 6.8b) were more common in the
joints with wider metal-plates (G3-2 by 2x6-in (51x152-mm), G4-1 by 3x6-in (76x152-
mm), G5-1 by 4x6-in (102x152-mm), and G6-1 by 6x6-in (152x152-mm)). For gusset-
plate joints, in-plane shear failure of OSB member was evident for all configurations,
especially for joints with glue. For joints without glue, gusset-plate staple withdrawal
(Figure 6.8h) controlled the smaller gussets (4, 6 and 8-in long) (102, 152 and 203-mm
long). When gusset length increased to 10-in (254-mm) and 12 in (305-mm), mixed failure
modes were observed which included: gusset-plate rupture (Figure 6.8g), OSB member
rupture (Figure 6.8f), gusset-plate staple withdrawal plus in-plane shear failure of OSB
member. The in-plane shear of OSB was the most dominant failure mode of the large
gusset plates. In configurations with 10-in (254-mm) long gusset-plates without glue, the
OSB member rupture was the most frequently observed. The discussion of load and
moment capacity presented below confirms this observation.
Out-of-plane load and moment capacity
Mean values and coefficients of variation (COV) of out-of-plane ultimate load and moment
capacities of metal-plate and gusset-plate OSB joints are summarized in Tables 6.3 and 6.4,
respectively. Statistical comparisons of results were performed using an ANOVA general
linear model and the Tukey’s multiple comparison tests.
169
In joints with one pair of metal-plates, an increase of metal-plate width from 2 to 3-in (51
to 76-mm), showed no significant difference in ultimate load (99 vs. 101 lbf) (440 vs. 449
N), whereas an increase from 3 to 4-in (76 to 102-mm), and from 4 to 6-in (102 to 152-
mm) significantly increased the mean ultimate load by 21% and 9%, respectively. In
assemblies with two pairs of metal-plates, significant differences were found. For example,
the mean ultimate load of two pairs of 2 by 6-in (51 by 152-mm) metal-plates (G3) was
17% higher than that of assemblies with two pairs of 1 by 6-in (25 by 152-mm) metal-
plates (G1). Assemblies made of two pairs of 1 by 6-in (25 by 152-mm) (G1) were, on
average, 14% stronger than those made with one pair of 2 by 6-in (51 by 152-mm) (G2)
and 12% stronger than those with one pair of 3 by 6-in (76 by 152-mm) (G4) metal-plates.
The mean ultimate load of assemblies with two pairs of 2 by 6-in (51 by 152-mm) (G3)
was 9% higher than that of assemblies with one pair of 4 by 6-in (102 by 152-mm) (G5),
and similar to that of assemblies with one pair of 6 by 6-in (152 by 152-mm) plates (G6).
The assembly with two pairs of 2 by-6 in (51 by 152-mm) (G3) metal-plates had the
second highest ultimate load among all configurations, but no significant differences were
found between this series and the one with the highest ultimate load (i.e., one pair of 6 by
6-in (152 by 152-mm) plates (G6)), as can be seen in Table 6.3 and Figure 6.9. Therefore,
for the ultimate unit load (Load/Area), the joint with two pairs of 2 by 6-in (51 by 152-mm)
(G3) metal-plates was almost 50% more efficient than one pair of 6 by 6-in (152 by 152-
mm) plates (G6) (5.5 vs. 3.7 lbf/in2) (37.9 vs. 25.5 KPa). It can be concluded that for this
particular joint geometry and size, the two pairs of 2 by 6-in (51 by 152-mm) (G3) metal-
plates was the optimum design configuration. Comparisons were made for the out-of-plane
moment capacities of tested assemblies (Table 6.3) with the previously obtained data of in-
plane moment capacities on assemblies with similar metal-plates configurations (Tables
6.1). The in-plane moment capacities were, on average 4.3 times higher than the out-of-
plane capacities, varying from 2.9 times (G2) to 5.0 times (G3), but both have exhibited
similar trends in terms of the tested configurations.
For unglued gusset-plate joints with twenty 1.5-in (38-mm) long staples, an increase of
gusset-plate length from 4 to 6 in (102 by 152-mm) and from 6 to 8 in (152 by 203-mm)
significantly increased the peak load by 43% and 24%, respectively. Further increase of
gusset-plate length did not increase the load capacity of the joints as can be seen in Table
170
6.4 and Figure 6.9. Therefore, for this particular joint geometry, the 8-in (203-mm) gusset-
plate presented the optimum design. Comparison of configurations f and g (Figures 6.3f
and 6.3g) shows that changing positions of staples in gusset-plates did influence the
ultimate load significantly (21% difference).
The load capacity of glued joints increased in proportion with the size of the gusset-plates
up to a length of 10 in (254-mm) (Figure 6.9). Further increase in length of the gusset-plate
did not result in any significant improvement due to the fact that the strength of the glue
bond exceeded the strength of the OSB material. For the same size of gusset-plate joints (4,
6, 8, 10 and 12-in) (102, 152, 203, 254 and 305-mm), either glued or unglued (with 20
staples), the mean ultimate load capacities of joints were not significantly different. In
comparison with in-plane moment capacities on assemblies with similar gusset-plates
configurations (Table 6.2), the in-plane capacities were, on average 3.9 times higher than
out-of-plane capacities varying from 2.9 times (configuration g) to 4.9 times (configuration
a).
Rotational stiffness
Moment-rotation curves in Figure 6.7 demonstrate a nonlinear relationship, but the lower
section of the curves can reasonably be assumed linear. In this study, the slope of the
straight section of the curve between 15-lbf (67-N) to 40% of ultimate load was used to
calculate the rotational stiffness of joints.
Generally, for metal-plate joints, similar tendency was observed for stiffness and ultimate
load. The stiffness of the joints with one pair of 6 by 6-in (152 by 152-mm) (G6) and two
pairs of 2 by 6-in (51 by 152-mm) (G3) metal-plates were the highest as shown in Table
6.3 and Figure 6.10. Assemblies with two pairs of 1 by 6-in (25 by 152-mm) (G1) metal-
plates were stiffer than those with one pair of 3 by 6-in (76 by 152-mm) (G4) metal-plates.
Among the joints with metal plates, the stiffness of one pair of 2 by 6-in (51 by 152-mm)
(G2) was the lowest.
The gusset-plate joints with glue were much stiffer than the joints without glue (see Table
6.4 and Figure 6.10). Different configurations with 10-in (254-mm) unglued gusset-plates
171
demonstrated no significant difference in stiffness. The stiffness values of metal-plate
joints and unglued gusset-plate joints were similar.
Table 6.7 Physical and mechanical properties of OSB.
Property Mean (COV%) Modulus of elasticity flatwise MOE, GPa 6.33 (8.2) Modulus of elasticity edgewise MOE, GPa 4.74 (5.4) Modulus of rupture flatwise MOR, MPa 32.2 (12.1) Modulus of rupture edgewise MOR, MPa 22.4 (11.7) Density, kg/m3 594 (6.8) Moisture content, % 6.8 (7.7) Internal bond, MPa 0.426 (18.2)
172
(a) In-plane shear of OSB (front) (b) In-plane shear of OSB (back)
(c) Metal-plate tooth pull-out (d) Metal-plate yield in tension
(e) Metal-plate bend (f) OSB member rupture
(g) Gusset-plate rupture (h) Gusset-plate staple withdrawal
Figure 6.8 Typical failure modes of test joints.
0
50
100
150
200
250
a b c d e f g h i 4 6 8 10 12 G1 G2 G3 G4 G5 G6
Gusset-plate and metal-plate configurations
Ulti
mat
e ou
t-of-p
lane
load
(lbf
)
Figure 6.9 Experimental mean ultimate out-of-plane loads of gusset-plated and metal-plated joints.
0
9000
18000
27000
36000
45000
54000
a b c d e f g h i 4 6 8 10 12 G1 G2 G3 G4 G5 G6
Gusset-plate and metal-plate configurations
Stiff
ness
(lbf
-in./r
ad)
Figure 6.10 Stiffness of all configurations of gusset-plated and metal-plated joints.
174
6.6 Conclusion Effects of metal-plate width, number of metal-plates, gusset-plate length, placement of
staples, and glue application on the out-of plane static bending resistance of T-shape OSB
metal-plate and gusset-plate joints were investigated. Comparison with in-plane moment
capacities of identical configurations were also made. The out-of-plane moment capacities
of both types of joints were, on average, 4 times lower than the in-plane capacities.
For the same width of metal-plates, two pairs were 14% stronger than one pair. An increase
in the width of metal-plates from 2 to 4-in (51 to 102-mm) boosted the joint load capacity
for assemblies with one pair or two pairs of metal-plate joints by 19% and 15%,
respectively. Among metal-plate joints, assemblies with two pairs of 2 by 6-in (51 by 152-
mm) plates (G3) showed the highest ultimate unit load. The stiffness values for the joints
with metal-plates demonstrated similar tendency with the values of the ultimate load.
Similar stiffness values were observed for metal-plate joints and unglued gusset-plate
joints.
For joints with gusset-plates, application of glue was the most important factor affecting
the stiffness of the joints, which allowed for a stiffness increase up to 87%, with little
increase in the mean ultimate load. Configurations with the same length of gusset-plate
showed similar mean ultimate load for both glued and unglued joints. An increase in length
of gusset-plate from 4 to 8-in (102 to 203-mm) increased load capacity for both glued and
unglued joints. However, a further increase in gusset-plate length did not enhance the
strength of the joints. Changing positions of staples in gusset-plates did affect the strength
of the joints of tested configurations.
Joints with gusset-plates resisted higher out-of-plane moment than metal-plate joints (max.
220 lbf. vs. 134 lbf) (979 N vs. 596 N). It can be concluded that metal-plate joints are not
as effective in resisting out-of-plane moment when compared to gusset-plate joints.
Chapter 7 Finite element model of sofa frames made of OSB
176
7.1 Introduction In order to use a new material in the assembly of a sofa frame, it is useful to perform
preliminary analysis using the finite element method. This method has been used to model
various structures in civil and mechanical engineering since the 1950s, but it is not widely
used in design of wooden furniture frame. Indeed, with the finite element analysis it is
possible to spare time and money, to carry out several modifications on a virtual model in
order to obtain an optimized design of structure, and it minimizes the need for full-scale
testing. Three configurations of sofa frames with two types of connections under three
levels of acceptance loads were modeled using the commercial finite element software
SAP2000 (1995). The properties of the connections were determined from tests presented
in Chapters 3 to 6. It does remain to validate the model predictions using experimental tests
on a real sofa. This chapter is a preliminary attempt of what can be accomplished using
computer assisted design of upholstered furniture.
7.2 Methodology
1) Mathematical model
The governing equations used in the model are described below. In the elastic domain, the
mechanical behaviour of OSB can be described by Hooke’s law. The linear relationship
between stress and strain for a bar in simple tension or compression can be expressed by
the equation:
εΕ=σ
(7.1)
Where: σ: stress (Pa)
E: modulus of elasticity for OSB (Pa)
ε: strain
In this study, an orthotropic version of Euation 7.1 was used for OSB, then Euation 7.1
becomes:
εσ C= (7.2)
Where:
C: elastic stiffness matrix for OSB (Pa)
177
The equations for the joints (spring links): In a joint local coordinate system, the spring
forces and moments F1, F2, F3, M1, M2, and M3, at a joint are given by:
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
=
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
⎪⎪⎪⎪
⎭
⎪⎪⎪⎪
⎬
⎫
3
2
1
3
2
1
3
2
1
3
2
1
3322.31211332313332221232231211131211
rrruuu
rrrrsymrrrrrrururuurururuuuurururuuuuuu
MMMFFF
where u1, u2, u3, r1, r2 and r3 are the joint displacements and rotations, and the terms u1,
u1u2, u2, … are the specified spring stiffness coefficients.
2) Description of the model and boundary conditions
Figure 7.1 shows the configuration of a typical three-seat sofa frame produced at one of the
upholstered furniture factories in Quebec. A typical sofa frame has structural components
such as front rail, back rail, front stump, back post, arm rail, top rail, etc. These are mainly
constructed with solid lumber or plywood as frame members connected by either screws,
or staples or metal-plates or gusset-plates and glue or a combination of thereof. All these
components must have sufficient strength and stiffness to resist the in-plane and out-of-
plane horizontal and vertical loads caused by people sitting or lying, and potentially,
impact forces due to children jumping on the sofa.
In this study, the sofa frame made entirely of OSB is modeled using finite element
commercial software SAP2000. The design of a three-seat sofa frame is using all
components of 23/32-in (18-mm) thick, 6-in (152-mm) wide OSB bars. The width of the
OSB members is based on recommendations by Chen (2003). The sofa frame is
represented by the 3D linear frame-type elements (beam element), and the connections
between the frames are represented by link elements (including screw, staple, metal-plate,
or gusset-plate, etc.). Here, each link element is a two-joint connecting link, which means a
link connecting two points. In this study, two types of links are used: rigid and semi-rigid.
178
In rigid connection, all degrees of freedom are fixed. In semi-rigid connection, each
element is assumed to be composed of six separate “springs”, one for each of six
deformational degrees of freedom (axial, shear, torsion, and pure bending). Each of these
springs possesses a dual set of properties, either linear or nonlinear. In our case, multi-
linear elastic force-deformation characteristics are defined for the link element, and a
nonlinear static analysis is used in this model. The link element length for screw and staple
is chosen as 1-in (25-mm). While for metal-plate it is chosen as 3-in (76-mm). Table 7.1
presents the material properties of members and joints used in the model.
The boundary conditions for the OSB sofa model were:
• The two front feet of sofa frame are assumed as two roller connections which are
free to rotate on x, y and z directions, and no translation on z direction.
• The two back feet are presumed as two pin connections which can only rotate in x,
y, and z directions, but no translation.
Figure 7.1 Typical three-seat sofa frame.
Top Rail
Front Stump
Top Arm Rail
Back Posts
Front Rail
Front Spring Rail
Stretcher
Upright
Middle Side Rail
Bottom Side Rail
Back Rail Back
Spring Rail
BACK FRAME SYSTEM
SEAT FRAME SYSTEM
SIDE FRAME SYSTEM
179
Table 7.1 Material properties of members and joints used in the finite element model.
Components Elements Properties
OSB members 3D frames E1 = 4740 MPa, E2 = 6330 MPa, A = 152 * 18 mm2,
I1 = 5267712 mm4, I2 = 73872 mm4
Gusset-plate
(OSB)
3D frames E1 = 5180 MPa, E2 = 6330 Mpa, A = 152 * 11 m m2,
I1 = 3219157 mm4, I2 = 16859 mm4
Metal-plate
connectors
Two joint link
Multi-linear
elastic
Rotation R2, R3 (See Figure 7.2 and Table II-1 in Appendix II)
Multi-linear elastic effective stiffness in translation directions
U1, U2 and U3 were assumed between free (0) to fixed (∞).
Screw Two joint link
Multi-linear
elastic
(for one screw)
U1a: Pmax = 890 N, ∆Pmax = 2 mm (Taking from Table 3.3
ave. screw edge withdrwal for 18-mm OSB)
Pfailure = 0.5 Pmax = 445 N, ∆Pfailure = 10 mm
U2 = U3: Pmax = 2224 N, ∆Pmax = 2 mm (Taking from Table 3.3
ave. screw lateral resistance for 18-mm OSB)
Pfailure = 0.5 Pmax = 1112 N, ∆Pfailure = 10mm
Multi-linear elastic effective stiffness in rotation directions R1,
R2 and R3 were assumed between free (0) to fixed (∞).
Staple Two joint link
Multi-linear
elastic
(for two staples
together =1.6
P1b)
U1: Pmax = 890 N, ∆Pmax = 1.5 mm (Taking from Table
3.4 ave. staple edge withdrwal for 18-mm OSB)
Pfailure = 0.5 Pmax = 445 N, ∆Pfailure = 10 mm
U2 = U3: Pmax = 1779 N, ∆Pmax = 1.5 mm (Taking from Erdil
et al. 2003a, ave. staple lateral resistance for OSB)
Pfailure = 0.5 Pmax = 889.5 N, ∆Pfailure= 10 mm
Multi-linear elastic effective stiffness in rotation directions R1,
R2 and R3 were assumed between free (0) to fixed (∞).
Notes: a U1, U2 and U3 are translation displacements. b P1 is the strength per staple.
180
-1500000
-1000000
-500000
0
500000
1000000
1500000
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
Rotation (rad.)
Mom
ent (
N-m
m)
In-planeOut-of-plane
Figure 7.2 Two of 2 x 6 metal-plate joint in-plane and out-of-plane rotation-moments (R3 and R2).
3) Loads Applied on the Sofa Frame
In order to conform to durability performance test standards such as the General Service
Administration (GSA) test regimen FNAE-80-214A (GSA 1998), design of upholstered
furniture frames requires information about the performance of each joint in a sofa frame.
According to the GSA, both in-plane and out-of-plane bending moments acting on the front
and back rails are considered. On a 72-in (1.83-m) long three-seat sofa of light-duty
category, three concentrated vertical loads of 300 lbf (1334 N) are applied to the front-rail
with a total of 900 lbf (4003 N) (Table 7.2). There are 15 springs attached to the front and
back rails to carry the loads, i.e. 5 springs per seat which carry the distributed vertical and
horizontal loads shown in Table 7.3 (Tackett and Zhang 2007) and Figure 7.3. It has to be
noticed that since the worse cases were chosen, the sum of vertical loads on the front and
181
back rails was 63% higher than each service acceptance level loads (300, 400 and 600 lbf)
(1334, 1779 and 2669 N).
Table 7.2 Acceptance performance level of upholstered furniture in accordance with GSA (1998).
Test Initial Loads
Load Increments
Number of Loads
Light-service
Acceptance Level
Medium-service
Acceptance Level
Heavy-service
Acceptance Level
(lbf) (lbf) (lbf) (lbf) (lbf) Cyclic Vertical Load Test on -- Front Rail
100 100 3 300 400 600
-- Back Rail 100 100 3 200 300 500
1.000 lbf = 4.448 N. Table 7.3 Distributed loads applied on each spring of a sofa seat for light, medium, and
heavy-service acceptance levels (from Tackett and Zhang 2007).
Spring 1 Spring 2 Spring 3 Spring 4 Spring 5 Load direction (lbf) Horizonta
l 61 76 81 76 61 Light-service acceptance
level (300lbf) Vertical 30 60 65 60 30
Horizontal 81.3 101.3 108 101.3 81.3 Medium-
service acceptance
level (400lbf) Vertical 40 80 86.7 80 40
Horizontal 101.7 126.7 135 126.7 101.7
(500lbf) Vertical 50 100 108.3 100 50
Horizontal 122 152 162 152 122 Heavy-service
acceptance level (600lbf) Vertical 60 120 130 120 60
1.000 lbf = 4.448 N.
182
Fi
gure
7.3
Lig
ht-s
ervi
ce a
ccep
tanc
e le
vel l
oads
dis
tribu
ted
on a
sofa
fram
e m
odel
.
183
4) Resistance Criteria
To verify if the frame elements can pass the resistance criteria, such as bending, axial
tension or compression, shear-through-thickness, and in-plane shear, the specified
capacities of OSB structural rated panels from the CSA-O86 standard (Wood Design
Manual 2001) shown in Table 7.4 were recalculated to the average short-term values using
the following formulae.
Table 7.4 Specified Strength, Stiffness, and Rigidity Capacities for Type 1 (Standard) Design OSB (Nominal thickness 18.5mm, Rating grade B) (Adapted from Table 7.3C CSA-O86) Unit Capacities relative to major axis at
0o Bending mp N-mm/mm 910 Axial tension tp N/mm 120 Axial compression pp N/mm 120 Shear-through-thickness Vp N/mm 59 Planar shear, bending Vpb N/mm 7.9 Planar shear, shear in-plane Vpf MPa 0.64
X05 = aXmean (1-1.645CV)
where,
X0.5 = 5th percentile value based on a normal distribution on 75% confidence level, from
Table 7.3C CSA-086;
a = 0.8, load duration factor to convert from short-term to standard term load;
CV = 15%, coefficient of variation assumed for OSB.
Recalculating for the width b = 1mm:
1) Bending: (N/mm2) σ = 6M / (bh2)
fb = 910 N-mm/mm x 6 / (bh2)
= 910 N-mm/mm x 6 / (18.5mm)2 = 15.95 N/mm2
fb, mean = fb / (1-1.645x15%) / a = 15.95 N/mm2 / 0.75325/ 0.8 = 26.5 N/mm2
2) Axial tension or compression: (N/mm2) σ = N / (bh)
fa = 120 N/mm / (1 x 18.5mm) = 6.49 N/mm2
184
fa, mean = fa / (1-1.645x15%) / a = 6.49 N/mm2 / 0.75325/ 0.8 = 10.8 N/mm2
3) Shear-through-thickness τ = F / (bh)
fvt = 59 N/mm / (1 x 18.5mm) = 3.19 N/mm2
fvt, mean = fvt / (1-1.645x15%) / a = 3.19 N/mm2 / 0.75325/ 0.8 = 5.3 N/mm2
4) Shear in-plane τ = F / (bh)
fvip = 7.9 N/mm / (1 x 18.5mm) = 0.43 N/mm2
fvip, mean = fvip / (1-1.645x15%) / a = 0.43 N/mm2 / 0.75325/ 0.8 = 0.7 N/mm2 (planar shear,
bending)
or fvip, mean = fvip / (1-1.645x15%) / a = 0.64 N/mm2 / 0.75325/ 0.8 = 1.1 N/mm2 (planar
shear, shear in plane)
5) Torsion
τ max = T / (α dl (dc)2) < fvip, mean
dl/dc = 6/(23/32) = 8.35 α = 0.30
τ max = T / (0.30 x 6 x (23/32)2) (shear, torsion)
Therefore, Table 7.5 shows the average short-term strength values of bending, axial tension
or compression, shear-through thickness, and shear in-plane, and they are the criteria which
should be compared with results of the analyses.
Table 7.5 The average short-term strength values
Type of strength N/mm2
Bending fb, mean 26.5
Axial tension or compression fa, mean 10.8
Shear-through-thickness fvt, mean 5.3
Shear in-plane fvip, mean 0.7
A total of three configurations were analyzed under light-service acceptance level load, and
then the optimized configuration was used to evaluate the performance under medium and
heavy-service acceptance levels loads. Figure 7.4 shows three configurations of a typical
three-seat OSB sofa frame which has the same size as the wooden one: 72-in (1.83-m)
long, 34-in (864-mm) wide and 27-in (686-mm) high. Two types of connections are used in
185
the model, either all joints with screws or staples with the exception of four metal-plates on
the bottom. The 1.5-in (38-mm) long screws or staples, and 6-in (152-mm) long metal-
plates are chosen as connectors in the frames. Figure 7.5 shows the types of connections
used in the model.
(a)
(b)
(c)
Figure 7.4 Configurations (a), (b) and (c) of a three-seat sofa made of OSB
186
(a
) A
ll jo
ints
with
scre
ws e
xcep
t fou
r met
al-p
late
s on
the
botto
m.
187
(b
) All
join
ts w
ith st
aple
s exc
ept f
our m
etal
-pla
tes o
n th
e bo
ttom
.
Figu
re 7
.5 T
ypes
of c
onne
ctio
ns u
sed
in so
fa fr
ame
mod
el.
188
7.3 Results and Discussion 1. Sofa frame model under light-service acceptance level load.
1) Configuration optimization with rigid joints
The sofa frame is analyzed making the assumption that all joints are rigid (fixed
connections). Table II-2 in Appendix II shows stresses in the frame elements. The
maximum torsion stress is 3.6 N/mm2 (in red) in the two bottom stretchers. In comparison
with the calculations of shear in-plane (0.7 N/mm2) in Table 7.5, it becomes clear that
configuration (a) in Figure 7.4 does not work, since two bottom stretchers are over-
stressed, as can be seen in Figure 7.6 (a).
With the same proceeding, configuration (b) was analyzed and results from Table II-3 in
the Appendix II demonstrate that the maximum torsion stress is still too large (about 2
N/mm2), which appears on the two front stumps and back posts, as can be seen in Figure
7.6 (b). When two more pieces of stretchers are added, as shown in configuration (c) in
Figure 7.4, the stress level is reduced and then becomes 0.2 N/mm2, as given in Table II-4
in the Appendix II and Figure 7.6 (c). It can be concluded that the configuration (c) is the
optimum among the three configurations.
189
(a)
(b)
(c)
Figure 7.6 OSB sofa frame with torsion stress bars for configurations (a), (b) and (c).
190
2) Semi-rigid joints
The sofa frame is then analysed with the assumption that all joints are semi-rigid. The
properties of each type of joint are used as inputs into the finite element model for the
frame of configuration (c). The results of joint displacements are given in Table 7.6. And
the results of element joint forces in the links are shown in Table 7.7.
Table 7.6 Joint displacements under light-service acceptance level load. Type of joint Translation displacement Rotation displacement
Effective stiffness
(N/mm) U1 (mm) U2 (mm) U3 (mm) R1(Radians) R2(Radians) R3(Radians)
Metal Screw/Staplea Screw/Staple Screw/Staple Screw/Staple Screw/Staple Screw/Staple Screw/Staple
fixed fixed 7.7/7.7 0.8/0.8 8.7/8.7 0.0079/0.0079 0.0170/0.0170 0.0086/0.0086
5000 fixed 10.6/10.6 0.7/0.7 9.6/9.6 0.0058/0.0058 0.0241/0.0241 0.0115/0.0115
1000 fixed 10.6/10.6 0.7/0.7 10.9/10.9 0.0060/0.0060 0.0241/0.0241 0.0115/0.0115
5000 1000 13.9/13.9 3.1/4.2 10.7/10.7 0.0067/0.0067 0.0311/0.0311 0.0339/0.0362
5000 500 13.9/13.9 3.1/4.2 10.7/10.7 0.0067/0.0067 0.0311/0.0311 0.0339/0.0362
1000 1000 13.9/13.9 3.1/4.2 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365
1000 500 13.9/13.9 3.1/4.2 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365
1000 200 13.9/ 3.1 12.0 0.0067 0.0311 0.0342
1000 100 13.9/13.9 3.1/4.1 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365
1000 50 13.9/13.9 3.0/4.1 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365
1000 10 13.9/13.9 10.4/12.6 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365
1000 8 13.9/13.9 13.5/16.3 12.0/12.0 0.0067/0.0066 0.0311/0.0311 0.0342/0.0365
1000 7 13.9 15.6 12.0 0.0067 0.0311 0.0342
1000 5 13.9/13.9 22.3/27.0 12.0/12.0 0.0067/0.0066 0.0311/0.0311 0.0342/0.0365
1000 1 13.9/13.9 95.1/117 12.0/12.0 0.1295/0.1600 0.0311/0.0311 0.0342/0.0365
1000 0 13.4/14.4 359/509 12.0/16.9 19.1/0.6740 0.0311/0.0311 0.0342/0.0366
400 100 14.0/14.0 3.0/4.1 14.5/14.5 0.0068/0.0067 0.0311/0.0311 0.0347/0.0369
400 10 14.0/14.0 14.5/13.5 14.5/14.5 0.0248/0.0221 0.0197/0.0311 0.0369/0.0347
300 100 14.0/14.0 3.0/4.1 15.8/15.8 0.0068/0.0067 0.0311/0.0311 0.0350/0.0371
200 100 14.1/14.1 3.0/4.1 18.5/18.5 0.0070/0.0068 0.0311/0.0311 0.0354/0.0375
100 100 14.3 3.0 26.7 0.0074 0.0385 0.0364
a All screws or staples joints except four bottom metal-plate joints.
191
Table 7.7 Element joint big forces in the links under light-service acceptance level load.
Translation Rotation Link
F1 F2 F3 M1 M2 M3
Discription No. (N) (N-mm)
4 399
4 -399
5 -521
Two joints
between upright
with top rail 5 521
10 1635
10 -1635 -124565 8209
11 1619 -192001
11 -1619 -8211
12 -1634 124565 -14646
12 1634
13 -1616 14645
Four joints
between front
rail with front
stump or back
rail with back
post
13 1616 108924
18 1758
18 -1758
19 1740
19 -1740
24 1740
24 -1740
25 1758
Four joints
between front
rail with
stretcher or
back rail with
stretcher
25 -1758
Compare with 890 1779 1779 210209 607376
192
From Table 7.6, with the exception of four metal-plate joints on the bottom of the sofa
frame, the joints using either screws or staples do not influence joint displacements. When
1000 N/mm used as metal-plate multi-linear elastic effective stiffness in U1, U2 and U3, the
multi-linear elastic effective stiffness of screw or staple in R1, R2 and R3 could be chosen
even as small as 10N/mm, the displacements were still acceptable (the blue line in Table
7.6) compared with the first line (when all joints are fixed). When metal-plate multi-linear
elastic effective stiffness in U1, U2 and U3, changed to 400N/mm, and the multi-linear
elastic effective stiffness of screw or staple in R1, R2 and R3 were 10N/mm, the results of
displacements were also acceptable. So that 400N/mm was the minimum multi-linear
elastic effective stiffness in U1, U2 and U3 for the metal-plate joint, and 10N/mm was the
minimum stiffness in R1, R2 and R3 for the screw or staple joint.
As can be seen in Table 7.7, the biggest axial force F1 was 521 N and it happened at the
joint between upright with top rail. Compared with screw or staple withdrawal forces (890
N) from Table 7.1, either screw or staple can hold this force. The biggest lateral forces (F2
and F3) were 1758 N and 1635 N, and they were at the four joints between front rail with
front stump and back rail with back post. Compared with screw or staple lateral forces
(2224 N or 1779 N) from Table 7.1, both screw and staple can support this force. The same
for the moment, the biggest out-of-plane moment was 192001 N-mm (M2), it also
happened at the joint between front rail with front stump and back rail with back post.
Comparison was made with G3 (two pairs of 51 by 152-mm) metal-plate out-of-plane
moment (210209 N-mm) from Table 6.3, this metal-plate joint can be used here. The
biggest in-plane moment (M3) (14646 N-mm) was at the joint between front rail with front
stump or back rail with back post, and it far smaller than any tested metal-plate in-plane
moment (min. 607376 N-mm) from Table 5.5. But be noticed that all these forces were
from either static analyse or static tests, if taking into account of fatigue effects (about
double of forces or moments), other stronger joints had to be found.
2. Sofa frame model under medium-service acceptance level load.
Table 7.8 presents the joint displacement under medium-service acceptance level load.
193
Table 7.8 Joint displacements under medium-service acceptance level load. Type of joint a Translation displacement Rotation displacement
Effective stiffness (N/mm) U1 U2 U3 R1 R2 R3
Metal Screw (mm) (mm) (mm) (Radians) (Radians) (Radians)
fixed fixed 10.2 1.0 11.7 0.0105 0.0227 0.0115
5000 fixed 14.2 0.9 12.7 0.0078 0.0321 0.0154
1000 fixed 14.2 0.9 14.5 0.0080 0.0321 0.0154
5000 5000 18.5 5.4 14.3 0.0089 0.0415 0.0485
5000 1000 18.5 5.6 14.3 0.0089 0.0415 0.0483
1000 2000 18.6 5.5 16.0 0.0089 0.0415 0.0487
1000 1000 18.6 5.6 16.0 0.0089 0.0415 0.0487
fixed 1000 11.7 5.4 13.0 0.0120 0.0256 0.0417
fixed 100 11.7 6.1 13.1 0.0132 0.0256 0.0416
fixed 50 11.7 12.5 13.3 0.0237 0.0256 0.0416
fixed 45 11.7 14.3 13.4 0.0260 0.0256 0.0416
fixed 40 11.7 16.5 13.5 0.0289 0.0256 0.0416
fixed 10 11.7 75.0 15.4 0.1057 0.0256 0.0416
fixed 1 11.7 632 34.0 0.8364 0.0256 0.0419 a All screws joints except four bottom metal-plate joints.
From Table 7.8, the results of joint displacements under medium-service acceptance level
load were rather different from the light-service acceptance level. When metal-plate multi-
linear elastic effective stiffness in U1, U2 and U3 were chosen 1000 N/mm, the multi-linear
elastic effective stiffness of screw or staple in R1, R2 and R3 should be fixed, then the
displacements were acceptable (the blue line in Table 7.7) comparing with the first line
(when all joints are fixed). But it is more reasonable to think that the screw multi-linear
elastic effective stiffness in R1, R2 and R3 were used 45N/mm, and metal-plates should be
fixed, these four critical joints on the bottom (front rail – front stump, back rail – back
post) should be reinforced (glued with corner block etc.) to create rigid connections.
Also, Table II-5 in the Appendix II gives stresses in the frame elements. The maximum
bending stress is 23.2 N/mm2 (in red). In comparison with the bending strength (26.5
N/mm2) in Table 7.5, it is found that this frame can serve the medium-service acceptance
level load, but it is close to the limit.
194
In addition, as can be seen in Table II-6 in Appendix II, the biggest lateral forces (F2) were
2307 N, and they were at the four joints between front rail with stretcher and back rail with
stretcher. Compared with screw or staple lateral forces (2224 N or 1779 N) from Table 7.1,
neither screw nor staple can support this force.
3. Sofa frame model under heavy-service acceptance level load.
The joint displacements under heavy-service acceptance level load presented in Table 7.9,
which showed that even if all joints are fixed, the displacements are still too large. Table II-
7 in the Appendix II shows stresses in the frame elements. The maximum bending stress is
34.8 N/mm2 (in red), higher than the bending strength (26.5 N/mm2) in Table 7.5. Also, the
maximum torsion stress is 2.6 N/mm2 (in red), which exceeds the shear in-plane strength
(0.7 N/mm2) in Table 7.5. Consequently, the frame can not serve this heavy-service
acceptance level load.
In addition, from Table II-8 in Appendix II, the biggest lateral forces (F2) were 3461 N and
at the four joints between front rail with stretcher and back rail with stretcher. They were
much bigger than screw or staple lateral forces (2224 N or 1779 N) from Table 7.1, neither
screw nor staple can support this force.
Table 7.9 Joint displacements under heavy-service acceptance level load.
Type of joint a Translation displacement Rotation displacement
Effective stiffness (N/mm) U1 U2 U3 R1 R2 R3
Metal Screw (mm) (mm) (mm) (Radians) (Radians) (Radians)
fixed fixed 15.4 1.0 17.5 0.0158 0.0341 0.0172
5000 fixed 21.3 1.4 19.1 0.0117 0.0481 0.0231
1000 1000 27.9 8.4 24.0 0.0133 0.0623 0.0730 a All screws joints except bottom four metal-plate joints.
195
7.4 Conclusions and Recommendations Three configurations of a three-seat sofa frame made of OSB with two types of joints
(screws with metal-plates and staples with metal-plates) under three levels of service
acceptance loads were modeled. Two types of connections were used in the model: rigid
(fixed) and semi-rigid (with real properties of connections). Results allowed making the
following conclusions.
1) The orientation of the components of the sofa frame has a strong impact on the
resistance.
2) When the sofa frame model is under light-service acceptance level load, using either
screws with four metal-plate joints or staples with four metal-plate joints does not change
the joint displacements remarkably. Regarding the inputs in semi-rigid joints model,
400N/mm was the minimum multi-linear elastic effective stiffness in U1, U2 and U3 for
metal-plate joint, and 10N/mm was the minimum effective stiffness in R1, R2 and R3 for
screw or staple joint. The biggest axial force F1 was smaller than screw or staple
withdrawal resistance. The biggest lateral forces F2 and F3 were smaller than screw or
staple lateral resistance. Out-of-plane moment M2 was less big than metal-plate (G3) out-
of-plane moment tested before. In-plane moment M3 was smaller than any metal-plate in-
plane moment tested. It could be concluded that using either all screws or all staples except
four metal-plate joints on the bottom of sofa frame can support light-service acceptance
level load.
3) When the sofa frame model is under medium-service acceptance level load, the limit
screw multi-linear elastic effective stiffness in R1, R2 and R3 could be 45N/mm, and metal-
plate should be fixed. In order to pass this acceptance level load, the four critical joints on
the bottom (front rail – front stump, back rail – back post) should be reinforced (e.g., glued
with corner block etc.) to create rigid connections. The biggest lateral forces (F2) were
bigger than screw or staple lateral resistance. Either screw or staple had difficulty to hold
this force.
4) It was found that the frame of configuration (c) could not serve the heavy-service
acceptance level load, because the bending strength of the frame material was exceeded
196
(34.8 vs. 26.5 N/mm2). The biggest lateral forces (F2) were much bigger than screw or
staple lateral resistance. Neither screw nor staple can support this force.
Summary and Conclusions
Summary
Designing, testing and modeling of joints and attachment systems for the use of OSB in
upholstered furniture frames is the focus of this dissertation. The key objective of the study
is to develop the information needed for the engineered design of joints used in upholstered
furniture frames constructed of OSB. To achieve the main objective, five aspects were
studied:
1. Localized OSB panel properties and fastener characteristics.
Basic material properties (density, density profile, internal bond, MOE, MOR and moisture
content) were evaluated in order to be used as input for the modeling of joints of OSB sofa
frame. The localized density effects on fastener holding capacities in wood-based panels
under static and cyclic loading were evaluated. The panels were: 11-mm OSB, 15-mm
OSB, 18-mm OSB, 16-mm MDF and 16-mm PB. Screws and staples were chosen as they
are common types of fasteners in upholstered furniture industry to determine their
performance in OSB joints. The tests including screw and staple face and edge withdrawal,
screw lateral resistance, and screw and staple head pull-through.
2. Moment capacities of OSB gusset-plate joints for upholstered furniture under
static and fatigue loads.
A) The static moment capacity of T-shaped, end-to-side joints with two gusset-plates was
determined experimentally and analytically for gusset-plates of different lengths (102, 152,
203, 254 and 305-mm) (4, 6, 8, 10 and 12-in) attached with 25-mm (1.0-in) and 38-mm
(1.5-in) long staples with and without adhesive. Effects of gusset-plate length, number and
length of staples, placement of staples, and glue application on the static load capacity of
T-shape OSB gusset-plate joints were investigated.
B) The fatigue performance of T-shaped, end-to-side gusset-plate joints made of OSB was
investigated. A total of 108 stapled and glued-stapled joints with gusset-plates of different
lengths (152, 203 and 254-mm) (6, 8 and 10-in) were subjected to one-side fatigue stepped
198
bending loads, and comparisons with their static moment resistance were made to
determine the influence of the gusset-plate size, material and fastening system on the static-
to-fatigue moment capacity ratio and on failure modes of the joints.
3. Static and fatigue bending resistance of metal-plated joints constructed of OSB for
upholstered furniture.
Metal-plate connectors are commonly used to connect critical joints in upholstered
furniture frames due to their high load resistance, rapid assembly, and easy connection of
members with uniform thickness.
A) Static moment capacity of T-shaped joints with metal-plates was determined
experimentally for six different configurations. Effects of metal-plate width and number of
metal-plates on the static bending resistance of T-shaped OSB metal-plated joints were
investigated.
B) The fatigue performance of T-shaped, end-to-side, metal-plated joints made of OSB was
evaluated. A total of 80 joints with metal plates of different configurations were subjected
to one-side fatigue stepped bending loads, and comparisons with their static moment
resistance were made to determine the influence of the metal-plate configuration, material
and fastening system on the static-to-fatigue moment capacity ratio and on failure modes of
the joints.
4. Static out-of-plane bending resistance of gusset-plate and metal-plate joints
constructed of OSB for upholstered furniture frames
The out-of-plane moment capacity of OSB joints is needed in upholstered furniture
designs, since the load acts on the sofa seat springs which transfer the out-of-plane bending
on the front rail. Static out-of-plane moment capacity of T-shaped joints with gusset-plates
and metal-plates were determined experimentally for different configurations, and the
comparison with the in-plane moment capacities were also made.
5. Finite element model of sofa frame made of OSB
199
In order to use a new material in the assembly of a conventional sofa structure, it is useful
to perform preliminary modeling using the finite elements method. Modeling allows the
elimination of numerous experimental tests and opens a new way to optimize the sofa
structure by the assistance of computer. Three configurations of three-seat sofa frame made
of OSB with two types of connections under three service level acceptance loads were
modeled using commercial finite element software SAP 2000. Two types of links were
used in the models: rigid (fixed) and semi-rigid (with the properties of joints determined
experimentally).
Conclusions
Based on the observations and results of experimental tests and finite element modeling,
the following conclusions were made about joints and attachment systems performance for
the use of OSB in upholstered furniture frames.
1 The localized density effects on fastener holding capacities in wood-based panels
under static and cyclic loading
• The composition of panel material was the most important factor for the fastener
holding capacity, but for the same type of panel and the same type of fastener
holding capacity, localized density was an importance factor.
• Among tested panels, OSB showed the highest density variation in plane and
through thickness, which was more critical to the screw than to the staple holding
capacities. The density of MDF panels varied the least, which generally led to a
more uniform fastener holding capacity.
• Cyclic tests of fasteners in wood-based panels showed similar results to the
corresponding static tests. For the type of cyclic loading regimes used in this study
(90 cycles at different load levels), no significant differences were observed
between static and cyclic behavior in terms of ultimate fastener holding capacity in
most cases.
200
• Generally, fasteners driven in low density zones fail at lower load levels than those
driven in high density zones. Increasing panel density will ultimately improve the
fastener holding capacity. However, reducing the variation in localized density by
producing panels with more consistent and uniform density distribution for use in
the upholstered furniture industry could be more effective and possibly more
economical for improving the fastener performance.
2 Moment capacities of OSB gusset-plate joints for upholstered furniture
• The application of glue was the most important factor affecting the performance of
the joints allowing strength increase up to 27%.
• For the tested configurations, an increase in length of gusset-plate from 102 to 203-
mm (4 to 8-in) increased the peak load for both glued and unglued joints, but
further increase of the gusset-plate length did not enhance the strength of the joints.
• Twice as many 25-mm (1.0-in) long staples had to be used to achieve similar load
levels with 38-mm (1.5-in) long staples for unglued gusset-plate joints.
• Changing positions of staples in gusset-plates did not affect the strength of the
joints of tested configurations.
• Failure modes depended on the size of the gusset-plates.
• Predicted and experimental reference resistance values for stapled joints were in
satisfactory agreement.
• The average value of 2.1 can be used as the passing static-to-fatigue ratio for design
of upholstered furniture frames with OSB gusset-plate joints. In other words, it is
advised to design gusset-plate joints so that they will not be loaded to more than 48
percent of their static moment capacity.
201
• In the stapled joints, the higher ratios were associated with the staple withdrawal as
dominating failure mode. In the glued-stapled joints lower ratios were associated
with in-plane shear, and the higher ratios – with the rupture of the OSB panels.
3 Static and fatigue bending resistance of metal-plate joints constructed of OSB for
upholstered furniture
• For the same total width of metal-plates, the use of two pairs of plates was the most
important factor that affected the performance of the joints, allowing for strength
increase up to 50% in comparison with one pair of plates.
• An increase in the width of metal-plates from 51 to 102-mm (2 to 4-in) increased
the mean ultimate load considerably for both one and two pairs of plates. In
assemblies with one pair of 152 by 152-mm (6 by 6-in) metal-plates, the mean
ultimate load was slightly lower than that for assemblies with two pairs of 51 by
152-mm (2 by 6-in) plates.
• The stiffness values for the joints with one pair of plates were lower than those for
joints with two pairs of plates. The type of failure modes observed depended on the
size and configuration of the plates. Among the tested configurations, the joint with
two pairs of 51 by 152-mm (2 by 6-in) plates was the strongest and showed the
highest stiffness.
• A static-to-fatigue ratio of 2.5 can be adopted as the passing ratio for design of
upholstered furniture frames with metal-plated joints. In other words, it is advised
to design metal-plate joints so that they will not be loaded to more than 40 percent
of their static moment capacity.
• In joints with two pairs of plates, a mixture of metal-plate yield and shear-out of
OSB was the dominant failure mode. In joints with one pair of plates, lower fatigue
life was associated with predominantly metal-plate yielding.
202
4 Static out-of-plane bending resistance of gusset-plate and metal-plate joints
constructed of OSB for upholstered furniture frames
• In general, all metal-plate and gusset-plated joints out-of-plane moment capacities
were, on average, 1/4 of the in-plane moment capacities.
• For the same width of metal-plates, the use of two pairs of plates affected
significantly the performance of the joints, allowing for strength increase up to 14%
in comparison with one pair of plates.
• An increase in the width of metal-plates from 51 by 102-mm (2 to 4-in) increased
the mean ultimate load considerably (19% and 15%) for both one pair and two pairs
of metal-plate joints.
• Assemblies with two pairs of 51 by 152-mm (2 by 6-in) metal-plates had the
highest ultimate unit load among all metal-plate configurations tested.
• The stiffness values for the joints with metal-plates demonstrated similar tendency
as the values of the ultimate load. Similar stiffness values were observed for metal-
plate joints and unglued gusset-plate joints.
• For gusset-plate joints, application of glue was the most important factor affecting
the stiffness of the joints, which allowed for stiffness increase up to 87%, but not
for the mean ultimate load of the joints.
• An increase in length of gusset-plate from 102 by 203-mm (4 to 8-in) increased the
peak load for both glued and unglued joints, but further increase of gusset-plate
length did not enhance the strength of the joints. Changing positions of staples in
gusset-plates did affect the strength of the joints of tested configurations.
• The gusset-plate joints resisted higher out-of-plane moments than the metal-plate
joints (max. 979 N (220 lbf) vs. max. 596 N (134 lbf)). It can be concluded that
metal-plates do not resist out-of-plane moment well.
203
5 Finite element model of sofa frame made of OSB
• The orientation of the components of the sofa frame has a strong impact on the
resistance.
• When the sofa frame model is under light-service acceptance level load, using
either screws with four metal-plate joints or staples with four metal-plate joints
does not change the joint displacements remarkably. Concerning the inputs in semi-
rigid joints model, 400N/mm was the minimum multi-linear elastic effective
stiffness in U1, U2 and U3 for metal-plate joint, and 10N/mm was the minimum
effective stiffness in R1, R2 and R3 for screw or staple joint.
• When the sofa frame model is under medium-service acceptance level load, the
limit screw multi-linear elastic effective stiffness in R1, R2 and R3 could be
45N/mm, and metal-plate should be fixed. In order to pass this acceptance level
load, the four critical joints on the bottom (front rail – front stump, back rail – back
post) should be reinforced (e.g., glued with corner block etc.) to create rigid
connections.
• It was found that the frame of configuration (c) could not serve the heavy-service
acceptance level load, because the bending strength of the frame material was
exceeded (34.8 vs. 26.5 N/mm2).
Recommendations for Future Work
Finite element modeling should be continued, and the experimental tests on the real-scale
sofa frame should be done for the verification and validation of the model.
For the experimental tests on joints and full-scale sofas, different types of joints should be
tested in various directions to obtain more data for modeling (e.g., face to face and face to
edge staples with glue, screws with glue; solid wood corner block glued and screwed
joints, etc.). Shear tests of joints could be included. Joints made with the use of other
materials, such as oriented strand lumber (OSL) or laminated strand lumber (LSL) could be
tested as well.
With the use of FEM, different sofa configurations should be designed and analyzed. Other
types of loading should be applied to the model, for instance, cyclic fatigue loads.
Bibliography Anonymous. 1980. MDF-Basic Properties and Performance. Furniture Industry Research
Association. FIRA Handbook No.1. APA – The Engineered Wood Association (APA). 1982. Technical Note E830A. Fastener
loads for plywood - screws. Tacoma, WA. ___________. 1993. Technical Topics. Form No. TT-051. Screw withdrawal from APA-
trademarked OSB. Tacoma, WA. ___________. 1997. Take a seat with engineered wood: wood structural panels add
strength and quality to furniture framing. American Society for Testing and Materials (ASTM). 2003a. D1037 Test methods for
evaluating properties of wood-base fiber and particle panel materials. Annual Book of ASTM Standards. West Conshohocken, PA.
___________. 2003b. D1761 Test methods for evaluating mechanical fasteners in wood.
Annual Book of ASTM Standards. ASTM, West Conshohocken, PA. ____________. 2003c. D4442. Test methods for direct moisture content measurement of
wood and wood-base materials. Annual Book of ASTM Standards. West Conshohocken, PA.
___________. 2005a. D1037-99 Test methods for evaluating properties of wood-base fiber
and particle panel materials. Annual Book of ASTM Standards. West Conshohocken, PA.
___________. 2005b. D5457-04 Standard specification for computing the reference
resistance of wood-based materials and structural connections for load and resistance factor design. Annual Book of ASTM Standards. West Conshohocken, PA.
Bao, Z, and C. A. Eckelman. 1995. Fatigue Life and Design Stresses for Wood Composites
Used In Furniture. Forest Products Journal 45 (7/8): 59-63. BIFMA-the Business and Institutional Furniture Manufacturer’s Association (BIFMA).
2001. Grand Rapids, MI. Canadian Standards Association (CSA). 2003 Rev. CAN/CSA-0325.0-92. Construction
Sheathing. Canadian Wood Council. 2005. Wood Design Manual – Canadian Standard Association
(CSA-O86). Engineered Design in Wood. Mississauga, ON, Canada.
206
Chen, B. 2003. Fatigue performance of wood-base composites as upholstered furniture frame stock. M.S. thesis. Mississippi State University, Starkville, MS, USA. 82 pp.
Chow, P., J. D. McNatt, S. J. LAmbrechts, and G. Z. Gertner. 1988. Direct withdrawal and
head pull-through performance of nails and staples in structural wood-based panel materials. Forest Prod. J. 38 (6): 19-25.
Composite Panel Association (CPA). 1999. American National Standard ANSI A208.1.
Particleboard. CPA, Gaithersburg, MD. ________________________(CPA). 2002. American National Standard ANSI A208.2.
Medium density fiberboard (MDF) for interior applications. CPA, Gaithersburg, MD.
Desroches-Noblecourt, C. 1963. Tutankhamen. New York Graphic Society, New York. Eckelman, C. A. 1967. Furniture mechanics: chair frame analysis and design. Forest Prod.
J. 17 (9): 100-106. ________. 1968. Furniture frame analysis and design. Unpublished Ph. D. thesis. Purdue
Univ., W. Lafayette, Ind. USA. 231 pp. ________. 1969. Engineering concepts of single-pin dowel joint design. Forest. Prod. J. 19
(12): 52-60. ________. 1970a. The fatigue strength of two-pin moment-resisting dowel joints. Forest
Prod. J. 20 (5):42-45. ________. 1970b. CODOFF-computer design of furniture frames-user’s manual. Purdue
Univ. Agri. Expt. Sta. Res. Bul. No.857, West Lafayette, Ind. USA. ________. 1970c. CODOFF-computer design of furniture frames-engineering concepts.
Purdue Univ. Agri. Expt. Sta. Res. Bul. No.863, West Lafayette, Ind. USA. ________. 1971a. Bending strength and moment-rotation characteristics of two-pin
moment-resisting dowel joints. Forest Prod. J. 21(3): 35-39. ________. 1971b. CODOFF-computer design of furniture frames-program documentation.
Purdue Univ. Agri. Expt. Sta. Res. Bul. No.876, West Lafayette, Ind. USA.
________. 1971c. Designing joints with gusset plates. Furniture Design and manufacturing 43(9): 72-79.
________. and M. D. Hill. 1971. Textured versus plain dowels-Which are stronger?
Furniture Design and Manufacturing, Vol. 43, No.4.
207
________. 1974. Reasonable design stresses for woods use in furniture. Purdue Univ. Agri. Expt. Sta. Res. Bul. No.916, West Lafayette, Ind. USA.
________. 1977. Evaluating the strength of library chairs and tables. Library Technology
Reports 13(4): 341-433. ________. 1978a. Strength design of furniture. Tim Tech, Inc., West Lafayette, Ind. USA.
231pp. ________. 1978b. Predicting withdrawal strength of sheet-metal-type screws in selected
hardwoods. Forest Prod. J. 28 (8): 25-28. ________. 1979. Withdrawal strength of dowel joints: Effect of shear strength. Forest
Prod. J. 29 (1): 48-52. ________, W. L. Hoover, R. W. Jokerst, and J. A. Youngquist. 1979. Utilization of red oak
press-lam as upholstered furniture frame stock. Forest Prod. J. 29 (5): 30-40. ________. 1980. The bending strength of furniture joints constructed with metal tooth
connector plates. International Journal of Furniture Research 2(1): 12-14 and 2(2): 40-42.
________, and D. Cassens. 1985. Withdrawal strength of dowels from wood composites.
Forest Prod. J. 35 (5): 55-60. ________. 1987. Bending strength, fatigue strength, stiffness, and allowable design
stresses for engineered strand lumber, oriented strand lumber plus, and engineered strand panel. A report prepared for the Weyerhauser Company. Furniture research center, Purdue Univ., West Lafayette, Ind. USA.
________. 1988a. The withdrawal strength of screws from a commerciality available
medium density fiberboard. Forest Prod. J. 38 (5): 21-24. ________. 1988b. Performance testing of furniture. Part II. A multipurpose universal
structural performance test method. Forest Prod. J. 38(4): 13-18. ________. 1989a. Strength of furniture joints constructed with through-bolts and dowel
nuts. Forest Prod. J. 39 (11/12): 41-48. ________. 1989b. Effective principles of product engineering and strength design for
furniture manufacturing. Product engineering and strength design manual presented Dec. 5-7, Grand Rapid, Michigan, USA.
________. 1991. Textbook of product engineering and strength design of furniture. Purdue
Univ., West Lafayette, Ind. USA.
208
________, and J. Zhang. 1995. Uses of the Gerneral Service Administration performance test method for upholstered furniture in the engineering of upholstered furniture frames. Holz als Roh-und Werkstoff 53: 261-267.
________. 1998. Holding strength of T-nuts in solid wood and wood composites. Holz als
Roh-und Werkstoff 56(1998):253-258. ________, and Y. Z. Erdil. 1998. Joint design manual for furniture frames constructed of
plywood and oriented strand board. 33 pp. ________, Y. Z. Erdil and J. Zhang. 2002. Withdrawal and bending strength of dowel
joints constructed of plywood and oriented strand board. Forest Prod. J. 52 (9): 66-74.
EN 1995-1-1: 2004 (E). 2004. Eurocode 5: Design of timber structures. European
Committee for Standardization (CEN), Brussels, Belgium. Erdil, Y. Z. 1998. Strength analysis and design of joints of furniture frames constructed of
plywood and oriented strand board. M. S. thesis. Purdue Univ., W. Lafayette, Ind. USA. 145 pp.
________, J. Zhang, and C. A. Eckelman. 2002. Holding strength of screws in plywood
and oriented strand board. Forest Prod. J. 52 (6): 55-62. ________, J. Zhang, and C. A. Eckelman. 2003a. Staple holding strength of furniture frame
joints constructed of plywood and oriented strand board. Forest Prod. J. 53 (1): 70-75.
________, J. Zhang and C. A. Eckelman. 2003b. Withdrawal and bending strength of
dowel-nuts in plywood and oriented strand board. Forest Prod. J. 53 (6): 54-57. Fakopp Enterprise. 2005. Screw withdrawal force meter. www.fakopp.com. Gebremedhin, K. G., M. C. Jorgensen, and C. B. Woelfel. 1992. Load-slip characteristics
of metal plate connected wood joints tested in tension and shear. Wood and Fiber Sciences, 24(2), 1992, pp. 118-132.
General Service Administration (GSA). 1998. Upholstered furniture test method. FNAE-
80-214A. Furniture Commodity Center, Federal Supply Services, Washington, D.C.
Geschwindner, L. F., R.O. Disque, and R. Bjorhovde. 1994. Load and resistance factor
design of steel structures. Prentice-Hall, Inc. Englewood Cliffs, N. J. USA. 456pp. Hayashi, T., H. Sasaki, and M. Masuda. 1980. Fatigue properties of wood butt joints with
metal plate connectors. Forest Prod. J. 30(20: 49-54.
209
Hill, M. D. and C. A. Eckelman. 1973. Flexibility and bending strength of mortise and tenon joints. Furniture design and manufacturing, Vol. 45, No.1 and 2. Journal # 4758.
Johansen, K. W. 1949. Theory of timber connections. International Association for Bridge
and Structural Engineering, 9: 249-262. Johnson, J. W. 1967. Screw-holding ability of particleboard and plywood. Oregon State
School of Forestry. Forest Resources Lab. Rep. T-22. Moura, J. D. D. M., C. Bastian, G. Duchanois, J. M. Leban, and P. Triboulot. 1995. The
influence of wood density on metal-plate connector mechanical behavior under cyclic loading. Forest. Prod. J. 45(11/12): 74-82.
Picado, F. 1988. Development of an expert system for upholstered furniture. Unpublished
M. S. thesis. Purdue Univ., West Lafayette, Ind. USA. 166pp. Rajak, Z. I. B. H. A., and C. A. Eckelman. 1993. Edge and face withdrawal strength of
large screws in particleboard and medium density fiberboard. Forest Prod. J. 43(4):25-30.
Resource Information Systems, Inc. (RISI). 2004. North American Wood Panels Forecast.
Volume 4, Number 1. Rosowsky, D. V. and M. O. Hunt. 1995. Increasing the competitiveness of structural wood
composites using probabilistic methods. Forest Prod. J. 45 (11/12): 83-86. Sackey, E., K. Semple, H. Park, and G. Smith. 2005. Properties survey of furniture grade
particleboard Part 1- Variation within M2 grade and a reassessment of the relationships between density, bond strength, and screw withdrawal resistance. Forest Products Society 59th international convention, June 19-22, 2005. Quebec city, Quebec, Canada.
Salmon, C. S. and J. E. Johnson.1990. Steel structures. 3rd ed. Harper Collins Publ. Inc.
New York, N. Y. USA. 1086 pp. SAP 2000. Structural Analysis Program. Computers and Structures., Inc. 1995 University
Ave., Berkeley, CA 94704, USA Website: csiberkeley.com Semple K., E. Sackey, H. Park, and G. Smith. 2005. Properties survey of furniture grade
particleboard Part 2- MS and M2 grade comparison and a practical in-situ test for internal bond strength. Forest Products Society 59th international convention, June 19-22, 2005. Quebec city, Quebec, Canada.
Structural Board Association (SBA). 2004. OSB expending beyond commodity sheathing
applications. http://www.osbguide.com/pdf_news/SBA-0407newsrelease.pdf
210
Tabarasi, E. 2002. Suitability of Oriented Strand Board for Upholstered Furniture: Market Analysis. Forintek Canada Corp. report No. 3251.
Tackett, B. and J. Zhang, 2007. A biaxial load cell design for simultaneous measurement of
horizontal and vertical spring forces in sinuous spring-supported seating. Journal of Testing and Evaluation, Vol. 35, No. 4 Paper ID JTE100112. Available online at: www.astm.org
Wang, S. and R. M. Knudson. 2002. Suitability of oriented strand board for upholstered
furniture technical analysis. Forintek report No. 3251. Canadian forest service value-added report . 64pp.
Wang, X., A. Salenikovich, and M. Mohammad. 2007a. Localized density effects on
fastener holding capacities in wood-based panels. Forest Prod. J. 57(1/2): 103-109. ________, A. Salenikovich, M. Mohammad, C. Echavarria, and J. Zhang. 2007b. Moment
capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1. Static Load. Forest Prod. J. 57(7/8): 39-45.
________, A. Salenikovich, M. Mohammad, and J. Zhang. 2007c. Moment capacity of
oriented strandboard gusset-plate joints for upholstered furniture. Part 2. Fatigue Load. Forest Prod. J. 57(7/8): 46-50.
________, M. Mohammad, A. Salenikovich, R. Knudson, and J. Zhang. 2007d. Static
bending strength of metal-plate joints constructed of oriented strandboard for upholstered furniture frames. Submitted to Forest Prod. J. February 2007.
________, M. Mohammad, A. Salenikovich, R. Knudson, and J. Zhang. 2007e. Fatigue
bending strength of metal-plate joints constructed of oriented strandboard for upholstered furniture frames. Accepted by Forest Prod. J. February 2007.
Williams, D. and R. Nielson. 1999. Machining and fastener withdrawal tests of MDF, OSB
and Plywood. Forintek report No. W-1882, 12 pp. Wood Handbook, 1999: wood as an engineering material, Forest products Laboratory.
Department of Agriculture, Forest Service. Madison, WI. 463p. Zhang, J. 1995. Structural analysis and design of sofa front rail. Unpublished Ph. D. thesis.
Purdue Univ., W. Lafayette, Ind. USA. 156 pp. ________. 2000. Research provides solutions for upholstered seating frame failures.
Modern Woodworking Magazine. 14(6): 33-36. ________, F. Quin, and B. Tackett. 2001a. Bending fatigue life of two-pin dowel joints
constructed of wood and wood composites. Forest Prod. J. 51 (10): 73-78.
211
________, D. Lyon, F. Quin, and B. Tackett. 2001b. Bending strength of gusset-plate joints constructed of wood composites. Forest Prod. J. 51(5): 40-44.
________,Y. Z. Erdil, and C. A. Eckelman. 2002a. Lateral holding strength of dowel joints
constructed of plywood and oriented strand board. Forest Prod. J. 52 (7/8): 83-89. ________, Y. Z. Erdil, and C. A. Eckelman. 2002b. Torsional strength of dowel joints
constructed of plywood and oriented strand board. Forest Prod. J. 52 (10): 89-94. ________, F. Quin, and B. Tackett. 2002c. Direct withdrawal strength of multi-staple joints
in pine plywood. Forest Prod. J. 52 (5): 61-66. ________, F. Quin, B. Tackett, and S. Park. 2002d. Direct withdrawal strength of single-
staple joints in pine plywood. Forest Prod. J. 52 (2): 86-91. ________, V. Yadama, and F. Quin. 2002e. Resistance of southern yellow pine to direct
withdrawal of staples. Forest Prod. J. 52 (9): 75-81. ________, G. Li, and T. Jr. 2003. Bending fatigue life of two-pin dowel joints in furniture
grade pine plywood. Forest Prod. J. 53 (6): 1-7. ________, and M. Maupin. 2004. Face lateral and withdrawal resistances of staple joints in
furniture-grade pine plywood. Forest Prod. J. 54(6): 40-46. ________, Y. Yu, and F. Quin. 2005. Moment capacity of metal-plate-connected joints in
furniture grade pine plywood. Forest Prod. J. 55(5): 45-51. ________, Y. Yu, and F. Quin. 2006. Bending fatigue life of metal-plate-connected joints
in furniture-grade pine plywood. Forest Prod. J. 56(11/12): 62-66.
APPENDIX I Visiting Several Upholstered Furniture
Companies
213
I.1 Objective of the Visit We visited upholstered furniture companies in order to understand the context of this
segment of the furniture industry and to see what are the industry issues of concerns
relating to the usage of OSB for framing material and whether it is possible to work
together to improve frame designs.
I.1.1 Berkline Upholstered Furniture
I.1.1.1 Profile
Berkline (Canada) is a branch of Berkline Furniture, a Moorestown, Tennessee, U.S. based
company. The Canadian branch has over 150 employees in Montréal. We observed that
Berkline (Canada) is a small traditional furniture company doing a lot of manual work.
Their total production in one year is equal to a week’s production at the company’s main
site in the United States.
Berkline (Canada) produces mainly recliners for one, two or three persons. The company
uses solid wood, plywood, OSB, particle board, MDF and combinations of these.
I.1.1.2 Design
New designs are usually not made by Berkline (Canada). If there is a new design, its
mechanical performance has to be tested in the head office in the U.S.
I.1.1.3 Material A combination of solid wood with all kinds of wood based panels is being used. The focus
is on plywood, however.
(1) Solid Wood Berkline (Canada) does not use panel products for the front and back rails, but soft or hard
wood depending on the model and shape. The three person sofa, for instance, uses 3” (76
mm) hardwood.
214
(2) Plywood Two types of plywood are used for the backs and seat frames.
a) Russian Plywood Berkline (Canada) used to rely on poplar plywood. After many call-backs due to broken
legs, the company switched to Russian birch plywood, No.1 or No.2, 1525 x 1525, 13
plies, 5/8” (16 mm) thickness. The company appreciates the high quality of the plywood,
and assures that it hardly has any problems with it.
b) SYP Plywood Apart from Russian birch plywood, Southern Yellow Pine plywood mixed with other hard
woods imported from the United States is also used. That plywood being used by Berkline
(Canada) is made of SYP for the exterior plies, while the interior is mostly made of yellow
poplar. More precisely, SYP is used for the front rail base of the sofas. It is 2” (51 mm)
thick. The back seat bases use plywood with clips on it, for back frames solid wood is
mixed with plywood.
(3) OSB OSB is only used for less structurally critical sections. The OSB used by Berkline (Canada)
is sources from Goodfellow, it is of the No. 1 Common sheathing panel grade, which is not
specially produced for furniture. Grade 1 has a uniform thickness of 3/8” (16 mm) for front
and 7/16” (11 mm) for back rails, while grade 2 has a high variation of thickness and
density.
The major problem of the company associated with OSB use is the splitting due to
fastening on edge. If there is too much glue inside the OSB, there can also be a problem
with staples bending. Moreover cutting OSB results in a considerable wear and tear on
saws and knives compared to plywood or solid wood.
(4) Particle Board
215
Berkline (Canada) uses particle board mainly for less structurally demanding parts,
particularly to make foot and arm rests. Since particle board is not expensive and not too
heavy (i.e. we have to think of the whole seat for the balance of a rocking mechanism),
MDF with its weight is often inappropriate.
The company staples on the face and edge of the particle board, without any signs of
splitting. A bending test of 60 lbf (27 kg) is done for typical particle board while 45 lbf (20
kg) is used to test lower grades.
(5) MDF MDF used by Berkline is made by Uniboard and is preferred due to its weight and its light
colour. Berkline (Canada) uses a combination of MDF and plywood for arm rails,
connected with staples. For a three person sofa, the middle seat is made of MDF because it
does not move. It is painted in black to make it invisible for the customer.
I.1.1.4 Joints Staples are the main type of fastener used in jointing the main frame members together
since they can be inserted quickly. Apart from staples, screws, dowels, t-nut, toothed metal
connector plates and a kind of tenon-mortise are used as well.
(1) Staples Berkline (Canada) uses standard staples grade 19 from SENCO with 1 ¾” (44 mm) legs
and 1 ½” (38 mm) crown. Most staples are inserted with glue, however some are used in a
combination with metal gang nail plates.
(2) Dowels Birch dowels are used for solid wood and solid wood and plywood connections. Some
wood dowels are also used for crossing and rocking sections. Solid wood dowels are being
used on solid wood 5/4 front rails.
(3) Screws
216
Screws manufactured by Robertson, are mainly used to reinforce certain glued joints in
some models. Nails are not used.
(4) Glue Berkline (Canada) uses Woodlok 40-0304 PVA (Polymer Vinyl Acetate) glue produced by
NACAN Ltd.
(5) Clips Clips made by Sigmatools Manufactory, Toronto, are used to attach springs for backs and
seats.
I.1.1.5 Testing
Mechanical tests are not conducted in the Canadian branch of the company. There are,
however, occasional drop tests, in which a sofa with a box is dropped from a height of 8
feet (2.44 m).
I.1.1.6 Recalls
With the poplar plywood previously used, leg joints often broke. Since the company has
switched to Russian plywood, broken leg joints have become very rare. Sometimes metal
plates are broken, though.
I.1.1.7 Possibility of switching to OSB instead of plywood The major problem with OSB at Berkline (Canada) is splitting once fasteners (i.e. staples,
screws) are driven in the panel edge. If there is too much glue inside, OSB staples can also
be bent due to the rigidity of the resin. Moreover, OSB cutting increases the wear and tear
on saws and knives. With wood material, the company saws 2000 to 3000 linear feet
without replacing the saw blade, while with OSB, after 400 feet, it has to be changed.
Cooperating with this small traditional furniture company with the aim of replacing the
materials used is difficult. My thought on this is that working with this company might be
easier but the benefit and impact on industry would be very limited because this company
217
is a tiny subsidiary of a large American company. Hence the technology transfer potential
of our work with it would be very limited. Plus, since they use many materials already, the
improvements we could have would be only incremental (marginal). They already use
OSB to a limited extent and all they could do is use a little more of it. The impact of our
work in such context would be limited.
Contact:
Luc Fernandez
Directeur d’usine
Berkline inc.
8491 Ernest Cormier, Ville d’Anjou, Qc, H1J 1B5
I.1.2 Elran Upholstered Furniture
I.1.2.1 Profile Elran has been in the upholstery furniture business for about 36 years. Since 1988 they
have used a 250,000 square feet (2.3 hectares) building located in Pointe Claire, Montréal.
It has 750 employees and 12 production lines. Our observation is that Elran is a quite large,
modern and efficient furniture company.
Elran produces mainly (90%) recliners for one (lazy boy), two (love seats) or three (sofa)
persons. They are the 7th biggest recliner company in the world and the leader in Canada in
their category. Recliners hold 20% of the upholstered furniture market in North-America.
They produce 135,000 pieces/year (with an average of 2.2 seats per piece). More than 50%
of the production is made of leather and the rest in other types of fabric. Their products are
exported to Europe, the USA, Israel, Japan and other countries. 20-25% of the exports go
to the United States.
I.1.2.2 Design There are currently 15 people working in the research and development department of the
company. They do create new designs, but most products are based on standard frames.
218
Backs and seats are all standardized, using the same frame concept design for all models.
The core of recliners is hence standardized and hundreds of options can be added to the
basic design to produce customized styles. The standard frame components are produced
on a continuous basis on stock while the custom options are produced on a Kanban basis.
I.1.2.3 Material They use plywood for most parts and timberstrand for a limited number of more
mechanically demanding applications. Particle board and OSB are sometimes used but to a
much lesser extent and mainly for non-structural or less structurally demanding parts.
(1) Timberstrand Elran uses Timberstrand for front and back rails with 7/8” (22 mm) thickness.
Timberstrand is not only 30% cheaper than solid wood, but it is also stronger than
plywood. Elran receives pre-cut pieces of Timberstrand from Weyerhaeuser with the
appropriate section. Thus Elran does not need machinery to cut the pieces for themselves
and there is no waste. Spring clips are inserted in the edges of the Timberstrand. There are
five springs on the seat frame with a 40 lbf (18 kg) load on each spring, totalling 200 lbf
(91 kg) in tension and the load of the people sitting on the furniture.
(2) Plywood Elran has used plywood for 25 years. The material is used for most frame parts. The
plywood is poplar plus pine or spruce with 6 or 5 plies, ¾” (19 mm) thick, of construction
sheathing grade, provided by Weyerhaeuser and Slocan, two domestic plywood
manufacturers not specialized on furniture.
(3) Particle Boards Elran uses particleboard mainly for less structurally demanding parts such as footrests,
because particleboard is cheap and not very heavy. MDF would be too heavy to get a
balance in the rocking mechanism. The company also uses particleboard for the drawer
underneath the central seat of 3-pieces sofa.
219
(4) OSB OSB is only used for reinforcing the sides since it is cut in one piece rather than having a
joint.
I.1.2.4 Joints Most connections are staples with glue, which does not take a long time. Screws and
dowels are also used for certain parts.
(1) Staples Staples and glue are their main material for joints. Those are mainly standard crown
galvanized ½ inch staples. Bigger staples are used to produce strong joints for certain
structurally demanding areas.
(2) Wood dowels Wood dowels are only used for the drawer underneath the middle seat of the sofa. Those
are mainly made of hardwoods (i.e. Birch) and have a spiral profile.
(3) Screws Screws—made by Robertson—are used additionally in critical places where twist is
significant.
(4) T-nuts T-nuts are being used for locations where extra connection strength is required, especially
to fix the seat to the mechanism frame. T-nuts are supplied by Sigma Tool
(www.sigmatool.com).
(5) Glue The type of glue used is Dural CL. 3132 G-2672.
(6) Clips
220
Clips are used to attach springs for backs and seats. The teeth of the clips are staggered to
avoid splitting of timber-strand.
I.1.2.5 Production lines
Elran has automated production lines with a Taylor CNC band saw, which has a 102°
rotation angle cutting 17 boards at same time. This method is very fast. In fact it has been
optimized, using up to 90% wood and only 10% waste. Elran is one out of only two or
three companies in Canada that run such CNC bandsaw. Such a machine costs about half a
million dollars, but its high efficiency makes it profitable, it allows the same throughput as
was achieved prior to its acquisition, with 12 less people.
Elran has 12 production lines with automated assembly machines to staple and apply glue
automatically. The T-nuts inserted by the machine are made by Sigma Tool, Toronto.
Some of the production lines are dedicated to the backs and seats of sofas. Two shifts are
operated every day.
I.1.2.6 Testing
Mechanical testing is not carried out at the company, but by the distributors and customers,
though there are occasional human test with people jumping up and down on the furniture.
I.1.2.7 Recalls The total annual revenue of the company is 100 million dollars with 1–1.5% recalls. The
main areas where recall occurs are (in decreasing order of frequency): leather and fabric,
mechanism, foam and wood frame structure. There are very few recalls related to the
structural frames.
I.1.2.8 Possibility to Change all Material to OSB
When asked about the potential change from plywood and Timber-strand to OSB, the R&D
manager replied that plywood is currently cheaper than OSB, but the company would
consider changing to OSB if its price decreased. However, Elran management does not
221
believe all seats and sofa parts could be made of OSB. They think only parts where the
fastener can be applied on a face is suitable to use OSB. They think everywhere a fastener
would have to be applied on edge, OSB would not be suitable.
On the other hand, it would be difficult for the company to envisage using two main
materials (plywood and OSB). This is due to the use of a Taylor CNC bandsaw, which
works more efficiently if all components are made of the same material. Using OSB and
plywood would increase the sawing time and significantly decrease the output. OSB is
currently used only to reinforce the sides because it is cut in one piece without joints.
The company has two main concerns regarding the reliability of OSB in critical places
such as side rails, especially at the location of attachment to the reclining mechanism:
(1) OSB can not carry as much load as plywood;
(2) Fasteners in OSB edges (staples and screws) are weak points.
With improved mechanical properties of OSB (fastener retention, end splitting, consistency
of thickness as well as structural resistance) or through appropriate design, the company
would consider using OSB in upholstery furniture frames, provided its cost would go down
again. Their aim is to save on costs as well as ensuring the required dynamic performance
of the frames.
We asked Elran to send us a sofa frame out of their real production in order to make some
mechanical tests in our laboratory. We also asked the company to make a sofa frame
entirely of OSB, so we can execute the same test twice, checking whether the whole sofa
could be made of OSB.
Contacts:
Yvan Tremblay
Directeur R&D
Elran, 2751 route Transcanadienne
Pointe-Claire, Qc, H9R 1B4
Marie-Claude Desjardins (graduate from UdeM in Industrial design)
APPENDIX II Tables in finite element modelling
224
Table II-1: Rotation-Moment of Metal-plate connectors
Rotation (rad.) Moment (N-mm)Rotation (rad.) Moment (N-mm)-0.0368 -5.19E+05 -2.30E-01 -1.77E+05-0.0122 -1.22E+06 -2.23E-01 -1.80E+05-0.0118 -1.22E+06 -2.08E-01 -1.87E+05
-9.86E-03 -1.15E+06 -2.07E-01 -1.86E+05-7.95E-03 -1.09E+06 -1.92E-01 -1.98E+05-6.56E-03 -1.02E+06 -1.77E-01 -2.02E+05-5.44E-03 -9.44E+05 -1.62E-01 -2.06E+05-4.44E-03 -8.72E+05 -1.48E-01 -2.10E+05-3.67E-03 -7.98E+05 -1.43E-01 -2.08E+05-3.18E-03 -7.27E+05 -1.28E-01 -2.08E+05-2.75E-03 -6.61E+05 -1.14E-01 -2.03E+05-2.37E-03 -5.90E+05 -1.00E-01 -1.97E+05-1.91E-03 -4.89E+05 -8.69E-02 -1.87E+05-1.51E-03 -4.20E+05 -7.35E-02 -1.78E+05-1.14E-03 -3.33E+05 -6.13E-02 -1.63E+05-7.89E-04 -2.50E+05 -4.95E-02 -1.43E+05-5.52E-04 -1.74E+05 -3.85E-02 -1.22E+05-3.36E-04 -1.11E+05 -2.79E-02 -9.92E+04-1.84E-04 -64378.8 -0.0177 -72129.5-8.07E-05 -34324.8 -8.43E-03 -47770-2.69E-05 -16292.41 -8.90E-04 -21670.490.00E+00 0 0.00E+00 02.69E-05 16292.414 8.90E-04 21670.4928.07E-05 34324.79 8.43E-03 47769.991.84E-04 64378.76 1.77E-02 72129.523.36E-04 110566.96 2.79E-02 99178.095.52E-04 173522.12 0.0385 122114.017.89E-04 2.50E+05 4.95E-02 143468.151.14E-03 3.33E+05 6.13E-02 162765.961.51E-03 4.20E+05 7.35E-02 1.78E+051.91E-03 4.89E+05 8.69E-02 1.87E+052.37E-03 5.90E+05 1.00E-01 1.97E+052.75E-03 6.61E+05 1.14E-01 2.03E+053.18E-03 7.27E+05 1.28E-01 2.08E+053.67E-03 7.98E+05 1.43E-01 2.08E+054.44E-03 8.72E+05 1.48E-01 2.10E+055.44E-03 9.44E+05 1.62E-01 2.06E+056.56E-03 1.02E+06 1.77E-01 2.02E+057.95E-03 1.09E+06 1.92E-01 1.98E+059.86E-03 1.15E+06 2.07E-01 1.86E+051.18E-02 1.22E+06 2.08E-01 1.87E+051.22E-02 1.22E+06 2.23E-01 1.80E+05
0.0368 5.19E+05 2.30E-01 1.77E+05
In-plane Out-of-plane
225
T
able
II -
2. E
lem
ent f
orce
s –fr
ames
for
conf
igur
atio
n (a
) sof
a fr
ame
226
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CaseT
yP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xtm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
21
0Po
inLin
St27
7.05
-161
0-7
96.5
1189
.97
-983
27.8
-479
337
220
152
18-6
.781
43-1
1.61
023
-18.
3917
-0.4
2931
9-0
.868
001
0.1
0.07
8059
946
110
2Po
inLin
St27
7.05
-161
0-7
96.5
1189
.97
-173
89-3
1569
422
101.
615
218
-4.4
6629
2-2
.053
236
-6.5
1953
-0.4
2931
9-0
.868
001
0.1
0.07
8059
946
110
2Po
inLin
St27
7.05
-147
7-5
25.1
1189
.97
-173
89-3
1569
422
101.
615
218
-4.4
6629
2-2
.053
236
-6.5
1953
-0.2
8306
1-0
.796
074
0.1
0.07
8059
946
120
3Po
inLin
St27
7.05
-147
7-5
25.1
1189
.97
3594
4-1
6570
322
203.
215
218
-2.3
4428
14.
2441
541.
8998
73-0
.283
061
-0.7
9607
40.
10.
0780
5994
61
203
PoinL
inSt
277.
05-1
210
-187
.111
89.9
735
944
-165
703
2220
3.2
152
18-2
.344
281
4.24
4154
1.89
9873
-0.1
0084
-0.6
5221
0.1
0.07
8059
946
130
5Po
inLin
St27
7.05
-121
0-1
87.1
1189
.97
5495
4.7
-427
42.7
2230
4.8
152
18-0
.604
703
6.48
8881
5.88
4178
-0.1
0084
-0.6
5221
0.1
0.07
8059
946
130
5Po
inLin
St27
7.05
-920
.917
3.2
1189
.97
5495
4.7
-427
42.7
2230
4.8
152
18-0
.604
703
6.48
8881
5.88
4178
0.09
3375
-0.4
9636
30.
10.
0780
5994
61
406
PoinL
inSt
277.
05-9
20.9
173.
211
89.9
737
354.
650
816.
6122
406.
415
218
0.71
8929
4.41
071
5.12
9639
0.09
3375
-0.4
9636
30.
10.
0780
5994
61
406
PoinL
inSt
277.
05-6
5451
1.3
1189
.97
3735
4.6
5081
6.61
2240
6.4
152
180.
7189
294.
4107
15.
1296
390.
2755
96-0
.352
503
0.1
0.07
8059
946
150
8Po
inLin
St27
7.05
-654
511.
311
89.9
7-1
4593
1172
59.5
2250
815
218
1.65
8932
-1.7
2309
3-0
.064
160.
2755
96-0
.352
503
0.1
0.07
8059
946
150
8Po
inLin
St27
7.05
-520
.578
2.6
1189
.97
-145
9311
7259
.522
508
152
181.
6589
32-1
.723
093
-0.0
6416
0.42
1859
-0.2
8057
10.
10.
0780
5994
61
610
PoinL
inSt
277.
05-5
20.5
782.
611
89.9
7-9
4108
.817
0144
.222
609.
615
218
2.40
712
-11.
1120
7-8
.704
950.
4218
59-0
.280
571
0.1
0.07
8059
946
20
PoinL
inSt
272.
21-5
44.9
-789
.6-0
.058
8-9
6221
.511
5325
230
152
181.
6315
64-1
1.36
153
-9.7
2997
-0.4
2558
4-0
.293
718
0.09
8-3
.859
14E-
062
102
PoinL
inSt
272.
21-5
44.9
-789
.6-0
.058
8-1
6002
.817
0688
2310
1.6
152
182.
4148
13-1
.889
555
0.52
5258
-0.4
2558
4-0
.293
718
0.09
8-3
.859
14E-
062
102
PoinL
inSt
272.
21-4
11.5
-518
.2-0
.058
8-1
6002
.817
0688
2310
1.6
152
182.
4148
13-1
.889
555
0.52
5258
-0.2
7932
6-0
.221
785
0.09
8-3
.859
14E-
062
203
PoinL
inSt
272.
21-4
11.5
-518
.2-0
.058
836
647.
721
2492
.823
203.
215
218
3.00
6248
4.32
7244
7.33
3491
-0.2
7932
6-0
.221
785
0.09
8-3
.859
14E-
062
203
PoinL
inSt
272.
21-1
44.6
-180
.2-0
.058
836
647.
721
2492
.823
203.
215
218
3.00
6248
4.32
7244
7.33
3491
-0.0
9710
5-0
.077
926
0.09
8-3
.859
14E-
062
305
PoinL
inSt
272.
21-1
44.6
-180
.2-0
.058
854
950.
822
7181
.223
304.
815
218
3.21
4053
6.48
8411
9.70
2464
-0.0
9710
5-0
.077
926
0.09
8-3
.859
14E-
062
305
PoinL
inSt
272.
2114
4.56
180.
2-0
.058
854
950.
822
7181
.223
304.
815
218
3.21
4053
6.48
8411
9.70
2464
0.09
711
0.07
7921
0.09
8-3
.859
14E-
062
406
Poi nL
inSt
272.
2114
4.56
180.
2-0
.058
836
646.
721
2493
.623
406.
415
218
3.00
6259
4.32
7129
7.33
3388
0.09
711
0.07
7921
0.09
8-3
.859
14E-
062
406
PoinL
inSt
272.
2141
1.46
518.
2-0
.058
836
653.
621
2493
.623
406.
415
218
3.00
6259
4.32
794
7.33
4199
0.27
9331
0.22
1785
0.09
8-3
.859
14E-
062
508
PoinL
inSt
272.
2141
1.46
518.
2-0
.058
8-1
5997
.817
0689
.623
508
152
182.
4148
36-1
.888
973
0.52
5863
0.27
9331
0.22
1785
0.09
8-3
.859
14E-
062
508
PoinL
inSt
272.
2154
4.9
789.
6-0
.058
8-1
6003
.317
0689
.623
508
152
182.
4148
36-1
.889
624
0.52
5212
0.42
5589
0.29
3712
0.09
8-3
.859
14E-
062
610
PoinL
inSt
272.
2154
4.9
789.
6-0
.058
8-9
6223
.111
5327
.523
609.
615
218
1.63
1598
-11.
3617
2-9
.730
120.
4255
890.
2937
120.
098
-3.8
5914
E-06
30
PoinL
inSt
277.
0552
0.52
-782
.7-1
189.
9-9
4111
.217
0146
.524
015
218
2.40
7152
-11.
1123
5-8
.705
2-0
.421
865
0.28
0571
0.1
-0.0
7805
6666
310
2Po
inLin
St27
7.05
520.
52-7
82.7
-118
9.9
-145
78.2
1172
5124
101.
615
218
1.65
8812
-1.7
2134
9-0
.062
54-0
.421
865
0.28
0571
0.1
-0.0
7805
6666
310
2Po
inLin
St27
7.05
653.
97-5
11.3
-118
9.9
-145
78.2
1172
48.3
2410
1.6
152
181.
6587
73-1
.721
349
-0.0
6258
-0.2
7560
70.
3525
030.
1-0
.078
0566
663
203
PoinL
inSt
277.
0565
3.97
-511
.3-1
189.
937
349.
850
831.
7924
203.
215
218
0.71
9144
4.41
0148
5.12
9292
-0.2
7560
70.
3525
030.
1-0
.078
0566
663
203
PoinL
inSt
277.
0592
0.86
-173
.2-1
189.
937
349.
850
837.
2124
203.
215
218
0.71
9221
4.41
0148
5.12
9369
-0.0
9338
0.49
6363
0.1
-0.0
7805
6666
330
5Po
inLin
St27
7.05
920.
86-1
73.2
-118
9.9
5495
4.7
-427
40.9
2430
4.8
152
18-0
.604
678
6.48
8881
5.88
4203
-0.0
9338
0.49
6363
0.1
-0.0
7805
6666
330
5Po
inLin
St27
7.05
1210
187.
1-1
189.
954
954.
7-4
2740
.924
304.
815
218
-0.6
0467
86.
4888
815.
8842
030.
1008
290.
6522
10.
1-0
.078
0566
663
406
PoinL
inSt
277.
0512
1018
7.1
-118
9.9
3594
9.1
-165
676
2440
6.4
152
18-2
.343
912
4.24
475
1.90
0839
0.10
0829
0.65
221
0.1
-0.0
7805
6666
340
6Po
inLin
St27
7.05
1476
.952
5.1
-118
9.9
3594
9.1
-165
676
2440
6.4
152
18-2
.343
912
4.24
475
1.90
0839
0.28
3056
0.79
6074
0.1
-0.0
7805
6666
350
8Po
inLin
St27
7.05
1476
.952
5.1
-118
9.9
-174
04-3
1572
824
508
152
18-4
.466
774
-2.0
5501
3-6
.521
790.
2830
560.
7960
740.
1-0
.078
0566
663
508
PoinL
inSt
277.
0516
10.3
796.
5-1
189.
9-1
7404
-315
728
2450
815
218
-4.4
6677
4-2
.055
013
-6.5
2179
0.42
9314
0.86
8001
0.1
-0.0
7805
6666
361
0Po
inLin
St27
7.05
1610
.379
6.5
-118
9.9
-983
25.4
-479
338
2460
9.6
152
18-6
.781
452
-11.
6099
5-1
8.39
140.
4293
140.
8680
010.
1-0
.078
0566
664
0Po
inLin
St-1
89.7
-118
578
2.2
758.
8593
953.
3-2
6594
725
015
218
-3.7
6249
411
.093
717.
3312
190.
4216
38-0
.638
729
-0.0
70.
0497
7923
410
2Po
inLin
St-1
89.7
-118
578
2.2
758.
8514
463
-145
529
2510
1.6
152
18-2
.058
872
1.70
7749
-0.3
5112
0.42
1638
-0.6
3872
9-0
.07
0.04
9779
234
102
PoinL
inSt
-189
.7-1
052
510.
975
8.85
1446
3-1
4553
125
101.
615
218
-2.0
5891
11.
7077
49-0
.351
160.
2753
8-0
.566
802
-0.0
70.
0497
7923
420
3Po
inLin
St-1
89.7
-105
251
0.9
758.
85-3
7422
.3-3
8738
.225
203.
215
218
-0.5
4804
9-4
.418
709
-4.9
6676
0.27
538
-0.5
6680
2-0
.07
0.04
9779
234
203
PoinL
inSt
-189
.7-7
84.6
172.
875
8.85
-374
22.3
-387
32.8
2520
3.2
152
18-0
.547
973
-4.4
1870
9-4
.966
680.
0931
54-0
.422
937
-0.0
70.
0497
7923
430
5Po
inLin
St-1
89.7
-784
.617
2.8
758.
85-5
4984
.641
002.
8925
304.
815
218
0.58
009
-6.4
9240
3-5
.912
310.
0931
54-0
.422
937
-0.0
70.
0497
7923
430
5Po
inLin
St-1
89.7
-495
.5-1
87.5
758.
85-5
4984
.641
002.
8925
304.
815
218
0.58
009
-6.4
9240
3-5
.912
31-0
.101
056
-0.2
6709
-0.0
70.
0497
7923
440
6Po
inLin
St-1
89.7
-495
.5-1
87.5
758.
85-3
5936
.291
346.
5225
406.
415
218
1.29
2327
-4.2
4323
2-2
.950
9-0
.101
056
-0.2
6709
-0.0
70.
0497
7923
440
6Po
inLin
St-1
89.7
-228
.6-5
25.6
758.
85-3
5936
.291
346.
5225
406.
415
218
1.29
2327
-4.2
4323
2-2
.950
9-0
.283
282
-0.1
2322
6-0
.07
0.04
9779
234
508
PoinL
inSt
-189
.7-2
28.6
-525
.675
8.85
1745
9.6
1145
73.8
2550
815
218
1.62
0936
2.06
1571
3.68
2507
-0.2
8328
2-0
.123
226
-0.0
70.
0497
7923
227
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CaseT
yP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xtm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
24
508
PoinL
inSt
-189
.7-9
5.17
-796
.975
8.85
1745
9.6
1145
73.8
2550
815
218
1.62
0936
2.06
1571
3.68
2507
-0.4
2954
-0.0
5129
9-0
.07
0.04
9779
234
610
Poi nL
inSt
-189
.7-9
5.17
-796
.975
8.85
9842
3.6
1242
42.9
2560
9.6
152
181.
7577
311
.621
5513
.379
28-0
.429
54-0
.051
299
-0.0
70.
0497
7923
50
Poi nL
inSt
379.
4-5
44.9
789.
60.
1396
230.
7-6
5008
260
152
18-0
.919
703
11.3
6262
10.4
4291
0.42
5589
-0.2
9371
20.
136
8.52
777E
-06
510
2Po
i nLin
St37
9.4
-544
.978
9.6
0.13
1601
1-9
645.
9826
101.
615
218
-0.1
3646
71.
8905
251.
7540
580.
4255
89-0
.293
712
0.13
68.
5277
7E-0
65
102
Poi nL
inSt
379.
4-4
11.5
518.
20.
1316
005.
5-9
645.
9826
101.
615
218
-0.1
3646
71.
8898
741.
7534
070.
2793
31-0
.221
785
0.13
68.
5277
7E-0
65
203
Poi nL
inSt
379.
4-4
11.5
518.
20.
13-3
6646
3215
7.9
2620
3.2
152
180.
4549
55-4
.327
039
-3.8
7208
0.27
9331
-0.2
2178
50.
136
8.52
777E
-06
520
3Po
i nLin
St37
9.4
-144
.618
0.2
0.13
-366
39.1
3215
7.9
2620
3.2
152
180.
4549
55-4
.326
228
-3.8
7127
0.09
711
-0.0
7792
10.
136
8.52
777E
-06
530
5Po
i nLin
St37
9.4
-144
.618
0.2
0.13
-549
43.1
4684
5.42
2630
4.8
152
180.
6627
47-6
.487
51-5
.824
760.
0971
1-0
.077
921
0.13
68.
5277
7E-0
65
305
Poi nL
inSt
379.
414
4.57
-180
.20.
13-5
4943
.146
845.
4226
304.
815
218
0.66
2747
-6.4
8751
-5.8
2476
-0.0
9710
50.
0779
260.
136
8.52
777E
-06
540
6Po
i nLin
St37
9.4
144.
57-1
80.2
0.13
-366
36.4
3215
3.95
2640
6.4
152
180.
4548
99-4
.325
91-3
.871
01-0
.097
105
0.07
7926
0.13
68.
5277
7E-0
65
406
Poi nL
inSt
379.
441
1.47
-518
.20.
13-3
6629
.532
153.
9526
406.
415
218
0.45
4899
-4.3
2509
9-3
.870
2-0
.279
326
0.22
1791
0.13
68.
5277
7E-0
65
508
Poi nL
inSt
379.
441
1.47
-518
.20.
1315
999.
9-9
634.
2326
508
152
18-0
.136
301
1.88
9213
1.75
2912
-0.2
7932
60.
2217
910.
136
8.52
777E
-06
550
8Po
inLin
St37
9.4
544.
91-7
89.6
0.13
1599
4.4
-963
4.23
2650
815
218
-0.1
3630
11.
8885
621.
7522
62-0
.425
584
0.29
3718
0.13
68.
5277
7E-0
65
610
Poi nL
inSt
379.
454
4.91
-789
.60.
1396
229.
1-6
5008
.426
609.
615
218
-0.9
1970
811
.362
4310
.442
73-0
.425
584
0.29
3718
0.13
68.
5277
7E-0
66
0Po
i nLin
St-1
89.7
95.1
679
6.9
-758
.98
9842
4.5
1242
42.7
270
152
181.
7577
2711
.621
6513
.379
380.
4295
40.
0512
93-0
.07
-0.0
4978
7757
610
2Po
i nLin
St-1
89.7
95.1
679
6.9
-758
.98
1746
0.1
1145
74.1
2710
1.6
152
181.
6209
412.
0616
363.
6825
760.
4295
40.
0512
93-0
.07
-0.0
4978
7757
610
2Po
i nLin
St-1
89.7
228.
6152
5.6
-758
.98
1746
0.1
1145
76.8
2710
1.6
152
181.
6209
792.
0616
363.
6826
150.
2832
820.
1232
26-0
.07
-0.0
4978
7757
620
3Po
i nLin
St-1
89.7
228.
6152
5.6
-758
.98
-359
35.9
9135
0.07
2720
3.2
152
181.
2923
78-4
.243
2-2
.950
820.
2832
820.
1232
26-0
.07
-0.0
4978
7757
620
3Po
i nLin
St-1
89.7
495.
518
7.5
-758
.98
-359
35.9
9134
4.65
2720
3.2
152
181.
2923
01-4
.243
2-2
.950
90.
1010
610.
2670
85-0
.07
-0.0
4978
7757
630
5Po
i nLin
St-1
89.7
495.
518
7.5
-758
.98
-549
84.6
4100
1.53
2730
4.8
152
180.
5800
7-6
.492
403
-5.9
1233
0.10
1061
0.26
7085
-0.0
7-0
.049
7877
576
305
Poi nL
inSt
-189
.778
4.64
-172
.8-7
58.9
8-5
4984
.641
001.
5327
304.
815
218
0.58
007
-6.4
9240
3-5
.912
33-0
.093
154
0.42
2937
-0.0
7-0
.049
7877
576
406
Poi nL
inSt
-189
.778
4.64
-172
.8-7
58.9
8-3
7422
.6-3
8733
.627
406.
415
218
-0.5
4798
5-4
.418
743
-4.9
6673
-0.0
9315
40.
4229
37-0
.07
-0.0
4978
7757
640
6Po
i nLin
St-1
89.7
1051
.5-5
10.9
-758
.98
-374
22.6
-387
3927
406.
415
218
-0.5
4806
1-4
.418
743
-4.9
668
-0.2
7537
50.
5667
97-0
.07
-0.0
4978
7757
650
8Po
i nLin
St-1
89.7
1051
.5-5
10.9
-758
.98
1446
2.5
-145
532
2750
815
218
-2.0
5891
61.
7076
84-0
.351
23-0
.275
375
0.56
6797
-0.0
7-0
.049
7877
576
508
Poi nL
inSt
-189
.711
85-7
82.2
-758
.98
1446
2.5
-145
529
2750
815
218
-2.0
5887
71.
7076
84-0
.351
19-0
.421
638
0.63
8729
-0.0
7-0
.049
7877
576
610
Poi nL
inSt
-189
.711
85-7
82.2
-758
.98
9395
2.5
-265
947
2760
9.6
152
18-3
.762
491
11.0
9362
7.33
1125
-0.4
2163
80.
6387
29-0
.07
-0.0
4978
7757
590
Poi nL
inSt
-792
.12.
87.
47-3
905.
1-9
1094
.889
1.86
10
18.3
152
0.10
5308
-1.2
8876
6-1
.183
460.
0040
260.
0015
09-0
.28
-0.2
5616
9681
5943
2Po
i nLin
St-7
92.1
2.8
7.47
-390
5.1
-943
22.4
-315
.19
143
1.8
18.3
152
-0.0
3721
7-1
.334
429
-1.3
7165
0.00
4026
0.00
1509
-0.2
8-0
.256
1696
8159
864
Poi nL
inSt
-792
.12.
87.
47-3
905.
1-9
7550
.1-1
522.
231
863.
618
.315
2-0
.179
74-1
.380
092
-1.5
5983
0.00
4026
0.00
1509
-0.2
8-0
.256
1696
8160
0Po
i nLin
St-7
92.1
2.79
-7.4
739
05.1
591
094
891.
682
018
.315
20.
1052
871.
2887
551.
3940
42-0
.004
026
0.00
1504
-0.2
80.
2561
7099
360
432
Poi nL
inSt
-792
.12.
79-7
.47
3905
.15
9432
0.9
-315
.12
243
1.8
18.3
152
-0.0
3720
81.
3344
071.
2971
99-0
.004
026
0.00
1504
-0.2
80.
2561
7099
360
864
Poi nL
inSt
-792
.12.
79-7
.47
3905
.15
9754
7.7
-152
1.93
286
3.6
18.3
152
-0.1
7970
51.
3800
591.
2003
54-0
.004
026
0.00
1504
-0.2
80.
2561
7099
361
0Po
i nLin
St-1
572
-24.
394.
84-5
4819
2066
.03
-198
75.2
30
18.3
152
-2.3
4679
90.
0292
29-2
.317
570.
0026
09-0
.013
147
-0.5
6-3
.596
0434
0661
432
Poi nL
inSt
-157
2-2
4.39
4.84
-548
19-2
3.32
-934
2.57
343
1.8
18.3
152
-1.1
0314
1-0
.000
33-1
.103
470.
0026
09-0
.013
147
-0.5
6-3
.596
0434
0661
864
Poi nL
inSt
-157
2-2
4.39
4.84
-548
19-2
112.
6811
90.0
33
863.
618
.315
20.
1405
15-0
.029
889
0.11
0626
0.00
2609
-0.0
1314
7-0
.56
-3.5
9604
3406
620
Poi nL
inSt
-157
2-2
4.38
-4.8
454
819
-206
8.28
-198
674
018
.315
2-2
.345
829
-0.0
2926
1-2
.375
09-0
.002
609
-0.0
1314
1-0
.56
3.59
6030
287
6243
2Po
i nLin
St-1
572
-24.
38-4
.84
5481
921
.79
-933
8.56
443
1.8
18.3
152
-1.1
0266
80.
0003
08-1
.102
36-0
.002
609
-0.0
1314
1-0
.56
3.59
6030
287
6286
4Po
i nLin
St-1
572
-24.
38-4
.84
5481
921
11.8
611
89.8
64
863.
618
.315
20.
1404
950.
0298
780.
1703
73-0
.002
609
-0.0
1314
1-0
.56
3.59
6030
287
630
PoinL
inSt
-4.4
20.
1128
4.5
012
2859
48.3
65
018
.315
20.
0057
11.
7381
471.
7438
570.
1533
685.
93E
-05
-00
6343
2Po
i nLin
St-4
.42
0.11
284.
50
4E-1
24.
31E
-15
543
1.8
18.3
152
5.09
E-1
95.
68E
-17
5.73
E-1
70.
1533
685.
93E
-05
-00
6386
4Po
i nLin
St-4
.42
0.11
284.
50
-122
859
-48.
365
863.
618
.315
2-0
.005
71-1
.738
147
-1.7
4386
0.15
3368
5.93
E-0
5-0
064
0Po
i nLin
St-4
.42
0.11
-284
.50
-122
859
48.3
66
018
.315
20.
0057
1-1
.738
147
-1.7
3244
-0.1
5336
85.
93E
-05
-00
6443
2Po
i nLin
St-4
.42
0.11
-284
.50
-1.8
E-1
17.
84E
-16
643
1.8
18.3
152
9.26
E-2
0-2
.5E
-16
-2.5
E-1
6-0
.153
368
5.93
E-0
5-0
064
864
Poi nL
inSt
-4.4
20.
11-2
84.5
012
2859
-48.
366
863.
618
.315
2-0
.005
711.
7381
471.
7324
37-0
.153
368
5.93
E-0
5-0
065
0Po
i nLin
St-5
27.7
-474
.114
.25
9338
.257
46.5
-145
053
70
18.3
152
-17.
1274
10.
0812
99-1
7.04
610.
0076
81-0
.255
566
-0.1
90.
6125
6954
765
610
Poi nL
inSt
-527
.7-4
74.1
14.2
593
38.2
-294
1.33
1439
75.4
760
9.6
18.3
152
17.0
0016
-0.0
4161
316
.958
550.
0076
81-0
.255
566
-0.1
90.
6125
6954
7
228
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CaseT
yP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xtm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
265
610
Poi
nLin
St
-109
2-0
.002
-0.0
123.
68-2
814.
4210
77.1
18
018
.315
20.
1271
82-0
.039
817
0.08
7365
-6.4
E-06
-9.6
1E-0
7-0
.39
0.00
0241
402
6512
19P
oinL
inS
t-1
092
-0.0
02-0
.012
3.68
-280
7.18
1078
.19
860
9.6
18.3
152
0.12
7309
-0.0
3971
50.
0875
95-6
.4E-
06-9
.61E
-07
-0.3
90.
0002
4140
265
1219
Poi
nLin
St
-527
.747
4.13
-14.
25-9
341.
9-2
934.
2114
3976
90
18.3
152
17.0
0023
-0.0
4151
216
.958
72-0
.007
681
0.25
5566
-0.1
9-0
.612
8102
9365
1829
Poi
nLin
St
-527
.747
4.13
-14.
25-9
341.
957
50.6
4-1
4505
49
609.
618
.315
2-1
7.12
747
0.08
1357
-17.
0461
-0.0
0768
10.
2555
66-0
.19
-0.6
1281
0293
680
Poi
nLin
St
-0.1
128
4.53
-4.4
2-7
77.7
3-1
688.
38-3
4534
610
015
218
-4.8
8579
1-0
.199
359
-5.0
8515
-0.0
0238
20.
1533
68-0
-0.0
5101
7724
6825
4P
oinL
inS
t-0
.11
284.
53-4
.42
-777
.73
-565
.8-4
1761
610
254
152
18-5
.908
231
-0.0
6680
8-5
.975
04-0
.002
382
0.15
3368
-0-0
.051
0177
2468
457
Poi
nLin
St
-0.1
128
4.53
-4.4
2-7
77.7
333
2.26
-475
432
1045
7.2
152
18-6
.726
182
0.03
9232
-6.6
8695
-0.0
0238
20.
1533
68-0
-0.0
5101
7724
6845
7P
oinL
inS
t0
2E-1
13E
-13
06.
4E-1
20
110
152
180
7.58
E-1
67.
58E
-16
1.36
E-16
8.72
E-1
50
068
508
Poi
nLin
St
02E
-11
3E-1
30
-6.4
E-1
2-8
.2E
-10
1150
.815
218
-1.1
6E-1
4-7
.58E
-16
-1.2
E-1
41.
36E-
168.
72E
-15
00
690
Poi
nLin
St
-0.1
1-2
84.5
-4.4
277
7.68
-168
7.86
3453
47.5
120
152
184.
8858
13-0
.199
297
4.68
6516
-0.0
0238
2-0
.153
368
-00.
0510
1444
569
254
Poi
nLin
St
-0.1
1-2
84.5
-4.4
277
7.68
-565
.71
4176
17.3
1225
415
218
5.90
8252
-0.0
6679
75.
8414
55-0
.002
382
-0.1
5336
8-0
0.05
1014
445
6945
7P
oinL
inS
t-0
.11
-284
.5-4
.42
777.
6833
2.01
4754
33.2
1245
7.2
152
186.
7262
040.
0392
036.
7654
06-0
.002
382
-0.1
5336
8-0
0.05
1014
445
6945
7P
oinL
inS
t0
00
0-6
.4E
-12
013
015
218
0-7
.58E
-16
-7.6
E-1
60
00
069
508
Poi
nLin
St
00
00
-6.4
E-1
20
1350
.815
218
0-7
.58E
-16
-7.6
E-1
60
00
070
0P
oinL
inS
t-4
74.1
-527
.7-1
4.25
0-1
628.
41-6
0315
.714
015
218
-0.8
5331
9-0
.192
278
-1.0
456
-0.0
0768
1-0
.284
441
-0.1
70
7022
9P
oinL
inS
t-4
74.1
-527
.7-1
4.25
016
28.4
160
315.
7414
228.
615
218
0.85
3319
0.19
2278
1.04
5596
-0.0
0768
1-0
.284
441
-0.1
70
7022
9P
oinL
inS
t-4
74-2
43.2
-9.8
3-2
858.
5-2
329.
7-6
519.
7515
015
218
-0.0
9223
8-0
.275
084
-0.3
6732
-0.0
0529
9-0
.131
074
-0.1
7-0
.187
5125
8870
368
Poi
nLin
St
-474
-243
.2-9
.83
-285
8.5
-956
.627
451.
0915
139.
715
218
0.38
8365
-0.1
1295
20.
2754
13-0
.005
299
-0.1
3107
4-0
.17
-0.1
8751
2588
7068
6P
oinL
inS
t-4
74-2
43.2
-9.8
3-2
858.
521
64.0
710
4657
.515
457.
215
218
1.48
0645
0.25
5527
1.73
6172
-0.0
0529
9-0
.131
074
-0.1
7-0
.187
5125
8870
686
Poi
nLin
St
0-3
252
39.9
90
2031
.37
-165
195
160
152
18-2
.337
094
0.23
9858
-2.0
9724
0.02
1555
-1.7
5282
00
7073
7P
oinL
inS
t0
-325
239
.99
00
2.57
E-1
116
50.8
152
183.
63E
-16
03.
63E
-16
0.02
1555
-1.7
5282
00
710
Poi
nLin
St
-474
.152
7.7
-14.
250
-162
8.97
6031
5.64
170
152
180.
8533
17-0
.192
344
0.66
0974
-0.0
0768
10.
2844
41-0
.17
071
229
Poi
nLin
St
-474
.152
7.7
-14.
250
1628
.97
-603
15.6
1722
8.6
152
18-0
.853
317
0.19
2344
-0.6
6097
-0.0
0768
10.
2844
41-0
.17
071
229
Poi
nLin
St
-474
243.
17-9
.83
2858
.52
-233
0.44
6519
.45
180
152
180.
0922
34-0
.275
171
-0.1
8294
-0.0
0529
90.
1310
74-0
.17
0.18
7513
971
368
Poi
nLin
St
-474
243.
17-9
.83
2858
.52
-956
.9-2
7451
.318
139.
715
218
-0.3
8836
7-0
.112
988
-0.5
0136
-0.0
0529
90.
1310
74-0
.17
0.18
7513
971
686
Poi
nLin
St
-474
243.
17-9
.83
2858
.52
2164
.78
-104
657
1845
7.2
152
18-1
.480
644
0.25
561
-1.2
2503
-0.0
0529
90.
1310
74-0
.17
0.18
7513
971
686
Poi
nLin
St
032
51.9
400
2031
.77
1651
94.8
190
152
182.
3370
980.
2399
052.
5770
030.
0215
611.
7528
260
071
737
Poi
nLin
St
032
51.9
400
0-5
.1E
-11
1950
.815
218
-7.2
7E-1
60
-7.3
E-1
60.
0215
611.
7528
260
072
0P
oinL
inS
t47
4.13
564.
2614
.26
-126
.9-9
334.
5214
2898
.320
015
218
2.02
1658
-1.1
0219
10.
9194
670.
0076
860.
3041
480.
17-0
.008
3244
1872
343
Poi
nLin
St
474.
1356
4.26
14.2
6-1
26.9
-142
25.5
-505
85.9
2034
2.9
152
18-0
.715
666
-1.6
7970
1-2
.395
370.
0076
860.
3041
480.
17-0
.008
3244
1872
686
Poi
nLin
St
474.
1356
4.26
14.2
6-1
26.9
-191
16.5
-244
070
2068
5.8
152
18-3
.452
989
-2.2
5721
2-5
.710
20.
0076
860.
3041
480.
17-0
.008
3244
1875
0P
oinL
inS
t47
4.13
-564
.314
.23
127.
03-9
345.
55-1
4289
821
015
218
-2.0
2165
-1.1
0349
3-3
.125
140.
0076
7-0
.304
148
0.17
0.00
8332
945
7534
3P
oinL
inS
t47
4.13
-564
.314
.23
127.
03-1
4226
.750
586.
1621
342.
915
218
0.71
5669
-1.6
7984
4-0
.964
170.
0076
7-0
.304
148
0.17
0.00
8332
945
7568
6P
oinL
inS
t47
4.13
-564
.314
.23
127.
03-1
9107
.924
4070
.121
685.
815
218
3.45
2988
-2.2
5619
61.
1967
920.
0076
7-0
.304
148
0.17
0.00
8332
945
474.
1332
51.9
796.
954
819
1228
5947
5433
.20
863.
6M
ax.
17.0
0023
11.6
2165
16.9
5872
0.42
954
1.75
2826
0.17
3.59
6030
287
-157
2-3
252
-796
.9-5
4819
-122
859
-479
338
00
Min
.-1
7.12
747
-11.
6102
3-1
8.39
17-0
.429
54-1
.752
82-0
.56
-3.5
9604
3406
Com
pare
with
26.5
0.7
5.3
10.8
0.7
229
T
able
II -
3. E
lem
ent f
orce
s –fr
ames
for
conf
igur
atio
n (b
) sof
a fr
ame
230
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
ameS
tatio
npu
tCase
TyP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
Text
mm
Text
Text
NN
NN
-mm
N-m
mN
-mm
Text
mm
hb
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m3
N/m
m2
10
Dis
tLin
Sta
-70.
07-1
640
-804
.364
84.6
4-8
2106
.59
-229
76.4
81
015
218
.3-0
.325
06-9
.694
887
-10.
0199
-0.4
3352
-0.8
8392
4-0
.03
0.42
5381
011
101.
6D
istL
inS
ta-7
0.07
-164
0-8
04.3
6484
.64
-392
.84
1436
34.1
21
102
152
18.3
2.03
2067
6-0
.046
385
1.98
5682
-0.4
3352
-0.8
8392
4-0
.03
0.42
5381
011
101.
6D
istL
inS
ta-7
0.07
-150
6-5
32.9
6484
.64
-387
.33
1436
34.1
21
102
152
18.3
2.03
2067
6-0
.045
735
1.98
6333
-0.2
8726
-0.8
1199
2-0
.03
0.42
5381
011
203.
2D
istL
inS
ta-7
0.07
-150
6-5
32.9
6484
.64
5375
8.11
2966
86.5
31
203
152
18.3
4.19
7380
86.
3475
8810
.544
97-0
.287
26-0
.811
992
-0.0
30.
4253
8101
120
3.2
Dis
tLin
Sta
-70.
07-1
240
-194
.964
84.6
453
751.
2429
6686
.53
120
315
218
.34.
1973
808
6.34
6777
10.5
4416
-0.1
0503
-0.6
6813
2-0
.03
0.42
5381
011
304.
8D
istL
inS
ta-7
0.07
-124
0-1
94.9
6484
.64
7354
9.29
4226
22.5
91
305
152
18.3
5.97
9064
78.
6844
6814
.663
53-0
.105
03-0
.668
132
-0.0
30.
4253
8101
130
4.8
Dis
tLin
Sta
-70.
07-9
50.4
165.
4464
84.6
473
549.
2942
2622
.59
130
515
218
.35.
9790
647
8.68
4468
14.6
6353
0.08
9176
-0.5
1228
-0.0
30.
4253
8101
140
6.4
Dis
tLin
Sta
-70.
07-9
50.4
165.
4464
84.6
456
740.
2651
9182
.59
140
615
218
.37.
3451
499
6.69
9711
14.0
4486
0.08
9176
-0.5
1228
-0.0
30.
4253
8101
140
6.4
Dis
tLin
Sta
-70.
07-6
83.5
503.
5164
84.6
456
747.
1351
9182
.59
140
615
218
.37.
3451
499
6.70
0522
14.0
4567
0.27
1402
-0.3
6842
1-0
.03
0.42
5381
011
508
Dis
tLin
Sta
-70.
07-6
83.5
503.
5164
84.6
455
90.7
5886
26.2
21
508
152
18.3
8.32
7605
60.
6601
328.
9877
380.
2714
02-0
.368
421
-0.0
30.
4253
8101
150
8D
istL
inS
ta-7
0.07
-550
.177
4.85
6484
.64
5590
.758
8626
.22
150
815
218
.38.
3276
056
0.66
0132
8.98
7738
0.41
766
-0.2
9648
8-0
.03
0.42
5381
011
609.
6D
istL
inS
ta-7
0.07
-550
.177
4.85
6484
.64
-731
34.0
364
4511
.68
161
015
218
.39.
1182
466
-8.6
3543
50.
4828
110.
4176
6-0
.296
488
-0.0
30.
4253
8101
20
Dis
tLin
Sta
-120
.6-5
44.3
-789
.8-2
.1-9
1653
.26
6404
55.8
42
015
218
.39.
0608
665
-10.
8221
3-1
.761
26-0
.425
7-0
.293
4-0
.04
-0.0
0013
776
210
1.6
Dis
tLin
Sta
-120
.6-5
44.3
-789
.8-2
.1-1
1413
.62
6957
58.3
210
215
218
.39.
8432
596
-1.3
4768
48.
4955
75-0
.425
7-0
.293
4-0
.04
-0.0
0013
776
210
1.6
Dis
tLin
Sta
-120
.6-4
10.9
-518
.4-2
.1-1
1408
.11
6957
58.3
210
215
218
.39.
8432
596
-1.3
4703
48.
4962
26-0
.279
44-0
.221
467
-0.0
4-0
.000
1377
62
203.
2D
istL
inS
ta-1
20.6
-410
.9-5
18.4
-2.1
4126
3.23
7375
02.5
82
203
152
18.3
10.4
3383
84.
8722
3215
.306
07-0
.279
44-0
.221
467
-0.0
4-0
.000
1377
62
203.
2D
istL
inS
ta-1
20.6
-144
-180
.4-2
.141
256.
3673
7502
.58
220
315
218
.310
.433
838
4.87
1421
15.3
0526
-0.0
9721
-0.0
7760
8-0
.04
-0.0
0013
776
230
4.8
Dis
tLin
Sta
-120
.6-1
44-1
80.4
-2.1
5958
0.31
7521
30.5
230
515
218
.310
.640
787
7.03
5055
17.6
7584
-0.0
9721
-0.0
7760
8-0
.04
-0.0
0013
776
230
4.8
Dis
tLin
Sta
-120
.614
5.16
179.
95-2
.159
580.
3175
2130
.52
305
152
18.3
10.6
4078
77.
0350
5517
.675
840.
0969
970.
0782
44-0
.04
-0.0
0013
776
240
6.4
Dis
tLin
Sta
-120
.614
5.16
179.
95-2
.141
297.
1773
7382
.36
240
615
218
.310
.432
137
4.87
624
15.3
0838
0.09
6997
0.07
8244
-0.0
4-0
.000
1377
62
406.
4D
istL
inS
ta-1
20.6
412.
0551
8.02
-2.1
4130
4.04
7373
82.3
62
406
152
18.3
10.4
3213
74.
8770
5115
.309
190.
2792
240.
2221
04-0
.04
-0.0
0013
776
250
8D
istL
inS
ta-1
20.6
412.
0551
8.02
-2.1
-113
26.4
969
5517
.86
250
815
218
.39.
8398
58-1
.337
396
8.50
2462
0.27
9224
0.22
2104
-0.0
4-0
.000
1377
62
508
Dis
tLin
Sta
-120
.654
5.5
789.
36-2
.1-1
1326
.49
6955
17.8
62
508
152
18.3
9.83
9858
-1.3
3739
68.
5024
620.
4254
810.
2940
36-0
.04
-0.0
0013
776
260
9.6
Dis
tLin
Sta
-120
.654
5.5
789.
36-2
.1-9
1525
.32
6400
95.1
82
610
152
18.3
9.05
5764
1-1
0.80
702
-1.7
5126
0.42
5481
0.29
4036
-0.0
4-0
.000
1377
63
0D
istL
inS
ta-6
8.76
551.
44-7
78.8
-643
6.32
-739
90.9
164
4153
.17
30
152
18.3
9.11
3174
6-8
.736
613
0.37
6561
-0.4
198
0.29
7238
-0.0
2-0
.422
2113
13
101.
6D
istL
inS
ta-6
8.76
551.
44-7
78.8
-643
6.32
5137
.53
5881
26.9
43
102
152
18.3
8.32
0542
0.60
6623
8.92
7165
-0.4
198
0.29
7238
-0.0
2-0
.422
2113
13
101.
6D
istL
inS
ta-6
8.76
684.
89-5
07.5
-643
6.32
5143
.04
5881
26.9
43
102
152
18.3
8.32
0542
0.60
7274
8.92
7816
-0.2
7354
0.36
917
-0.0
2-0
.422
2113
13
203.
2D
istL
inS
ta-6
8.76
684.
89-5
07.5
-643
6.32
5670
3.18
5185
42.5
33
203
152
18.3
7.33
6094
66.
6953
3314
.031
43-0
.273
540.
3691
7-0
.02
-0.4
2221
131
320
3.2
Dis
tLin
Sta
-68.
7695
1.78
-169
.4-6
436.
3256
696.
3151
8542
.53
320
315
218
.37.
3360
946
6.69
4521
14.0
3062
-0.0
9132
0.51
3029
-0.0
2-0
.422
2113
13
304.
8D
istL
inS
ta-6
8.76
951.
78-1
69.4
-643
6.32
7390
9.06
4218
41.7
63
305
152
18.3
5.96
8017
98.
7269
4914
.694
97-0
.091
320.
5130
29-0
.02
-0.4
2221
131
330
4.8
Dis
tLin
Sta
-68.
7612
40.9
190.
89-6
436.
3273
909.
0642
1841
.76
330
515
218
.35.
9680
179
8.72
6949
14.6
9497
0.10
2894
0.66
8876
-0.0
2-0
.422
2113
13
406.
4D
istL
inS
ta-6
8.76
1240
.919
0.89
-643
6.32
5451
4.72
2957
64.9
33
406
152
18.3
4.18
4342
46.
4369
2610
.621
270.
1028
940.
6688
76-0
.02
-0.4
2221
131
340
6.4
Dis
tLin
Sta
-68.
7615
07.8
528.
95-6
436.
3254
521.
5929
5764
.93
340
615
218
.34.
1843
424
6.43
7737
10.6
2208
0.28
5115
0.81
2741
-0.0
2-0
.422
2113
13
508
Dis
tLin
Sta
-68.
7615
07.8
528.
95-6
436.
3277
9.85
1425
71.7
43
508
152
18.3
2.01
7037
60.
0920
822.
1091
20.
2851
150.
8127
41-0
.02
-0.4
2221
131
350
8D
istL
inS
ta-6
8.76
1641
.380
0.3
-643
6.32
779.
8514
2571
.74
350
815
218
.32.
0170
376
0.09
2082
2.10
912
0.43
1378
0.88
4668
-0.0
2-0
.422
2113
13
609.
6D
istL
inS
ta-6
8.76
1641
.380
0.3
-643
6.32
-805
30.1
8-2
4179
.63
361
015
218
.3-0
.342
082
-9.5
0875
-9.8
5083
0.43
1378
0.88
4668
-0.0
2-0
.422
2113
14
0D
istL
inS
ta-1
447
-157
853
3.44
6967
.95
7043
.91
-359
760
40
152
18.3
-5.0
8971
40.
8317
23-4
.257
990.
2875
35-0
.850
478
-0.5
20.
4570
853
410
1.6
Dis
tLin
Sta
-144
7-1
578
533.
4469
67.9
5-4
7153
.42
-199
453.
24
102
152
18.3
-2.8
2177
-5.5
6772
7-8
.389
50.
2875
35-0
.850
478
-0.5
20.
4570
853
410
1.6
Dis
tLin
Sta
-144
7-1
444
262.
169
67.9
5-4
7158
.93
-199
453.
24
102
152
18.3
-2.8
2177
-5.5
6837
8-8
.390
150.
1412
77-0
.778
551
-0.5
20.
4570
853
420
3.2
Dis
tLin
Sta
-144
7-1
444
262.
169
67.9
5-7
3787
.96
-527
04.5
74
203
152
18.3
-0.7
4563
9-8
.712
649
-9.4
5829
0.14
1277
-0.7
7855
1-0
.52
0.45
7085
34
203.
2D
istL
inS
ta-1
447
-117
7-7
5.97
6967
.95
-737
81.0
9-5
2704
.57
420
315
218
.3-0
.745
639
-8.7
1183
8-9
.457
48-0
.040
95-0
.634
686
-0.5
20.
4570
853
430
4.8
Dis
tLin
Sta
-144
7-1
177
-75.
9769
67.9
5-6
6062
.73
6692
7.69
430
515
218
.30.
9468
613
-7.8
0047
9-6
.853
62-0
.040
95-0
.634
686
-0.5
20.
4570
853
430
4.8
Dis
tLin
Sta
-144
7-8
88.4
-436
.369
67.9
5-6
6062
.73
6692
7.69
430
515
218
.30.
9468
613
-7.8
0047
9-6
.853
62-0
.235
16-0
.478
839
-0.5
20.
4570
853
440
6.4
Dis
tLin
Sta
-144
7-8
88.4
-436
.369
67.9
5-2
1737
.28
1571
83.8
94
406
152
18.3
2.22
3763
4-2
.566
669
-0.3
4291
-0.2
3516
-0.4
7883
9-0
.52
0.45
7085
34
406.
4D
istL
inS
ta-1
447
-621
.5-7
74.3
6967
.95
-217
44.1
515
7183
.89
440
615
218
.32.
2237
634
-2.5
6748
1-0
.343
72-0
.417
39-0
.334
98-0
.52
0.45
7085
34
508
Dis
tLin
Sta
-144
7-6
21.5
-774
.369
67.9
556
928.
6922
0323
.74
450
815
218
.33.
1170
361
6.72
196
9.83
8996
-0.4
1739
-0.3
3498
-0.5
20.
4570
853
231
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
ameS
tatio
npu
tCase
TyP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
Text
mm
Text
Text
NN
NN
-mm
N-m
mN
-mm
Text
mm
hb
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m3
N/m
m2
450
8D
istL
inS
ta-1
447
-488
-774
.369
67.9
556
928.
6922
0323
.74
450
815
218
.33.
1170
361
6.72
196
9.83
8996
-0.4
1739
-0.2
6304
8-0
.52
0.45
7085
34
609.
6D
istL
inS
ta-1
447
-488
-774
.369
67.9
513
5601
.526
9905
.44
610
152
18.3
3.81
8494
16.0
114
19.8
299
-0.4
1739
-0.2
6304
8-0
.52
0.45
7085
35
0D
istL
inS
ta-1
085
-545
.574
7.62
-1.1
1019
59.9
7695
1.68
50
152
18.3
1.08
8676
12.0
391
13.1
2778
0.40
2983
-0.2
9400
9-0
.39
-7.2
158E
-05
510
1.6
Dis
tLin
Sta
-108
5-5
45.5
747.
62-1
.126
001.
4613
2369
.04
510
215
218
.31.
8726
946
3.07
017
4.94
2865
0.40
2983
-0.2
9400
9-0
.39
-7.2
158E
-05
510
1.6
Dis
tLin
Sta
-108
5-4
1247
6.28
-1.1
2599
5.94
1323
69.0
45
102
152
18.3
1.87
2694
63.
0695
194.
9422
130.
2567
25-0
.222
077
-0.3
9-7
.215
8E-0
55
203.
2D
istL
inS
ta-1
085
-412
476.
28-1
.1-2
2394
.17
1742
28.2
15
203
152
18.3
2.46
4898
4-2
.644
233
-0.1
7933
0.25
6725
-0.2
2207
7-0
.39
-7.2
158E
-05
520
3.2
Dis
tLin
Sta
-108
5-1
45.1
138.
22-1
.1-2
2387
.317
4228
.21
520
315
218
.32.
4648
984
-2.6
4342
2-0
.178
520.
0745
03-0
.078
217
-0.3
9-7
.215
8E-0
55
304.
8D
istL
inS
ta-1
085
-145
.113
8.22
-1.1
-364
30.0
318
8971
.02
530
515
218
.32.
6734
727
-4.3
0154
3-1
.628
070.
0745
03-0
.078
217
-0.3
9-7
.215
8E-0
55
304.
8D
istL
inS
ta-1
085
144.
03-2
22.1
-1.1
-364
30.0
318
8971
.02
530
515
218
.32.
6734
727
-4.3
0154
3-1
.628
07-0
.119
710.
0776
35-0
.39
-7.2
158E
-05
540
6.4
Dis
tLin
Sta
-108
514
4.03
-222
.1-1
.1-1
3865
.67
1743
37.7
85
406
152
18.3
2.46
6448
5-1
.637
215
0.82
9234
-0.1
1971
0.07
7635
-0.3
9-7
.215
8E-0
55
406.
4D
istL
inS
ta-1
085
410.
92-5
60.2
-1.1
-138
72.5
417
4337
.78
540
615
218
.32.
4664
485
-1.6
3802
60.
8284
23-0
.301
940.
2214
94-0
.39
-7.2
158E
-05
550
8D
istL
inS
ta-1
085
410.
92-5
60.2
-1.1
4303
9.22
1325
88.1
75
508
152
18.3
1.87
5794
85.
0819
356.
9577
3-0
.301
940.
2214
94-0
.39
-7.2
158E
-05
550
8D
istL
inS
ta-1
085
544.
37-5
60.2
-1.1
4303
9.22
1325
88.1
75
508
152
18.3
1.87
5794
85.
0819
356.
9577
3-0
.301
940.
2934
27-0
.39
-7.2
158E
-05
560
9.6
Dis
tLin
Sta
-108
554
4.37
-560
.2-1
.199
950.
9777
280.
395
610
152
18.3
1.09
3326
411
.801
912
.895
22-0
.301
940.
2934
27-0
.39
-7.2
158E
-05
60
Dis
tLin
Sta
-144
748
6.7
965.
12-7
051.
3213
8276
.126
9630
.62
60
152
18.3
3.81
4606
616
.327
2120
.141
810.
5202
20.
2623
41-0
.52
-0.4
6255
423
610
1.6
Dis
tLin
Sta
-144
748
6.7
965.
12-7
051.
3240
220.
0322
0182
.39
610
215
218
.33.
1150
364
4.74
9054
7.86
4091
0.52
022
0.26
2341
-0.5
2-0
.462
5542
36
101.
6D
istL
inS
ta-1
447
620.
1469
3.78
-705
1.32
4021
4.52
2201
82.3
96
102
152
18.3
3.11
5036
44.
7484
047.
8634
40.
3739
620.
3342
68-0
.52
-0.4
6255
423
620
3.2
Dis
tLin
Sta
-144
762
0.14
693.
78-7
051.
32-3
0273
.25
1571
75.9
96
203
152
18.3
2.22
3651
6-3
.574
57-1
.350
920.
3739
620.
3342
68-0
.52
-0.4
6255
423
620
3.2
Dis
tLin
Sta
-144
788
7.04
355.
71-7
051.
32-3
0266
.38
1571
75.9
96
203
152
18.3
2.22
3651
6-3
.573
759
-1.3
5011
0.19
1735
0.47
8133
-0.5
2-0
.462
5542
36
304.
8D
istL
inS
ta-1
447
887.
0435
5.71
-705
1.32
-664
06.7
667
053.
236
305
152
18.3
0.94
8637
4-7
.841
101
-6.8
9246
0.19
1735
0.47
8133
-0.5
2-0
.462
5542
36
304.
8D
istL
inS
ta-1
447
1176
.2-4
.59
-705
1.32
-664
06.7
667
053.
236
305
152
18.3
0.94
8637
4-7
.841
101
-6.8
9246
-0.0
0247
0.63
398
-0.5
2-0
.462
5542
36
406.
4D
istL
inS
ta-1
447
1176
.2-4
.59
-705
1.32
-659
40.0
5-5
2445
.59
640
615
218
.3-0
.741
975
-7.7
8599
3-8
.527
97-0
.002
470.
6339
8-0
.52
-0.4
6255
423
640
6.4
Dis
tLin
Sta
-144
714
43.1
-342
.7-7
051.
32-6
5946
.92
-524
45.5
96
406
152
18.3
-0.7
4197
5-7
.786
804
-8.5
2878
-0.1
847
0.77
7839
-0.5
2-0
.462
5542
36
508
Dis
tLin
Sta
-144
714
43.1
-342
.7-7
051.
32-3
1132
.82
-199
060.
786
508
152
18.3
-2.8
1621
8-3
.676
065
-6.4
9228
-0.1
847
0.77
7839
-0.5
2-0
.462
5542
36
508
Dis
tLin
Sta
-144
715
76.5
-342
.7-7
051.
32-3
1132
.82
-199
060.
786
508
152
18.3
-2.8
1621
8-3
.676
065
-6.4
9228
-0.1
847
0.84
9772
-0.5
2-0
.462
5542
36
609.
6D
istL
inS
ta-1
447
1576
.5-3
42.7
-705
1.32
3681
.28
-359
234.
146
610
152
18.3
-5.0
8227
50.
4346
74-4
.647
6-0
.184
70.
8497
72-0
.52
-0.4
6255
423
70
Dis
tLin
Sta
-826
.7-1
7.83
76.4
1-9
180.
5813
702.
62-1
5449
.94
70
152
18.3
-0.2
1857
81.
6179
621.
3993
840.
0411
87-0
.009
611
-0.3
-0.6
0222
995
743
1.8
Dis
tLin
Sta
-826
.7-1
7.83
76.4
1-9
180.
58-1
9289
.97
-775
0.06
743
215
218
.3-0
.109
644
-2.2
7769
9-2
.387
340.
0411
87-0
.009
611
-0.3
-0.6
0222
995
786
3.6
Dis
tLin
Sta
-826
.7-1
7.83
76.4
1-9
180.
58-5
2282
.56
-50.
187
864
152
18.3
-0.0
0071
-6.1
7336
-6.1
7407
0.04
1187
-0.0
0961
1-0
.3-0
.602
2299
58
0D
istL
inS
ta-1
565
5.74
50.5
6-4
055.
8425
144.
1611
442.
198
015
218
.30.
1618
787
2.96
8943
3.13
0822
0.02
7253
0.00
3094
-0.5
6-0
.266
0559
98
431.
8D
istL
inS
ta-1
565
5.74
50.5
6-4
055.
8433
12.4
689
64.4
78
432
152
18.3
0.12
6825
10.
3911
250.
5179
50.
0272
530.
0030
94-0
.56
-0.2
6605
599
886
3.6
Dis
tLin
Sta
-156
55.
7450
.56
-405
5.84
-185
19.2
364
86.7
48
864
152
18.3
0.09
1771
3-2
.186
692
-2.0
9492
0.02
7253
0.00
3094
-0.5
6-0
.266
0559
99
0D
istL
inS
ta-1
568
5.94
-51.
8740
57.9
9-2
7259
.93
1156
4.38
90
152
18.3
0.16
3607
4-3
.218
767
-3.0
5516
-0.0
2796
0.00
3202
-0.5
60.
2661
9703
943
1.8
Dis
tLin
Sta
-156
85.
94-5
1.87
4057
.99
-486
2.76
8999
.39
432
152
18.3
0.12
7317
8-0
.574
179
-0.4
4686
-0.0
2796
0.00
3202
-0.5
60.
2661
9703
986
3.6
Dis
tLin
Sta
-156
85.
94-5
1.87
4057
.99
1753
4.41
6434
.22
986
415
218
.30.
0910
283
2.07
0408
2.16
1436
-0.0
2796
0.00
3202
-0.5
60.
2661
9703
100
Dis
tLin
Sta
-819
-26.
19-7
7.79
9169
.67
-153
55.0
9-2
3579
.97
100
152
18.3
-0.3
3359
8-1
.813
081
-2.1
4668
-0.0
4193
-0.0
1411
7-0
.29
0.60
1514
2710
431.
8D
istL
inS
ta-8
19-2
6.19
-77.
7991
69.6
718
236.
47-1
2269
.56
1043
215
218
.3-0
.173
584
2.15
3305
1.97
9721
-0.0
4193
-0.0
1411
7-0
.29
0.60
1514
2710
863.
6D
istL
inS
ta-8
19-2
6.19
-77.
7991
69.6
751
828.
03-9
59.1
510
864
152
18.3
-0.0
1357
6.11
969
6.10
6121
-0.0
4193
-0.0
1411
7-0
.29
0.60
1514
2711
0D
istL
inS
ta22
.45
-8.7
7-6
.34
-108
98.3
-352
97.1
9-3
745.
2311
018
.315
2-0
.442
225
-0.4
9936
8-0
.941
59-0
.003
42-0
.004
727
0.00
8-0
.714
912
1143
1.8
Dis
tLin
Sta
22.4
5-8
.77
-6.3
4-1
0898
.3-3
2560
.61
41.9
611
432
18.3
152
0.00
4954
5-0
.460
652
-0.4
557
-0.0
0342
-0.0
0472
70.
008
-0.7
1491
211
863.
6D
istL
inS
ta22
.45
-8.7
7-6
.34
-108
98.3
-298
24.0
338
29.1
511
864
18.3
152
0.45
2133
9-0
.421
936
0.03
0198
-0.0
0342
-0.0
0472
70.
008
-0.7
1491
212
0D
istL
inS
ta18
.74
-6.7
79.
0310
879.
536
504.
19-2
752.
3212
018
.315
2-0
.324
985
0.51
6444
0.19
1459
0.00
4867
-0.0
0364
90.
007
0.71
3674
1612
431.
8D
istL
inS
ta18
.74
-6.7
79.
0310
879.
532
603.
1716
9.24
1243
218
.315
20.
0199
833
0.46
1254
0.48
1238
0.00
4867
-0.0
0364
90.
007
0.71
3674
1612
863.
6D
istL
inS
ta18
.74
-6.7
79.
0310
879.
528
702.
1530
90.7
912
864
18.3
152
0.36
4950
70.
4060
640.
7710
150.
0048
67-0
.003
649
0.00
70.
7136
7416
130
Dis
tLin
Sta
-436
.7-5
1.75
-45.
7311
019.
414
550.
66-1
5989
.97
130
18.3
152
-1.8
8804
50.
2058
56-1
.682
19-0
.024
65-0
.027
894
-0.1
60.
7228
507
1360
9.6
Dis
tLin
Sta
-436
.7-5
1.75
-45.
7311
019.
442
430.
2815
558.
1713
610
18.3
152
1.83
7059
60.
6002
842.
4373
43-0
.024
65-0
.027
894
-0.1
60.
7228
507
232
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
ameS
tatio
npu
tCase
TyP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
Text
mm
Text
Text
NN
NN
-mm
N-m
mN
-mm
Text
mm
hb
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m3
N/m
m2
1360
9.6
Dis
tLin
Sta
-747
.8-0
.052
-3.0
918
2.11
5092
7.78
-823
.85
140
18.3
152
-0.0
9727
80.
7205
020.
6232
25-0
.001
67-2
.83E
-05
-0.2
70.
0119
461
1312
19.2
Dis
tLin
Sta
-747
.8-0
.052
-3.0
918
2.11
5280
8.74
-791
.89
1461
018
.315
2-0
.093
504
0.74
7113
0.65
3609
-0.0
0167
-2.8
3E-0
5-0
.27
0.01
1946
113
1219
.2D
istL
inS
ta-4
37.6
51.6
839
.82
-106
29.5
4174
3.53
1553
4.38
150
18.3
152
1.83
4250
60.
5905
682.
4248
180.
0214
640.
0278
57-0
.16
-0.6
9727
853
1318
28.8
Dis
tLin
Sta
-437
.651
.68
39.8
2-1
0629
.517
467.
83-1
5969
.77
1561
018
.315
2-1
.885
660.
2471
27-1
.638
530.
0214
640.
0278
57-0
.16
-0.6
9727
853
140
Dis
tLin
Sta
-51.
7543
6.68
45.7
3-1
4550
.711
019.
3615
989.
9716
015
218
.30.
2262
185
1.30
1131
1.52
735
0.02
4649
0.23
538
-0.0
2-0
.954
4977
814
228.
6D
istL
inS
ta-5
1.75
436.
6845
.73
-145
50.7
564.
51-8
3835
.53
1622
915
218
.3-1
.186
065
0.06
6656
-1.1
1941
0.02
4649
0.23
538
-0.0
2-0
.954
4977
814
228.
6D
istL
inS
ta-6
0.52
430.
3423
.29
2074
6.5
4309
.73
-729
37.1
917
015
218
.3-1
.031
881
0.50
8879
-0.5
230.
0125
540.
2319
62-0
.02
1.36
0935
9914
368.
3D
istL
inS
ta-6
0.52
430.
3423
.29
2074
6.5
1056
.75
-133
056.
317
140
152
18.3
-1.8
8241
80.
1247
78-1
.757
640.
0125
540.
2319
62-0
.02
1.36
0935
9914
685.
8D
istL
inS
ta-6
0.52
430.
3423
.29
2074
6.5
-633
6.38
-269
690.
6517
457
152
18.3
-3.8
1545
6-0
.748
18-4
.563
640.
0125
540.
2319
62-0
.02
1.36
0935
9914
685.
8D
istL
inS
ta-1
656
1953
.731
6.57
016
081.
5199
249.
9418
015
218
.31.
4041
412
1.89
8854
3.30
2995
0.17
0638
1.05
3106
-0.6
014
736.
6D
istL
inS
ta-1
656
1953
.731
6.57
00
-5.0
18E
-11
1850
.815
218
.3-7
.1E
-16
0-7
.1E-
160.
1706
381.
0531
06-0
.60
150
Dis
tLin
Sta
51.7
311.
16-4
2.65
-849
7.5
-108
37.2
616
382.
0219
015
218
.30.
2317
651
-1.2
7962
9-1
.047
86-0
.022
990.
1677
220.
019
-0.5
5742
1115
342.
9D
istL
inS
ta51
.731
1.16
-42.
65-8
497.
537
86.9
9-9
0313
.77
1934
315
218
.3-1
.277
717
0.44
7156
-0.8
3056
-0.0
2299
0.16
7722
0.01
9-0
.557
4211
1568
5.8
Dis
tLin
Sta
51.7
311.
16-4
2.65
-849
7.5
1841
1.24
-197
009.
5619
686
152
18.3
-2.7
8719
82.
1739
41-0
.613
26-0
.022
990.
1677
220.
019
-0.5
5742
1116
0D
istL
inS
ta51
.73
-310
.2-4
2.91
1106
5.2
-108
11.6
4-1
6326
.27
200
152
18.3
-0.2
3097
6-1
.276
604
-1.5
0758
-0.0
2313
-0.1
6720
40.
019
0.72
5857
7216
342.
9D
istL
inS
ta51
.73
-310
.2-4
2.91
1106
5.2
3901
.48
9004
0.97
2034
315
218
.31.
2738
571
0.46
0674
1.73
4532
-0.0
2313
-0.1
6720
40.
019
0.72
5857
7216
685.
8D
istL
inS
ta51
.73
-310
.2-4
2.91
1106
5.2
1861
4.6
1964
08.2
220
686
152
18.3
2.77
8690
72.
1979
534.
9766
44-0
.023
13-0
.167
204
0.01
90.
7258
5772
170
Dis
tLin
Sta
-51.
68-4
37.6
39.8
217
467.
810
629.
53-1
5969
.77
210
152
18.3
-0.2
2593
31.
2551
011.
0291
690.
0214
64-0
.235
897
-0.0
21.
1458
5902
1722
8.6
Dis
tLin
Sta
-51.
68-4
37.6
39.8
217
467.
815
26.1
484
074.
7621
229
152
18.3
1.18
945
0.18
0202
1.36
9652
0.02
1464
-0.2
3589
7-0
.02
1.14
5859
0217
228.
6D
istL
inS
ta-5
8.45
-428
.621
.08
-190
36.4
4278
.46
7319
5.3
220
152
18.3
1.03
5532
50.
5051
871.
5407
20.
0113
63-0
.231
03-0
.02
-1.2
4875
184
1736
8.3
Dis
tLin
Sta
-58.
45-4
28.6
21.0
8-1
9036
.413
33.2
713
3071
.53
2214
015
218
.31.
8826
331
0.15
7428
2.04
0061
0.01
1363
-0.2
3103
-0.0
2-1
.248
7518
417
685.
8D
istL
inS
ta-5
8.45
-428
.621
.08
-190
36.4
-536
0.35
2691
53.8
722
457
152
18.3
3.80
7861
7-0
.632
933
3.17
4929
0.01
1363
-0.2
3103
-0.0
2-1
.248
7518
417
685.
8D
istL
inS
ta-1
661
-195
449
7.46
025
270.
94-9
9249
.94
230
152
18.3
-1.4
0414
12.
9839
131.
5797
720.
2681
41-1
.053
106
-0.6
017
736.
6D
istL
inS
ta-1
661
-195
449
7.46
03.
14E-
121.
004E
-10
2350
.815
218
.31.
42E
-15
3.7E
-16
1.79
E-15
0.26
8141
-1.0
5310
6-0
.60
180
Dis
tLin
Sta
8.77
6.34
22.4
5-2
9824
3829
.15
-108
98.3
424
015
218
.3-0
.154
185
0.45
2134
0.29
7949
0.01
2101
0.00
3417
0.00
3-1
.956
4040
818
254
Dis
tLin
Sta
8.77
6.34
22.4
5-2
9824
-187
2.85
-125
08.1
2425
415
218
.3-0
.176
959
-0.2
2114
-0.3
981
0.01
2101
0.00
3417
0.00
3-1
.956
4040
818
457.
2D
istL
inS
ta8.
776.
3422
.45
-298
24-6
434.
45-1
3795
.924
457
152
18.3
-0.1
9517
8-0
.759
76-0
.954
940.
0121
010.
0034
170.
003
-1.9
5640
408
1845
7.2
Dis
tLin
Sta
-161
30
00
00
250
152
18.3
00
00
0-0
.58
018
508
Dis
tLin
Sta
-161
30
00
00
2550
.815
218
.30
00
00
-0.5
80
190
Dis
tLin
Sta
6.77
-9.0
318
.74
2870
2.2
3090
.79
1087
9.47
260
152
18.3
0.15
3917
60.
3649
510.
5188
680.
0101
01-0
.004
867
0.00
21.
8828
1072
1925
4D
istL
inS
ta6.
77-9
.03
18.7
428
702.
2-1
669.
1913
174.
1826
254
152
18.3
0.18
6382
1-0
.197
093
-0.0
1071
0.01
0101
-0.0
0486
70.
002
1.88
2810
7219
457.
2D
istL
inS
ta6.
77-9
.03
18.7
428
702.
2-5
477.
1715
009.
9626
457
152
18.3
0.21
2353
8-0
.646
727
-0.4
3437
0.01
0101
-0.0
0486
70.
002
1.88
2810
7219
457.
2D
istL
inS
ta-1
608
00
00
027
015
218
.30
00
00
-0.5
80
1950
8D
istL
inS
ta-1
608
00
00
027
50.8
152
18.3
00
00
0-0
.58
0M
ax10
.640
787
16.3
2721
20.1
4181
0.52
022
1.05
3106
0.01
91.
8828
1072
Min
-5.0
8971
4-1
0.82
213
-10.
0199
-0.4
3352
-1.0
5310
6-0
.6-1
.956
4040
8co
mpa
re w
ith26
.50.
75.
310
.80.
7
233
T
able
II -
4. E
lem
ent f
orce
s –fr
ames
for
conf
igur
atio
n (c
) sof
a fr
ame
234
TAB
LE:
Elem
ent F
orce
s - F
ram
esra
mSta
tionp
utCas
eTy
PV2
V3T
M2
M3
ameE
lemSt
ati
hb
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V2
2/(2
bh)
P/(b
h)T/
(alfa
*dl*d
c2)
Text
mm
Text
Text
NN
NN
-mm
N-m
mN
-mm
Text
mm
mm
mm
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m3
N/m
m2
20
Dis
tLin
S35
8.74
-544
.91
-789
.6-0
.002
1-9
0435
.528
9415
.76
10
152
184.
1755
51-1
1.01
797
-6.8
4242
2-0
.432
867
-0.2
9874
50.
1311
-1.4
5048
E-0
72
102
Dis
tLin
S35
8.74
-544
.91
-789
.6-0
.002
1-1
0216
.934
4778
.51
101.
615
218
4.97
4297
-1.2
4475
33.
7295
447
-0.4
3286
7-0
.298
745
0.13
11-1
.450
48E
-07
210
2D
istL
inS
358.
74-4
11.4
6-5
18.2
-0.0
021
-102
11.4
3447
78.5
110
1.6
152
184.
9742
97-1
.244
083.
7302
172
-0.2
8410
6-0
.225
581
0.13
11-1
.450
48E
-07
220
3D
istL
inS
358.
74-4
11.4
6-5
18.2
-0.0
021
4243
8.88
3865
83.0
71
203.
215
218
5.57
7433
5.17
0428
810
.747
862
-0.2
8410
6-0
.225
581
0.13
11-1
.450
48E
-07
220
3D
istL
inS
358.
74-1
44.5
7-1
80.2
-0.0
021
4243
2.01
3865
83.0
71
203.
215
218
5.57
7433
5.16
9591
910
.747
025
-0.0
9876
6-0
.079
260.
1311
-1.4
5048
E-0
72
305
Dis
tLin
S35
8.74
-144
.57
-180
.2-0
.002
160
734.
9140
1271
.27
130
4.8
152
185.
7893
487.
3994
773
13.1
8882
5-0
.098
766
-0.0
7926
0.13
11-1
.450
48E
-07
230
5D
istL
inS
358.
7414
4.57
180.
16-0
.002
160
734.
9140
1271
.27
130
4.8
152
185.
7893
487.
3994
773
13.1
8882
50.
0987
719
0.07
9259
90.
1311
-1.4
5048
E-0
72
406
Dis
tLin
S35
8.74
144.
5718
0.16
-0.0
021
4243
0.72
3865
83.4
21
406.
415
218
5.57
7439
5.16
9434
710
.746
873
0.09
8771
90.
0792
599
0.13
11-1
.450
48E
-07
240
6D
istL
inS
358.
7441
1.46
518.
22-0
.002
142
437.
5938
6583
.42
140
6.4
152
185.
5774
395.
1702
717
10.7
4771
0.28
4111
80.
2255
811
0.13
11-1
.450
48E
-07
250
8D
istL
inS
358.
7441
1.46
518.
22-0
.002
1-1
0214
3447
79.2
150
815
218
4.97
4307
-1.2
4439
43.
7299
130.
2841
118
0.22
5581
10.
1311
-1.4
5048
E-0
72
508
Dis
tLin
S35
8.74
544.
9178
9.57
-0.0
021
-102
1434
4779
.21
508
152
184.
9743
07-1
.244
394
3.72
9913
0.43
2878
30.
2987
445
0.13
11-1
.450
48E
-07
261
0D
istL
inS
358.
7454
4.91
789.
57-0
.002
1-9
0433
.928
9416
.81
160
9.6
152
184.
1755
66-1
1.01
777
-6.8
4220
60.
4328
783
0.29
8744
50.
1311
-1.4
5048
E-0
75
0D
istL
inS
185.
31-5
44.9
178
9.56
0.00
333
9158
0.49
6634
6.84
20
152
180.
9572
211
.157
467
12.1
1468
70.
4328
728
-0.2
9874
50.
0677
2.25
119E
-07
510
2D
istL
inS
185.
31-5
44.9
178
9.56
0.00
333
1136
1.45
1217
09.5
92
101.
615
218
1.75
5967
1.38
4192
33.
1401
593
0.43
2872
8-0
.298
745
0.06
772.
2511
9E-0
75
102
Dis
tLin
S18
5.31
-411
.46
518.
220.
0033
311
355.
9412
1709
.59
210
1.6
152
181.
7559
671.
3835
213.
1394
880.
2841
118
-0.2
2558
10.
0677
2.25
119E
-07
520
3D
istL
inS
185.
31-4
11.4
651
8.22
0.00
333
-412
94.8
1635
14.1
52
203.
215
218
2.35
9103
-5.0
3104
3-2
.671
940.
2841
118
-0.2
2558
10.
0677
2.25
119E
-07
520
3D
istL
inS
185.
31-1
44.5
718
0.15
0.00
333
-412
87.9
1635
14.1
52
203.
215
218
2.35
9103
-5.0
3020
6-2
.671
103
0.09
8766
4-0
.079
260.
0677
2.25
119E
-07
530
5D
istL
inS
185.
31-1
44.5
718
0.15
0.00
333
-595
91.3
1782
02.3
62
304.
815
218
2.57
1017
-7.2
6014
5-4
.689
128
0.09
8766
4-0
.079
260.
0677
2.25
119E
-07
530
5D
istL
inS
185.
3114
4.57
-180
.20.
0033
3-5
9591
.317
8202
.36
230
4.8
152
182.
5710
17-7
.260
145
-4.6
8912
8-0
.098
766
0.07
9259
90.
0677
2.25
119E
-07
540
6D
istL
inS
185.
3114
4.57
-180
.20.
0033
3-4
1287
.516
3514
.52
406.
415
218
2.35
9108
-5.0
3015
7-2
.671
049
-0.0
9876
60.
0792
599
0.06
772.
2511
9E-0
75
406
Dis
tLin
S18
5.31
411.
46-5
18.2
0.00
333
-412
94.4
1635
14.5
240
6.4
152
182.
3591
08-5
.030
994
-2.6
7188
6-0
.284
112
0.22
5581
10.
0677
2.25
119E
-07
550
8D
istL
inS
185.
3141
1.46
-518
.20.
0033
311
356.
7412
1710
.29
250
815
218
1.75
5977
1.38
3618
43.
1395
956
-0.2
8411
20.
2255
811
0.06
772.
2511
9E-0
75
508
Dis
tLin
S18
5.31
544.
91-7
89.6
0.00
333
1136
2.25
1217
10.2
92
508
152
181.
7559
771.
3842
897
3.14
0266
9-0
.432
873
0.29
8744
50.
0677
2.25
119E
-07
561
0D
istL
inS
185.
3154
4.91
-789
.60.
0033
391
581.
6966
347.
892
609.
615
218
0.95
7235
11.1
5761
312
.114
849
-0.4
3287
30.
2987
445
0.06
772.
2511
9E-0
77
0D
istL
inS
99.2
95.
560.
12-2
245.
3-1
01.5
522
96.7
93
015
218
0.03
3137
-0.0
1237
20.
0207
649
6.57
9E-0
50.
0030
482
0.03
63-0
.151
9723
317
432
Dis
tLin
S99
.29
5.56
0.12
-224
5.3
-155
.34
-105
.66
343
1.8
152
18-0
.001
524
-0.0
1892
5-0
.020
456.
579E
-05
0.00
3048
20.
0363
-0.1
5197
2331
786
4D
istL
inS
99.2
95.
560.
12-2
245.
3-2
09.1
2-2
508.
13
863.
615
218
-0.0
3618
6-0
.025
478
-0.0
6166
36.
579E
-05
0.00
3048
20.
0363
-0.1
5197
2331
80
Dis
tLin
S-1
494
-8.0
62.
83-1
607
-246
1.19
-503
5.89
40
152
18-0
.072
655
-0.2
9985
3-0
.372
508
0.00
1551
5-0
.004
419
-0.5
46-0
.108
7658
388
432
Dis
tLin
S-1
494
-8.0
62.
83-1
607
-368
3.32
-155
5.05
443
1.8
152
18-0
.022
436
-0.4
4874
8-0
.471
183
0.00
1551
5-0
.004
419
-0.5
46-0
.108
7658
388
864
Dis
tLin
S-1
494
-8.0
62.
83-1
607
-490
5.45
1925
.79
486
3.6
152
180.
0277
84-0
.597
643
-0.5
6985
80.
0015
515
-0.0
0441
9-0
.546
-0.1
0876
5838
90
Dis
tLin
S-1
494
-8.0
6-2
.83
1606
.95
2461
.42
-503
5.5
50
152
18-0
.072
650.
2998
806
0.22
7230
8-0
.001
552
-0.0
0441
9-0
.546
0.10
8765
838
943
2D
istL
inS
-149
4-8
.06
-2.8
316
06.9
536
83.2
6-1
554.
865
431.
815
218
-0.0
2243
30.
4487
403
0.42
6307
5-0
.001
552
-0.0
0441
9-0
.546
0.10
8765
838
986
4D
istL
inS
-149
4-8
.06
-2.8
316
06.9
549
05.1
119
25.7
95
863.
615
218
0.02
7784
0.59
7601
10.
6253
855
-0.0
0155
2-0
.004
419
-0.5
460.
1087
6583
810
0D
istL
inS
99.2
85.
56-0
.12
2245
.310
1.5
2296
.77
60
152
180.
0331
370.
0123
660.
0455
027
-6.5
8E-0
50.
0030
482
0.03
630.
1519
7233
110
432
Dis
tLin
S99
.28
5.56
-0.1
222
45.3
155.
33-1
05.6
56
431.
815
218
-0.0
0152
40.
0189
242
0.01
74-6
.58E
-05
0.00
3048
20.
0363
0.15
1972
331
1086
4D
istL
inS
99.2
85.
56-0
.12
2245
.320
9.17
-250
8.08
686
3.6
152
18-0
.036
185
0.02
5483
7-0
.010
702
-6.5
8E-0
50.
0030
482
0.03
630.
1519
7233
111
0D
istL
inS
-2.3
80.
0091
-364
.40
-157
347
3.94
70
1815
20.
0004
8-2
.270
127
-2.2
6964
7-0
.199
781
5.00
7E-0
6-9
E-0
40
1143
2D
istL
inS
-2.3
80.
0091
-364
.40
-3.1
E-1
2-5
.742
E-16
743
1.8
1815
2-7
E-2
0-4
.52E
-17
-4.5
3E-1
7-0
.199
781
5.00
7E-0
6-9
E-0
40
1186
4D
istL
inS
-2.3
80.
0091
-364
.40
1573
47.1
-3.9
47
863.
618
152
-0.0
0048
2.27
0127
42.
2696
474
-0.1
9978
15.
007E
-06
-9E
-04
012
0D
istL
inS
-2.3
80.
0091
364.
40
1573
483.
948
018
152
0.00
048
2.27
0140
82.
2706
208
0.19
9780
75.
007E
-06
-9E
-04
012
432
Dis
tLin
S-2
.38
0.00
9136
4.4
0-3
.1E
-12
-1.9
14E-
168
431.
818
152
-2.3
3E-2
0-4
.52E
-17
-4.5
3E-1
70.
1997
807
5.00
7E-0
6-9
E-0
40
1286
4D
istL
inS
-2.3
80.
0091
364.
40
-157
348
-3.9
48
863.
618
152
-0.0
0048
-2.2
7014
1-2
.270
621
0.19
9780
75.
007E
-06
-9E
-04
013
0D
istL
inS
-764
.3-3
8.67
5.1
-344
.98
3042
.57
-114
46.9
39
018
152
-1.3
9460
60.
0438
967
-1.3
5071
0.00
2796
1-0
.021
201
-0.2
79-0
.023
3498
4813
610
Dis
tLin
S-7
64.3
-38.
675.
1-3
44.9
8-6
6.53
1212
6.6
960
9.6
1815
21.
4774
12-0
.000
961.
4764
524
0.00
2796
1-0
.021
201
-0.2
79-0
.023
3498
4813
610
Dis
tLin
S-1
039
-3E
-05
-4E
-04
0.09
386
-297
6.35
-679
.68
100
1815
2-0
.082
807
-0.0
4294
1-0
.125
748
-2.1
3E-0
7-1
.48E
-08
-0.3
86.
3528
8E-0
613
1219
Dis
tLin
S-1
039
-3E
-05
-4E
-04
0.09
386
-297
6.12
-679
.66
1060
9.6
1815
2-0
.082
805
-0.0
4293
8-0
.125
743
-2.1
3E-0
7-1
.48E
-08
-0.3
86.
3528
8E-0
613
1219
Dis
tLin
S-7
64.3
38.6
7-5
.134
4.88
-66.
2712
126.
6111
018
152
1.47
7413
-0.0
0095
61.
4764
574
-0.0
0279
60.
0212
007
-0.2
790.
0233
4308
1318
29D
istL
inS
-764
.338
.67
-5.1
344.
8830
42.7
-114
46.9
411
609.
618
152
-1.3
9460
80.
0438
986
-1.3
5070
9-0
.002
796
0.02
1200
7-0
.279
0.02
3343
0814
0D
istL
inS
-38.
6776
4.26
-5.1
0-5
82.9
687
354.
9712
015
218
1.26
0315
-0.0
7102
31.
1892
918
-0.0
0279
60.
4190
022
-0.0
140
1422
9D
istL
inS
-38.
6776
4.26
-5.1
058
2.96
-873
54.9
712
228.
615
218
-1.2
6031
50.
0710
234
-1.1
8929
2-0
.002
796
0.41
9002
2-0
.014
0
235
TAB
LE:
Elem
ent F
orce
s - F
ram
esra
mSta
tionp
utCas
eTy
PV2
V3T
M2
M3
ameE
lemSt
ati
hb
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V2
2/(2
bh)
P/(b
h)T/
(alfa
*dl*d
c2)
Text
mm
Text
Text
NN
NN
-mm
N-m
mN
-mm
Text
mm
mm
mm
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m3
N/m
m2
1422
9D
istL
inS
-38.
6639
9.86
-2.7
221
7.57
-632
.53
1850
9.91
130
152
180.
2670
52-0
.077
063
0.18
9989
4-0
.001
491
0.21
9221
5-0
.014
0.01
4726
148
1436
8D
istL
inS
-38.
6639
9.86
-2.7
221
7.57
-252
.39
-373
50.8
613
139.
715
218
-0.5
3888
-0.0
3074
9-0
.569
629
-0.0
0149
10.
2192
215
-0.0
140.
0147
2614
814
686
Dis
tLin
S-3
8.66
399.
86-2
.72
217.
5761
1.58
-164
307.
1713
457.
215
218
-2.3
7054
40.
0745
102
-2.2
9603
4-0
.001
491
0.21
9221
5-0
.014
0.01
4726
148
1468
6D
istL
inS
048
31.1
5.06
025
6.96
2454
19.3
214
015
218
3.54
0791
0.03
1306
3.57
2097
20.
0027
741
2.64
8623
90
014
737
Dis
tLin
S0
4831
.15.
060
-4.9
E-1
40
1450
.815
218
0-5
.97E
-18
-5.9
7E-1
80.
0027
741
2.64
8623
90
015
0D
istL
inS
38.6
727
4.79
5.1
2909
.82
345.
0712
806.
2815
015
218
0.18
4763
0.04
2040
70.
2268
035
0.00
2796
10.
1506
524
0.01
410.
1969
5013
1534
3D
istL
inS
38.6
727
4.79
5.1
2909
.82
-140
3.93
-814
20.6
915
342.
915
218
-1.1
7469
8-0
.171
044
-1.3
4574
20.
0027
961
0.15
0652
40.
0141
0.19
6950
1315
686
Dis
tLin
S38
.67
274.
795.
129
09.8
2-3
152.
94-1
7564
7.65
1568
5.8
152
18-2
.534
159
-0.3
8413
-2.9
1828
90.
0027
961
0.15
0652
40.
0141
0.19
6950
1316
0D
istL
inS
38.6
7-2
74.7
95.
1-2
909.
934
4.79
-128
06.2
716
015
218
-0.1
8476
30.
0420
066
-0.1
4275
60.
0027
961
-0.1
5065
20.
0141
-0.1
9695
216
1634
3D
istL
inS
38.6
7-2
74.7
95.
1-2
909.
9-1
403.
8881
420.
716
342.
915
218
1.17
4698
-0.1
7103
81.
0036
605
0.00
2796
1-0
.150
652
0.01
41-0
.196
9521
616
686
Dis
tLin
S38
.67
-274
.79
5.1
-290
9.9
-315
2.54
1756
47.6
716
685.
815
218
2.53
416
-0.3
8408
12.
1500
782
0.00
2796
1-0
.150
652
0.01
41-0
.196
9521
617
0D
istL
inS
-38.
67-7
64.2
6-5
.10
-582
.93
-873
54.9
617
015
218
-1.2
6031
5-0
.071
02-1
.331
335
-0.0
0279
6-0
.419
002
-0.0
140
1722
9D
istL
inS
-38.
67-7
64.2
6-5
.10
582.
9387
354.
9617
228.
615
218
1.26
0315
0.07
1019
71.
3313
348
-0.0
0279
6-0
.419
002
-0.0
140
1722
9D
istL
inS
-38.
66-3
99.8
6-2
.72
-217
.54
-632
.51
-185
09.4
180
152
18-0
.267
045
-0.0
7706
-0.3
4410
5-0
.001
491
-0.2
1922
1-0
.014
-0.0
1472
4117
1736
8D
istL
inS
-38.
66-3
99.8
6-2
.72
-217
.54
-252
.38
3735
1.07
1813
9.7
152
180.
5388
83-0
.030
748
0.50
8135
1-0
.001
491
-0.2
1922
1-0
.014
-0.0
1472
4117
1768
6D
istL
inS
-38.
66-3
99.8
6-2
.72
-217
.54
611.
5516
4306
.69
1845
7.2
152
182.
3705
370.
0745
066
2.44
5044
-0.0
0149
1-0
.219
221
-0.0
14-0
.014
7241
1717
686
Dis
tLin
S0
-483
1.1
5.06
025
6.96
-245
419.
3819
015
218
-3.5
4079
20.
0313
06-3
.509
486
0.00
2774
1-2
.648
624
00
1773
7D
istL
inS
0-4
831.
15.
060
-4.9
E-1
40
1950
.815
218
0-5
.97E
-18
-5.9
7E-1
80.
0027
741
-2.6
4862
40
018
0D
istL
inS
-0.0
0936
4.4
-2.3
8-1
99.7
7-5
57.2
-197
384.
6520
015
218
-2.8
4777
-0.0
6788
5-2
.915
655
-0.0
0130
50.
1997
807
-3E
-06
-0.0
1352
1361
1825
4D
istL
inS
-0.0
0936
4.4
-2.3
8-1
99.7
747
.09
-289
941.
7520
254
152
18-4
.183
139
0.00
5737
1-4
.177
402
-0.0
0130
50.
1997
807
-3E
-06
-0.0
1352
1361
1845
7D
istL
inS
-0.0
0936
4.4
-2.3
8-1
99.7
753
0.52
-363
987.
4320
457.
215
218
-5.2
5143
50.
0646
345
-5.1
868
-0.0
0130
50.
1997
807
-3E
-06
-0.0
1352
1361
1845
7D
istL
inS
0-2
E-1
20
00
021
015
218
00
00
-1.0
8E-1
50
018
508
Dis
tLin
S0
-2E
-12
00
01.
004E
-10
2150
.815
218
1.45
E-1
50
1.44
9E-1
50
-1.0
8E-1
50
019
0D
istL
inS
-0.0
09-3
64.4
-2.3
819
9.8
-557
.17
1973
83.8
522
015
218
2.84
7759
-0.0
6788
12.
7798
774
-0.0
0130
5-0
.199
781
-3E
-06
0.01
3523
392
1925
4D
istL
inS
-0.0
09-3
64.4
-2.3
819
9.8
47.0
928
9941
.522
254
152
184.
1831
360.
0057
371
4.18
8872
8-0
.001
305
-0.1
9978
1-3
E-0
60.
0135
2339
219
457
Dis
tLin
S-0
.009
-364
.4-2
.38
199.
853
0.5
3639
87.6
122
457.
215
218
5.25
1437
0.06
4632
15.
3160
692
-0.0
0130
5-0
.199
781
-3E
-06
0.01
3523
392
1945
7D
istL
inS
0-4
E-1
20
00
4.01
4E-1
023
015
218
5.79
E-1
50
5.79
1E-1
50
-2.1
7E-1
50
019
508
Dis
tLin
S0
-4E
-12
00
06.
021E
-10
2350
.815
218
8.69
E-1
50
8.68
7E-1
50
-2.1
7E-1
50
033
0D
istL
inS
364.
27-1
626.
596
.91
1977
.58
-408
.88
-366
232.
7324
015
218
-5.2
8382
9-0
.049
815
-5.3
3364
30.
0531
305
-0.8
9173
80.
1331
0.13
3851
798
3376
.2D
istL
inS
364.
27-1
626.
596
.91
1977
.58
-779
3.32
-242
290.
8824
76.2
152
18-3
.495
656
-0.9
4947
9-4
.445
134
0.05
3130
5-0
.891
738
0.13
310.
1338
5179
834
0D
istL
inS
361.
57-1
626.
7-8
74.9
1925
.79
-708
62.4
-244
460.
3625
015
218
-3.5
2695
6-8
.633
332
-12.
1602
9-0
.479
644
-0.8
9180
90.
1322
0.13
0346
4134
25.4
Dis
tLin
S36
1.57
-162
6.7
-874
.919
25.7
9-4
8649
.6-2
0315
9.67
2525
.39
152
18-2
.931
089
-5.9
2709
1-8
.858
18-0
.479
644
-0.8
9180
90.
1322
0.13
0346
4134
25.4
Dis
tLin
S36
1.57
-149
3.2
-603
.519
25.7
9-4
8649
.6-2
0315
9.67
2525
.39
152
18-2
.931
089
-5.9
2709
1-8
.858
18-0
.330
883
-0.8
1865
10.
1322
0.13
0346
4134
127
Dis
tLin
S36
1.57
-149
3.2
-603
.519
25.7
912
676.
7-5
1430
.02
2512
715
218
-0.7
4200
71.
5444
323
0.80
2424
8-0
.330
883
-0.8
1865
10.
1322
0.13
0346
4134
127
Dis
tLin
S36
1.57
-122
6.3
-265
.519
25.7
912
676.
7-5
1430
.02
2512
715
218
-0.7
4200
71.
5444
323
0.80
2424
8-0
.145
537
-0.6
7232
50.
1322
0.13
0346
4134
229
Dis
tLin
S36
1.57
-122
6.3
-265
.519
25.7
939
651.
2773
179.
8825
228.
615
218
1.05
5804
4.83
0807
75.
8866
116
-0.1
4553
7-0
.672
325
0.13
220.
1303
4641
3422
9D
istL
inS
361.
57-9
37.1
994
.84
1925
.79
3965
1.27
7317
9.88
2522
8.6
152
181.
0558
044.
8308
077
5.88
6611
60.
0519
956
-0.5
1381
0.13
220.
1303
4641
3433
0D
istL
inS
361.
57-9
37.1
994
.84
1925
.79
3001
9.24
1683
60.0
625
330.
215
218
2.42
9017
3.65
7314
86.
0863
323
0.05
1995
6-0
.513
810.
1322
0.13
0346
4134
330
Dis
tLin
S36
1.57
-670
.29
432.
9119
25.7
930
019.
2416
8360
.06
2533
0.2
152
182.
4290
173.
6573
148
6.08
6332
30.
2373
41-0
.367
484
0.13
220.
1303
4641
3443
2D
istL
inS
361.
57-6
70.2
943
2.91
1925
.79
-139
7523
6478
.99
2543
1.8
152
183.
4118
04-1
.702
612
1.70
9192
40.
2373
41-0
.367
484
0.13
220.
1303
4641
3443
2D
istL
inS
361.
57-5
36.8
570
4.25
1925
.79
-139
78.5
2364
78.9
925
431.
815
218
3.41
1804
-1.7
0303
11.
7087
733
0.38
6102
-0.2
9432
60.
1322
0.13
0346
4134
533
Dis
tLin
S36
1.57
-536
.85
704.
2519
25.7
9-8
5530
.129
1022
.71
2553
3.4
152
184.
1987
35-1
0.42
033
-6.2
2159
40.
3861
02-0
.294
326
0.13
220.
1303
4641
350
Dis
tLin
S36
1.57
536.
84-7
04.2
-192
5.8
-855
28.8
2910
23.7
626
015
218
4.19
875
-10.
4201
7-6
.221
421
-0.3
8609
60.
2943
202
0.13
22-0
.130
3464
135
102
Dis
tLin
S36
1.57
536.
84-7
04.2
-192
5.8
-139
77.6
2364
80.3
426
101.
615
218
3.41
1824
-1.7
0292
81.
7088
963
-0.3
8609
60.
2943
202
0.13
22-0
.130
3464
135
102
Dis
tLin
S36
1.57
670.
29-4
32.9
-192
5.8
-139
74.2
2364
80.3
426
101.
615
218
3.41
1824
-1.7
0250
71.
7093
166
-0.2
3733
60.
3674
836
0.13
22-0
.130
3464
135
203
Dis
tLin
S36
1.57
670.
29-4
32.9
-192
5.8
3000
8.65
1683
78.7
426
203.
215
218
2.42
9287
3.65
6024
66.
0853
116
-0.2
3733
60.
3674
836
0.13
22-0
.130
3464
135
203
Dis
tLin
S36
1.57
937.
18-9
4.84
-192
5.8
3001
7.24
1683
78.7
426
203.
215
218
2.42
9287
3.65
7071
26.
0863
581
-0.0
5199
60.
5138
048
0.13
22-0
.130
3464
135
305
Dis
tLin
S36
1.57
937.
18-9
4.84
-192
5.8
3965
2.68
7316
0.77
2630
4.8
152
181.
0555
284.
8309
795
5.88
6507
7-0
.051
996
0.51
3804
80.
1322
-0.1
3034
641
3530
5D
istL
inS
361.
5712
26.3
265.
47-1
925.
839
647.
1973
160.
7726
304.
815
218
1.05
5528
4.83
0310
75.
8858
389
0.14
5542
80.
6723
246
0.13
22-0
.130
3464
135
406
Dis
tLin
S36
1.57
1226
.326
5.47
-192
5.8
1267
5.54
-514
33.2
526
406.
415
218
-0.7
4205
41.
5442
909
0.80
2236
90.
1455
428
0.67
2324
60.
1322
-0.1
3034
641
236
TAB
LE:
Elem
ent F
orce
s - F
ram
esra
mSta
tionp
utCas
eTy
PV2
V3T
M2
M3
ameE
lemSt
ati
hb
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V2
2/(2
bh)
P/(b
h)T/
(alfa
*dl*d
c2)
Text
mm
Text
Text
NN
NN
-mm
N-m
mN
-mm
Text
mm
mm
mm
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m2
N/m
m3
N/m
m2
3540
6D
istL
inS
361.
5714
93.2
603.
53-1
925.
812
674.
68-5
1433
.25
2640
6.4
152
18-0
.742
054
1.54
4186
20.
8021
321
0.33
0882
70.
8186
458
0.13
22-0
.130
3464
135
508
Dis
tLin
S36
1.57
1493
.260
3.53
-192
5.8
-486
44.4
-203
143.
6326
508
152
18-2
.930
858
-5.9
2645
7-8
.857
315
0.33
0882
70.
8186
458
0.13
22-0
.130
3464
135
508
Dis
tLin
S36
1.57
1626
.787
4.88
-192
5.8
-486
41.6
-203
143.
6326
508
152
18-2
.930
858
-5.9
2612
1-8
.856
979
0.47
9649
10.
8918
092
0.13
22-0
.130
3464
135
533
Dis
tLin
S36
1.57
1626
.787
4.88
-192
5.8
-708
63.4
-244
460.
7726
533.
415
218
-3.5
2696
2-8
.633
459
-12.
1604
20.
4796
491
0.89
1809
20.
1322
-0.1
3034
641
360
Dis
tLin
S36
4.28
1626
.5-9
6.91
-197
7.6
-779
3.14
-242
291.
2927
015
218
-3.4
9566
2-0
.949
457
-4.4
4511
8-0
.053
130.
8917
379
0.13
31-0
.133
8517
9836
76.2
Dis
tLin
S36
4.28
1626
.5-9
6.91
-197
7.6
-408
.97
-366
232.
9127
76.2
152
18-5
.283
831
-0.0
4982
6-5
.333
657
-0.0
5313
0.89
1737
90.
1331
-0.1
3385
1798
370
Dis
tLin
S-9
5.02
-160
4.2
-102
1942
.17
319.
12-4
0748
1.19
280
152
18-5
.878
941
0.03
8879
1-5
.840
062
-0.0
5592
1-0
.879
518
-0.0
350.
1314
5508
437
76.2
Dis
tLin
S-9
5.02
-160
4.2
-102
1942
.17
8091
.9-2
8523
7.91
2876
.215
218
-4.1
1527
50.
9858
553
-3.1
2941
9-0
.055
921
-0.8
7951
8-0
.035
0.13
1455
084
380
Dis
tLin
S-9
2.32
-160
4.1
869.
7718
82.9
568
823.
48-2
8306
8.42
290
152
18-4
.083
974
8.38
4926
94.
3009
527
0.47
6847
6-0
.879
446
-0.0
340.
1274
468
3825
.4D
istL
inS
-92.
32-1
604.
186
9.77
1882
.95
4674
0.03
-242
340.
2229
25.3
915
218
-3.4
9636
75.
6944
481
2.19
8080
70.
4768
476
-0.8
7944
6-0
.034
0.12
7446
838
25.4
Dis
tLin
S-9
2.32
-147
0.7
598.
4318
82.9
546
740.
03-2
4234
0.22
2925
.39
152
18-3
.496
367
5.69
4448
12.
1980
807
0.32
8086
6-0
.806
288
-0.0
340.
1274
468
3812
7D
istL
inS
-92.
32-1
470.
759
8.43
1882
.95
-140
68.4
-929
01.7
429
127
152
18-1
.340
341
-1.7
1398
4-3
.054
325
0.32
8086
6-0
.806
288
-0.0
340.
1274
468
3812
7D
istL
inS
-92.
32-1
203.
826
0.37
1882
.95
-140
68.4
-929
01.7
429
127
152
18-1
.340
341
-1.7
1398
4-3
.054
325
0.14
2746
7-0
.659
962
-0.0
340.
1274
468
3822
9D
istL
inS
-92.
32-1
203.
826
0.37
1882
.95
-405
25.1
2941
729
228.
615
218
0.42
4414
-4.9
3727
-4.5
1285
50.
1427
467
-0.6
5996
2-0
.034
0.12
7446
838
229
Dis
tLin
S-9
2.32
-914
.64
-99.
9418
82.9
5-4
0525
.129
417
2922
8.6
152
180.
4244
14-4
.937
27-4
.512
855
-0.0
5479
2-0
.501
447
-0.0
340.
1274
468
3833
0D
istL
inS
-92.
32-9
14.6
4-9
9.94
1882
.95
-303
75.5
1223
07.2
229
330.
215
218
1.76
4589
-3.7
0071
9-1
.936
129
-0.0
5479
2-0
.501
447
-0.0
340.
1274
468
3833
0D
istL
inS
-92.
32-6
47.7
5-4
3818
82.9
5-3
0375
.512
2307
.22
2933
0.2
152
181.
7645
89-3
.700
719
-1.9
3612
9-0
.240
132
-0.3
5512
6-0
.034
0.12
7446
838
432
Dis
tLin
S-9
2.32
-647
.75
-438
1882
.95
1413
6.68
1881
34.7
2943
1.8
152
182.
7143
161.
7223
051
4.43
6621
5-0
.240
132
-0.3
5512
6-0
.034
0.12
7446
838
432
Dis
tLin
S-9
2.32
-514
.3-7
09.3
1882
.95
1414
0.12
1881
34.7
2943
1.8
152
182.
7143
161.
7227
242
4.43
7040
6-0
.388
893
-0.2
8196
3-0
.034
0.12
7446
838
533
Dis
tLin
S-9
2.32
-514
.3-7
09.3
1882
.95
8620
9.48
2403
87.5
429
533.
415
218
3.46
8195
10.5
0310
413
.971
299
-0.3
8889
3-0
.281
963
-0.0
340.
1274
468
390
Dis
tLin
S-9
2.32
514.
370
9.35
-188
386
210.
4224
0388
.630
015
218
3.46
821
10.5
0321
913
.971
429
0.38
8898
0.28
1962
7-0
.034
-0.1
2744
7477
3910
2D
istL
inS
-92.
3251
4.3
709.
35-1
883
1414
0.72
1881
36.1
630
101.
615
218
2.71
4337
1.72
2797
34.
4371
348
0.38
8898
0.28
1962
7-0
.034
-0.1
2744
7477
3910
2D
istL
inS
-92.
3264
7.74
438.
01-1
883
1413
7.27
1881
36.1
630
101.
615
218
2.71
4337
1.72
2376
94.
4367
144
0.24
0137
10.
3551
206
-0.0
34-0
.127
4474
7739
203
Dis
tLin
S-9
2.32
647.
7443
8.01
-188
3-3
0364
.112
2325
.53
3020
3.2
152
181.
7648
54-3
.699
334
-1.9
3448
0.24
0137
10.
3551
206
-0.0
34-0
.127
4474
7739
203
Dis
tLin
S-9
2.32
914.
6499
.94
-188
3-3
0372
.712
2325
.53
3020
3.2
152
181.
7648
54-3
.700
379
-1.9
3552
50.
0547
917
0.50
1447
4-0
.034
-0.1
2744
7477
3930
5D
istL
inS
-92.
3291
4.64
99.9
4-1
883
-405
26.7
2939
8.54
3030
4.8
152
180.
4241
48-4
.937
466
-4.5
1331
80.
0547
917
0.50
1447
4-0
.034
-0.1
2744
7477
3930
5D
istL
inS
-92.
3212
03.8
-260
.4-1
883
-405
21.2
2939
8.54
3030
4.8
152
180.
4241
48-4
.936
797
-4.5
1264
9-0
.142
741
0.65
9961
6-0
.034
-0.1
2744
7477
3940
6D
istL
inS
-92.
3212
03.8
-260
.4-1
883
-140
68.2
-929
04.5
3040
6.4
152
18-1
.340
381
-1.7
1395
6-3
.054
337
-0.1
4274
10.
6599
616
-0.0
34-0
.127
4474
7739
406
Dis
tLin
S-9
2.32
1470
.7-5
98.4
-188
3-1
4067
.3-9
2904
.530
406.
415
218
-1.3
4038
1-1
.713
851
-3.0
5423
2-0
.328
087
0.80
6282
9-0
.034
-0.1
2744
7477
3950
8D
istL
inS
-92.
3214
70.7
-598
.4-1
883
4673
3.18
-242
323.
9130
508
152
18-3
.496
132
5.69
3613
52.
1974
814
-0.3
2808
70.
8062
829
-0.0
34-0
.127
4474
7739
508
Dis
tLin
S-9
2.32
1604
.1-8
69.8
-188
346
730.
42-2
4232
3.91
3050
815
218
-3.4
9613
25.
6932
773
2.19
7145
2-0
.476
848
0.87
9446
3-0
.034
-0.1
2744
7477
3953
3D
istL
inS
-92.
3216
04.1
-869
.8-1
883
6882
2.61
-283
068.
3130
533.
415
218
-4.0
8397
38.
3848
209
4.30
0848
3-0
.476
848
0.87
9446
3-0
.034
-0.1
2744
7477
400
Dis
tLin
S-9
5.02
1604
.210
2.01
-194
2.2
8092
.14
-285
237.
7931
015
218
-4.1
1527
30.
9858
845
-3.1
2938
80.
0559
265
0.87
9517
5-0
.035
-0.1
3145
5084
4076
.2D
istL
inS
-95.
0216
04.2
102.
01-1
942.
231
9.03
-407
480.
7831
76.2
152
18-5
.878
936
0.03
8868
2-5
.840
067
0.05
5926
50.
8795
175
-0.0
35-0
.131
4550
8441
0D
istL
inS
-971
.8-0
.13
2.71
-216
9.5
-607
31.6
-59.
2232
018
152
-0.0
0721
5-0
.876
206
-0.8
8342
10.
0014
857
-7.1
3E-0
5-0
.355
-0.1
4684
1158
4143
2D
istL
inS
-971
.8-0
.13
2.71
-216
9.5
-619
00.3
-3.7
132
431.
818
152
-0.0
0045
2-0
.893
068
-0.8
9352
0.00
1485
7-7
.13E
-05
-0.3
55-0
.146
8411
5841
864
Dis
tLin
S-9
71.8
-0.1
32.
71-2
169.
5-6
3069
.151
.79
3286
3.6
1815
20.
0063
1-0
.909
93-0
.903
620.
0014
857
-7.1
3E-0
5-0
.355
-0.1
4684
1158
420
Dis
tLin
S-9
71.8
-0.1
3-2
.71
2169
.48
6073
0.47
-59.
2233
018
152
-0.0
0721
50.
8761
898
0.86
8974
9-0
.001
486
-7.1
3E-0
5-0
.355
0.14
6840
481
4243
2D
istL
inS
-971
.8-0
.13
-2.7
121
69.4
861
900.
38-3
.71
3343
1.8
1815
2-0
.000
452
0.89
3068
70.
8926
167
-0.0
0148
6-7
.13E
-05
-0.3
550.
1468
4048
142
864
Dis
tLin
S-9
71.8
-0.1
3-2
.71
2169
.48
6307
0.29
51.7
933
863.
618
152
0.00
631
0.90
9947
60.
9162
573
-0.0
0148
6-7
.13E
-05
-0.3
550.
1468
4048
136
4.28
4831
.187
4.88
2909
.82
1573
4840
1271
.27
Max
.5.
7893
4811
.157
613
13.9
7142
90.
4796
491
2.64
8623
90.
1331
0.19
6950
13-1
494
-483
1.1
-874
.9-2
909.
9-1
5734
8-4
0748
1.19
Min
.-5
.878
941
-11.
0179
7-1
2.16
042
-0.4
7964
4-2
.648
624
-0.5
46-0
.196
9521
6C
ompa
re w
ith26
.50.
75.
310
.80.
7
237
T
able
II -
5. E
lem
ent f
orce
s –fr
ames
for
conf
igur
atio
n (c
) sof
a fr
ame
unde
r m
ediu
m-s
ervi
ce
acce
ptan
ce le
vel l
oad
238
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CseT
yP
V2V3
TM
2M
3m
eEm
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xtm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
220
0P
oncL
inS
-218
08E
-12
-34.
80
08E
-10
10
152.
418
.26
1.13
6E-1
40
1.14
E-1
4-0
.018
758
4.26
E-1
5-0
.78
020
38.1
Pon
cLin
S-2
180
8E-1
2-3
4.8
013
265E
-10
138
.115
2.4
18.2
67.
099E
-15
0.15
6572
0.15
6572
-0.0
1875
84.
26E
-15
-0.7
80
2076
.2P
oncL
inS
-218
08E
-12
-34.
80
2652
2E-1
01
76.2
152.
418
.26
2.83
9E-1
50.
3131
430.
3131
43-0
.018
758
4.26
E-1
5-0
.78
021
0P
oncL
inS
-218
0-0
-34.
780
-2E-
12-8
E-1
02
015
2.4
18.2
6-1
.14E
-14
-1.8
5E-1
6-1
.15E
-14
-0.0
1874
7-8
.52E
-15
-0.7
80
2138
.1P
oncL
inS
-218
0-0
-34.
780
1325
-2E
-10
238
.115
2.4
18.2
6-2
.84E
-15
0.15
6452
0.15
6452
-0.0
1874
7-8
.52E
-15
-0.7
80
2176
.2P
oncL
inS
-218
0-0
-34.
780
2650
4E-1
02
76.2
152.
418
.26
5.67
9E-1
50.
3129
020.
3129
02-0
.018
747
-8.5
2E-1
5-0
.78
022
0P
oncL
inS
-218
032
7034
.80
8E-1
3-2
E-1
03
015
2.4
18.2
6-2
.84E
-15
9.26
E-1
7-2
.75E
-15
0.01
8758
1.76
2776
-0.7
80
2238
.1P
oncL
inS
-218
032
7034
.80
-132
6-1
2460
03
38.1
152.
418
.26
-1.7
6277
8-0
.156
563
-1.9
1934
0.01
8758
1.76
2776
-0.7
80
2276
.2P
oncL
inS
-218
032
7034
.80
-265
2-2
4919
93
76.2
152.
418
.26
-3.5
2555
5-0
.313
126
-3.8
3868
10.
0187
581.
7627
76-0
.78
023
0P
oncL
inS
-218
0-3
270
34.7
80
8E-1
30
40
152.
418
.26
09.
26E
-17
9.26
E-1
70.
0187
47-1
.762
776
-0.7
80
2338
.1P
oncL
inS
-218
0-3
270
34.7
80
-132
512
4600
438
.115
2.4
18.2
61.
7627
775
-0.1
5646
1.60
6317
0.01
8747
-1.7
6277
6-0
.78
023
76.2
Pon
cLin
S-2
180
-327
034
.78
0-2
650
2491
994
76.2
152.
418
.26
3.52
5555
1-0
.312
923.
2126
350.
0187
47-1
.762
776
-0.7
80
650
Pon
cLin
S-2
673
-215
6-1
011
-100
27-1
E+0
5-4
1963
35
015
2.4
18.2
6-5
.936
768
-12.
0365
5-1
7.97
332
-0.5
4496
6-1
.162
258
-0.9
6-0
.657
7267
265
88.9
Pon
cLin
S-2
673
-215
6-1
011
-100
27-1
2058
-227
943
588
.915
2.4
18.2
6-3
.224
827
-1.4
2374
-4.6
4856
6-0
.544
966
-1.1
6225
8-0
.96
-0.6
5772
672
6588
.9P
oncL
inS
-267
3-1
978
-649
.4-1
0027
-120
58-2
2794
35
88.9
152.
418
.26
-3.2
2482
7-1
.423
74-4
.648
566
-0.3
5003
5-1
.066
356
-0.9
6-0
.657
7267
265
178
Pon
cLin
S-2
673
-197
8-6
49.4
-100
2745
673
-520
70.5
517
815
2.4
18.2
6-0
.736
669
5.39
2924
4.65
6255
-0.3
5003
5-1
.066
356
-0.9
6-0
.657
7267
265
178
Pon
cLin
S-2
673
-162
2-1
98.8
-100
2745
673
-520
70.5
517
815
2.4
18.2
6-0
.736
669
5.39
2924
4.65
6255
-0.1
0714
7-0
.874
54-0
.96
-0.6
5772
672
6526
7P
oncL
inS
-267
3-1
622
-198
.8-1
0027
6334
592
166
526
715
2.4
18.2
61.
3039
212
7.47
9573
8.78
3494
-0.1
0714
7-0
.874
54-0
.96
-0.6
5772
672
6526
7P
oncL
inS
-267
3-1
237
281.
62-1
0027
6334
592
166
526
715
2.4
18.2
61.
3039
212
7.47
9573
8.78
3494
0.15
1799
-0.6
6666
1-0
.96
-0.6
5772
672
6535
6P
oncL
inS
-267
3-1
237
281.
62-1
0027
3830
920
2117
535
615
2.4
18.2
62.
8594
596
4.52
3364
7.38
2824
0.15
1799
-0.6
6666
1-0
.96
-0.6
5772
672
6535
6P
oncL
inS
-267
3-8
8173
2.23
-100
2738
317
2021
175
356
152.
418
.26
2.85
9459
64.
5243
17.
3837
70.
3946
87-0
.474
845
-0.9
6-0
.657
7267
265
445
Pon
cLin
S-2
673
-881
732.
23-1
0027
-267
7828
0433
544
515
2.4
18.2
63.
9674
304
-3.1
6191
10.
8055
190.
3946
87-0
.474
845
-0.9
6-0
.657
7267
265
445
Pon
cLin
S-2
673
-703
1093
.9-1
0027
-267
7828
0433
544
515
2.4
18.2
63.
9674
304
-3.1
6191
10.
8055
190.
5896
19-0
.378
937
-0.9
6-0
.657
7267
265
533
Pon
cLin
S-2
673
-703
1093
.9-1
0027
-1E
+05
3429
305
533
152.
418
.26
4.85
1617
4-1
4.64
428
-9.7
9266
70.
5896
19-0
.378
937
-0.9
6-0
.657
7267
272
0P
oncL
inS
-226
7-7
27-1
052
-0.1
1-1
E+0
594
518.
16
015
2.4
18.2
61.
3371
98-1
4.84
648
-13.
5092
8-0
.567
265
-0.3
9164
7-0
.81
-7.2
158E
-06
7210
2P
oncL
inS
-226
7-7
27-1
052
-0.1
1-1
8812
1683
406
102
152.
418
.26
2.38
1587
8-2
.221
273
0.16
0314
-0.5
6726
5-0
.391
647
-0.8
1-7
.215
8E-0
672
102
Pon
cLin
S-2
267
-549
-690
.8-0
.11
-188
1216
8340
610
215
2.4
18.2
62.
3815
878
-2.2
2127
30.
1603
14-0
.372
334
-0.2
9573
9-0
.81
-7.2
158E
-06
7220
3P
oncL
inS
-226
7-5
49-6
90.8
-0.1
151
369
2240
836
203
152.
418
.26
3.17
0224
66.
0654
719.
2356
95-0
.372
334
-0.2
9573
9-0
.81
-7.2
158E
-06
7220
3P
oncL
inS
-226
7-1
93-2
40.2
-0.1
151
369
2240
836
203
152.
418
.26
3.17
0224
66.
0654
719.
2356
95-0
.129
446
-0.1
0392
3-0
.81
-7.2
158E
-06
7230
5P
oncL
inS
-226
7-1
93-2
40.2
-0.1
175
768
2436
726
305
152.
418
.26
3.44
7355
48.
9464
8512
.393
84-0
.129
446
-0.1
0392
3-0
.81
-7.2
158E
-06
7230
5P
oncL
inS
-226
719
2.9
240.
26-0
.11
7576
824
3672
630
515
2.4
18.2
63.
4473
554
8.94
6485
12.3
9384
0.12
9505
0.10
3956
-0.8
1-7
.215
8E-0
672
406
Pon
cLin
S-2
267
192.
924
0.26
-0.1
151
358
2240
776
406
152.
418
.26
3.17
0141
76.
0642
349.
2343
760.
1295
050.
1039
56-0
.81
-7.2
158E
-06
7240
6P
oncL
inS
-226
754
8.7
690.
86-0
.11
5136
822
4077
640
615
2.4
18.2
63.
1701
417
6.06
5316
9.23
5458
0.37
2388
0.29
5771
-0.8
1-7
.215
8E-0
672
508
Pon
cLin
S-2
267
548.
769
0.86
-0.1
1-1
8824
1683
286
508
152.
418
.26
2.38
1422
-2.2
2266
60.
1587
560.
3723
880.
2957
71-0
.81
-7.2
158E
-06
7250
8P
oncL
inS
-226
772
6.7
1052
.5-0
.11
-188
2416
8328
650
815
2.4
18.2
62.
3814
22-2
.222
666
0.15
8756
0.56
7319
0.39
1679
-0.8
1-7
.215
8E-0
672
610
Pon
cLin
S-2
267
726.
710
52.5
-0.1
1-1
E+0
594
500.
66
610
152.
418
.26
1.33
6949
4-1
4.84
911
-13.
5121
60.
5673
190.
3916
79-0
.81
-7.2
158E
-06
800
Pon
cLin
S-2
673
703.
1-1
094
1002
7-1
E+0
534
2948
70
152.
418
.26
4.85
1863
8-1
4.64
279
-9.7
9092
1-0
.589
559
0.37
8964
-0.9
60.
6577
3656
480
88.9
Pon
cLin
S-2
673
703.
1-1
094
1002
7-2
6776
2804
457
88.9
152.
418
.26
3.96
7609
1-3
.161
588
0.80
6021
-0.5
8955
90.
3789
64-0
.96
0.65
7736
564
8088
.9P
oncL
inS
-267
388
1-7
32.1
1002
7-2
6776
2804
457
88.9
152.
418
.26
3.96
7609
1-3
.161
588
0.80
6021
-0.3
9462
80.
4748
72-0
.96
0.65
7736
564
8017
8P
oncL
inS
-267
388
1-7
32.1
1002
738
309
2021
257
178
152.
418
.26
2.85
9570
74.
5234
587.
3830
28-0
.394
628
0.47
4872
-0.9
60.
6577
3656
480
178
Pon
cLin
S-2
673
1237
-281
.510
027
3830
920
2125
717
815
2.4
18.2
62.
8595
707
4.52
3458
7.38
3028
-0.1
5174
0.66
6688
-0.9
60.
6577
3656
480
267
Pon
cLin
S-2
673
1237
-281
.510
027
6333
692
169.
17
267
152.
418
.26
1.30
3964
37.
4784
898.
7824
53-0
.151
740.
6666
88-0
.96
0.65
7736
564
8026
7P
oncL
inS
-267
316
2319
8.9
1002
763
336
9216
9.1
726
715
2.4
18.2
61.
3039
643
7.47
8489
8.78
2453
0.10
7211
0.87
4567
-0.9
60.
6577
3656
480
356
Pon
cLin
S-2
673
1623
198.
910
027
4565
4-5
2072
.27
356
152.
418
.26
-0.7
3669
35.
3906
644.
6539
70.
1072
110.
8745
67-0
.96
0.65
7736
564
8035
6P
oncL
inS
-267
319
7864
9.5
1002
745
662
-520
72.2
735
615
2.4
18.2
6-0
.736
693
5.39
161
4.65
4916
0.35
0094
1.06
6383
-0.9
60.
6577
3656
480
445
Pon
cLin
S-2
673
1978
649.
510
027
-120
79-2
2794
97
445
152.
418
.26
-3.2
2491
9-1
.426
229
-4.6
5114
80.
3500
941.
0663
83-0
.96
0.65
7736
564
8044
5P
oncL
inS
-267
321
5610
11.1
1002
7-1
2079
-227
949
744
515
2.4
18.2
6-3
.224
919
-1.4
2622
9-4
.651
148
0.54
5025
1.16
2291
-0.9
60.
6577
3656
4
239
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CseT
yP
V2V3
TM
2M
3m
eEm
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xtm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
2
8053
3P
oncL
inS
-267
321
5610
11.1
1002
7-1
E+0
5-4
1964
47
533
152.
418
.26
-5.9
3692
8-1
2.04
022
-17.
9771
50.
5450
251.
1622
91-0
.96
0.65
7736
564
870
Pon
cLin
S19
.61
-214
0-1
036
1015
7-1
E+0
594
383.
58
015
2.4
18.2
61.
3352
927
-12.
9690
1-1
1.63
372
-0.5
5844
2-1
.153
283
0.00
70.
6662
8795
287
88.9
Pon
cLin
S19
.61
-214
0-1
036
1015
7-1
7732
2845
938
88.9
152.
418
.26
4.02
6282
6-2
.093
793
1.93
249
-0.5
5844
2-1
.153
283
0.00
70.
6662
8795
287
88.9
Pon
cLin
S19
.61
-196
2-6
74.4
1015
7-1
7726
2845
938
88.9
152.
418
.26
4.02
6282
6-2
.093
034
1.93
3249
-0.3
6351
-1.0
5737
60.
007
0.66
6287
952
8717
8P
oncL
inS
19.6
1-1
962
-674
.410
157
4222
745
8984
817
815
2.4
18.2
66.
4934
886
4.98
6036
11.4
7952
-0.3
6351
-1.0
5737
60.
007
0.66
6287
952
8717
8P
oncL
inS
19.6
1-1
606
-223
.810
157
4221
945
8984
817
815
2.4
18.2
66.
4934
886
4.98
5089
11.4
7858
-0.1
2062
2-0
.865
560.
007
0.66
6287
952
8726
7P
oncL
inS
19.6
1-1
606
-223
.810
157
6211
360
1740
826
715
2.4
18.2
68.
5131
269
7.33
4144
15.8
4727
-0.1
2062
2-0
.865
560.
007
0.66
6287
952
8726
7P
oncL
inS
19.6
1-1
220
256.
6310
157
6211
360
1740
826
715
2.4
18.2
68.
5131
269
7.33
4144
15.8
4727
0.13
8329
-0.6
5768
10.
007
0.66
6287
952
8735
6P
oncL
inS
19.6
1-1
220
256.
6310
157
3929
971
0210
835
615
2.4
18.2
610
.047
714
4.64
0341
14.6
8805
0.13
8329
-0.6
5768
10.
007
0.66
6287
952
8735
6P
oncL
inS
19.6
1-8
6470
7.23
1015
739
307
7102
108
356
152.
418
.26
10.0
4771
44.
6412
8714
.689
0.38
1212
-0.4
6586
50.
007
0.66
6287
952
8744
5P
oncL
inS
19.6
1-8
6470
7.23
1015
7-2
3565
7870
448
445
152.
418
.26
11.1
3473
3-2
.782
538.
3522
020.
3812
12-0
.465
865
0.00
70.
6662
8795
287
445
Pon
cLin
S19
.61
-686
1068
.910
157
-235
6578
7044
844
515
2.4
18.2
611
.134
733
-2.7
8253
8.35
2202
0.57
6143
-0.3
6995
70.
007
0.66
6287
952
8753
3P
oncL
inS
19.6
1-6
8610
68.9
1015
7-1
E+0
584
8061
853
315
2.4
18.2
611
.997
968
-14.
0025
-2.0
0453
0.57
6143
-0.3
6995
70.
007
0.66
6287
952
940
Pon
cLin
S13
.56
-727
-105
2-0
.076
-1E
+05
8423
379
015
2.4
18.2
611
.916
979
-14.
6190
6-2
.702
078
-0.5
6726
5-0
.391
647
0.00
5-4
.969
7E-0
694
102
Pon
cLin
S13
.56
-727
-105
2-0
.076
-168
8691
6158
910
215
2.4
18.2
612
.961
365
-1.9
9385
410
.967
51-0
.567
265
-0.3
9164
70.
005
-4.9
697E
-06
9410
2P
oncL
inS
13.5
6-5
49-6
90.8
-0.0
76-1
6879
9161
589
102
152.
418
.26
12.9
6136
5-1
.992
986
10.9
6838
-0.3
7233
4-0
.295
739
0.00
5-4
.969
7E-0
694
203
Pon
cLin
S13
.56
-549
-690
.8-0
.076
5330
297
1901
920
315
2.4
18.2
613
.749
998
6.29
3759
20.0
4376
-0.3
7233
4-0
.295
739
0.00
5-4
.969
7E-0
694
203
Pon
cLin
S13
.56
-193
-240
.2-0
.076
5329
397
1901
920
315
2.4
18.2
613
.749
998
6.29
2678
20.0
4268
-0.1
2944
6-0
.103
923
0.00
5-4
.969
7E-0
694
305
Pon
cLin
S13
.56
-193
-240
.2-0
.076
7769
399
1489
930
515
2.4
18.2
614
.027
124
9.17
3693
23.2
0082
-0.1
2944
6-0
.103
923
0.00
5-4
.969
7E-0
694
305
Pon
cLin
S13
.56
192.
924
0.26
-0.0
7677
693
9914
899
305
152.
418
.26
14.0
2712
49.
1736
9323
.200
820.
1295
050.
1039
560.
005
-4.9
697E
-06
9440
6P
oncL
inS
13.5
619
2.9
240.
26-0
.076
5328
397
1895
940
615
2.4
18.2
613
.749
906
6.29
1442
20.0
4135
0.12
9505
0.10
3956
0.00
5-4
.969
7E-0
694
406
Pon
cLin
S13
.56
548.
769
0.86
-0.0
7653
292
9718
959
406
152.
418
.26
13.7
4990
66.
2925
2420
.042
430.
3723
880.
2957
710.
005
-4.9
697E
-06
9450
8P
oncL
inS
13.5
654
8.7
690.
86-0
.076
-169
0091
6145
950
815
2.4
18.2
612
.961
182
-1.9
9545
710
.965
720.
3723
880.
2957
710.
005
-4.9
697E
-06
9450
8P
oncL
inS
13.5
672
6.7
1052
.5-0
.076
-169
0091
6145
950
815
2.4
18.2
612
.961
182
-1.9
9545
710
.965
720.
5673
190.
3916
790.
005
-4.9
697E
-06
9461
0P
oncL
inS
13.5
672
6.7
1052
.5-0
.076
-1E
+05
8423
179
610
152.
418
.26
11.9
1670
5-1
4.62
19-2
.705
191
0.56
7319
0.39
1679
0.00
5-4
.969
7E-0
610
20
Pon
cLin
S19
.69
686.
4-1
069
-101
57-1
E+0
584
8042
100
152.
418
.26
11.9
9769
5-1
4.00
095
-2.0
0326
-0.5
7608
90.
3699
890.
007
-0.6
6626
762
102
88.9
Pon
cLin
S19
.69
686.
4-1
069
-101
57-2
3561
7870
2010
88.9
152.
418
.26
11.1
3438
2-2
.782
062
8.35
232
-0.5
7608
90.
3699
890.
007
-0.6
6626
762
102
88.9
Pon
cLin
S19
.69
864.
3-7
07.1
-101
57-2
3555
7870
2010
88.9
152.
418
.26
11.1
3438
2-2
.781
302
8.35
3079
-0.3
8115
80.
4658
970.
007
-0.6
6626
762
102
178
Pon
cLin
S19
.69
864.
3-7
07.1
-101
5739
309
7101
8010
178
152.
418
.26
10.0
4728
54.
6414
414
.688
72-0
.381
158
0.46
5897
0.00
7-0
.666
2676
210
217
8P
oncL
inS
19.6
912
20-2
56.5
-101
5739
301
7101
8010
178
152.
418
.26
10.0
4728
54.
6404
9414
.687
78-0
.138
270.
6577
130.
007
-0.6
6626
762
102
267
Pon
cLin
S19
.69
1220
-256
.5-1
0157
6210
660
1704
1026
715
2.4
18.2
68.
5126
27.
3332
2315
.845
84-0
.138
270.
6577
130.
007
-0.6
6626
762
102
267
Pon
cLin
S19
.69
1606
223.
89-1
0157
6210
660
1704
1026
715
2.4
18.2
68.
5126
27.
3332
2315
.845
840.
1206
810.
8655
920.
007
-0.6
6626
762
102
356
Pon
cLin
S19
.69
1606
223.
89-1
0157
4220
245
8943
1035
615
2.4
18.2
66.
4929
037
4.98
3093
11.4
760.
1206
810.
8655
920.
007
-0.6
6626
762
102
356
Pon
cLin
S19
.69
1962
674.
49-1
0157
4221
045
8943
1035
615
2.4
18.2
66.
4929
037
4.98
4039
11.4
7694
0.36
3564
1.05
7408
0.00
7-0
.666
2676
210
244
5P
oncL
inS
19.6
919
6267
4.49
-101
57-1
7752
2845
4610
445
152.
418
.26
4.02
5619
8-2
.096
104
1.92
9516
0.36
3564
1.05
7408
0.00
7-0
.666
2676
210
244
5P
oncL
inS
19.6
921
4010
36.1
-101
57-1
7752
2845
4610
445
152.
418
.26
4.02
5619
8-2
.096
104
1.92
9516
0.55
8496
1.15
3316
0.00
7-0
.666
2676
210
253
3P
oncL
inS
19.6
921
4010
36.1
-101
57-1
E+0
594
331.
110
533
152.
418
.26
1.33
4552
-12.
9724
-11.
6378
50.
5584
961.
1533
160.
007
-0.6
6626
762
112
0P
oncL
inS
-164
911
.541
.44
-125
5173
815
4631
.59
110
18.2
615
2.4
0.54
6883
51.
0442
971.
5911
810.
0223
370.
0061
99-0
.59
-0.8
2332
491
112
406
Pon
cLin
S-1
649
11.5
41.4
4-1
2551
5697
3-4
3.41
1140
618
.26
152.
4-0
.005
126
0.80
6027
0.80
0901
0.02
2337
0.00
6199
-0.5
9-0
.823
3249
111
281
3P
oncL
inS
-164
911
.541
.44
-125
5140
131
-471
8.42
1181
318
.26
152.
4-0
.557
136
0.56
7756
0.01
062
0.02
2337
0.00
6199
-0.5
9-0
.823
3249
114
60
Pon
cLin
S-1
649
11.5
-41.
4712
551
-738
3746
30.9
912
018
.26
152.
40.
5468
127
-1.0
4461
5-0
.497
803
-0.0
2235
30.
0061
99-0
.59
0.82
3300
635
146
406
Pon
cLin
S-1
649
11.5
-41.
4712
551
-569
83-4
3.5
1240
618
.26
152.
4-0
.005
136
-0.8
0616
6-0
.811
303
-0.0
2235
30.
0061
99-0
.59
0.82
3300
635
146
813
Pon
cLin
S-1
649
11.5
-41.
4712
551
-401
28-4
718
1281
318
.26
152.
4-0
.557
087
-0.5
6771
7-1
.124
804
-0.0
2235
30.
0061
99-0
.59
0.82
3300
635
180
0P
oncL
inS
594
43.4
50.
66-1
2551
-549
.914
632.
213
015
2.4
18.2
60.
2070
097
-0.0
6492
70.
1420
830.
0003
560.
0234
20.
213
-0.8
2332
491
180
406
Pon
cLin
S59
443
.45
0.66
-125
51-8
17.7
-302
4.97
1340
615
2.4
18.2
6-0
.042
796
-0.0
9654
9-0
.139
345
0.00
0356
0.02
342
0.21
3-0
.823
3249
118
081
3P
oncL
inS
594
43.4
50.
66-1
2551
-108
5-2
0682
.213
813
152.
418
.26
-0.2
9260
1-0
.128
17-0
.420
771
0.00
0356
0.02
342
0.21
3-0
.823
3249
121
40
Pon
cLin
S59
4.2
-43.
5-0
.66
1255
1-1
086
-207
11.5
140
152.
418
.26
-0.2
9301
7-0
.128
211
-0.4
2122
8-0
.000
356
-0.0
2344
70.
214
0.82
3300
635
240
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CseT
yP
V2V3
TM
2M
3m
eEm
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xtm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
2
214
406
Pon
cLin
S59
4.2
-43.
5-0
.66
1255
1-8
17.8
-303
1.24
1440
615
2.4
18.2
6-0
.042
885
-0.0
9656
6-0
.139
45-0
.000
356
-0.0
2344
70.
214
0.82
3300
635
214
813
Pon
cLin
S59
4.2
-43.
5-0
.66
1255
1-5
49.8
1464
9.1
1481
315
2.4
18.2
60.
2072
48-0
.064
920.
1423
28-0
.000
356
-0.0
2344
70.
214
0.82
3300
635
247
0P
oncL
inS
-8.2
3-6
1.7
-15.
7412
847
-405
3-4
2674
.415
015
2.4
18.2
6-0
.603
737
-0.4
7854
5-1
.082
283
-0.0
0848
4-0
.033
263
-00.
8427
6429
124
721
6P
oncL
inS
-8.2
3-6
1.7
-15.
7412
847
-654
.3-2
9351
.915
216
152.
418
.26
-0.4
1525
6-0
.077
261
-0.4
9251
7-0
.008
484
-0.0
3326
3-0
0.84
2764
291
247
432
Pon
cLin
S-8
.23
-61.
7-1
5.74
1284
727
44.2
-160
29.3
1543
215
2.4
18.2
6-0
.226
775
0.32
4023
0.09
7248
-0.0
0848
4-0
.033
263
-00.
8427
6429
126
50
Pon
cLin
S-8
.29
61.8
3-1
5.87
-128
47-4
087
4273
2.3
160
152.
418
.26
0.60
4556
4-0
.482
536
0.12
202
-0.0
0855
40.
0333
28-0
-0.8
4276
626
265
216
Pon
cLin
S-8
.29
61.8
3-1
5.87
-128
47-6
60.7
2938
416
216
152.
418
.26
0.41
5711
2-0
.078
010.
3377
01-0
.008
554
0.03
3328
-0-0
.842
7662
626
543
2P
oncL
inS
-8.2
961
.83
-15.
87-1
2847
2765
.316
035.
716
432
152.
418
.26
0.22
6866
10.
3265
170.
5533
83-0
.008
554
0.03
3328
-0-0
.842
7662
628
30
Pon
cLin
S63
.81
400
25-1
748
1456
425
4137
170
152.
418
.26
3.59
5409
21.
7196
355.
3150
440.
0134
760.
2156
190.
023
-0.1
1466
967
283
330
Pon
cLin
S63
.81
400
25-1
748
6309
.612
2051
1733
015
2.4
18.2
61.
7267
189
0.74
5012
2.47
1731
0.01
3476
0.21
5619
0.02
3-0
.114
6696
728
366
0P
oncL
inS
63.8
140
025
-174
8-1
945
-100
35.1
1766
015
2.4
18.2
6-0
.141
971
-0.2
2961
-0.3
7158
10.
0134
760.
2156
190.
023
-0.1
1466
967
311
0P
oncL
inS
63.8
140
0.1
24.9
917
44.4
1941
.310
037.
718
015
2.4
18.2
60.
1420
084
0.22
9218
0.37
1226
0.01
347
0.21
5646
0.02
30.
1144
2892
631
133
0P
oncL
inS
63.8
140
0.1
24.9
917
44.4
-631
0-1
2206
718
330
152.
418
.26
-1.7
2694
7-0
.745
078
-2.4
7202
50.
0134
70.
2156
460.
023
0.11
4428
926
311
660
Pon
cLin
S63
.81
400.
124
.99
1744
.4-1
4561
-254
172
1866
015
2.4
18.2
6-3
.595
903
-1.7
1937
4-5
.315
277
0.01
347
0.21
5646
0.02
30.
1144
2892
633
70
Pon
cLin
S-6
17-6
3.8
24.9
1-2
575
2669
4-1
9814
190
18.2
615
2.4
-2.3
3957
50.
3776
6-1
.961
914
0.01
3427
-0.0
344
-0.2
2-0
.168
9305
733
761
0P
oncL
inS
-617
-63.
824
.91
-257
511
509
1908
9.4
1961
018
.26
152.
42.
2540
126
0.16
2821
2.41
6834
0.01
3427
-0.0
344
-0.2
2-0
.168
9305
733
80
Pon
cLin
S-1
017
-0-0
.078
0.75
9764
.4-1
110.
2120
018
.26
152.
4-0
.131
090.
1381
430.
0070
53-4
.22E
-05
-1.6
E-0
6-0
.37
4.91
987E
-05
338
610
Pon
cLin
S-1
017
-0-0
.078
0.75
9812
.1-1
108.
4120
610
18.2
615
2.4
-0.1
3087
80.
1388
170.
0079
4-4
.22E
-05
-1.6
E-0
6-0
.37
4.91
987E
-05
339
0P
oncL
inS
-617
63.8
1-2
5.08
2580
.311
560
1908
7.1
210
18.2
615
2.4
2.25
3746
90.
1635
482.
4172
95-0
.013
519
0.03
4395
-0.2
20.
1692
6053
233
961
0P
oncL
inS
-617
63.8
1-2
5.08
2580
.326
846
-198
11.3
2161
018
.26
152.
4-2
.339
256
0.37
9808
-1.9
5944
8-0
.013
519
0.03
4395
-0.2
20.
1692
6053
234
00
Pon
cLin
S-1
5.7
-8.2
3-6
1.71
-144
62-1
2847
-314
422
018
.26
152.
4-0
.371
234
-0.1
8175
8-0
.552
992
-0.0
3326
3-0
.004
436
-0.0
1-0
.948
6792
234
041
9P
oncL
inS
-15.
7-8
.23
-61.
71-1
4462
1301
430
5.08
2241
918
.26
152.
40.
0360
229
0.18
4117
0.22
014
-0.0
3326
3-0
.004
436
-0.0
1-0
.948
6792
234
083
8P
oncL
inS
-15.
7-8
.23
-61.
71-1
4462
3887
537
54.1
522
838
18.2
615
2.4
0.44
3278
20.
5499
910.
9932
7-0
.033
263
-0.0
0443
6-0
.01
-0.9
4867
922
374
0P
oncL
inS
-15.
9-8
.29
61.8
314
465
1284
7-3
168.
3523
018
.26
152.
4-0
.374
109
0.18
1759
-0.1
9235
0.03
3328
-0.0
0446
8-0
.01
0.94
8902
254
374
419
Pon
cLin
S-1
5.9
-8.2
961
.83
1446
5-1
3064
306.
7123
419
18.2
615
2.4
0.03
6215
3-0
.184
823
-0.1
4860
80.
0333
28-0
.004
468
-0.0
10.
9489
0225
437
483
8P
oncL
inS
-15.
9-8
.29
61.8
314
465
-389
7537
81.7
723
838
18.2
615
2.4
0.44
6539
5-0
.551
405
-0.1
0486
50.
0333
28-0
.004
468
-0.0
10.
9489
0225
440
80
Pon
cLin
S-5
5.6
-555
-9.1
713
748
-334
9-3
6073
324
015
2.4
18.2
6-5
.103
485
-0.3
9539
-5.4
9887
5-0
.004
943
-0.2
9937
8-0
.02
0.90
1867
655
408
330
Pon
cLin
S-5
5.6
-555
-9.1
713
748
-320
.7-1
7733
624
330
152.
418
.26
-2.5
0886
-0.0
3787
2-2
.546
732
-0.0
0494
3-0
.299
378
-0.0
20.
9018
6765
540
845
6P
oncL
inS
-55.
6-5
55-9
.17
1374
883
3.39
-107
429
2445
615
2.4
18.2
6-1
.519
861
0.09
8404
-1.4
2145
7-0
.004
943
-0.2
9937
8-0
.02
0.90
1867
655
408
456
Pon
cLin
S-6
3.8
-617
-24.
91-2
6694
-314
8-1
2196
225
015
2.4
18.2
6-1
.725
454
-0.3
7167
-2.0
9712
5-0
.013
427
-0.3
3264
1-0
.02
-1.7
5110
912
408
660
Pon
cLin
S-6
3.8
-617
-24.
91-2
6694
1942
.541
39.1
225
204
152.
418
.26
0.05
8558
30.
2293
640.
2879
23-0
.013
427
-0.3
3264
1-0
.02
-1.7
5110
912
436
0P
oncL
inS
-63.
8-6
17-2
5.08
2684
6-1
943
-413
4.98
260
152.
418
.26
-0.0
585
-0.2
2946
3-0
.287
963
-0.0
1351
9-0
.332
673
-0.0
21.
7610
6693
143
620
3P
oncL
inS
-63.
8-6
17-2
5.08
2684
631
4112
1004
2620
315
2.4
18.2
61.
7119
063
0.37
0877
2.08
2783
-0.0
1351
9-0
.332
673
-0.0
21.
7610
6693
143
620
3P
oncL
inS
-55.
5-5
55-9
.21
-136
99-8
44.4
1065
6627
015
2.4
18.2
61.
5076
423
-0.0
9970
61.
4079
36-0
.004
964
-0.2
9934
5-0
.02
-0.8
9866
252
436
330
Pon
cLin
S-5
5.5
-555
-9.2
1-1
3699
328.
9617
7340
2712
715
2.4
18.2
62.
5089
218
0.03
8843
2.54
7764
-0.0
0496
4-0
.299
345
-0.0
2-0
.898
6625
243
666
0P
oncL
inS
-55.
5-5
55-9
.21
-136
9933
69.2
3607
1727
458
152.
418
.26
5.10
3255
60.
3978
265.
5010
81-0
.004
964
-0.2
9934
5-0
.02
-0.8
9866
252
472
0P
oncL
inS
-212
1-4
0.2
-6.1
357
24.7
120.
04-2
3568
.228
015
2.4
18.2
6-0
.333
432
0.01
4174
-0.3
1925
8-0
.003
304
-0.0
2168
5-0
.76
0.37
5527
659
472
406
Pon
cLin
S-2
121
-40.
2-6
.13
5724
.726
11.6
-721
6.73
2840
615
2.4
18.2
6-0
.102
099
0.30
8364
0.20
6265
-0.0
0330
4-0
.021
685
-0.7
60.
3755
2765
947
281
3P
oncL
inS
-212
1-4
0.2
-6.1
357
24.7
5103
.191
34.7
428
813
152.
418
.26
0.12
9234
0.60
2554
0.73
1788
-0.0
0330
4-0
.021
685
-0.7
60.
3755
2765
950
60
Pon
cLin
S-2
121
-40.
26.
04-5
725
-156
.4-2
3566
.429
015
2.4
18.2
6-0
.333
406
-0.0
1847
2-0
.351
878
0.00
3256
-0.0
2168
5-0
.76
-0.3
7552
307
506
406
Pon
cLin
S-2
121
-40.
26.
04-5
725
-261
2-7
215.
5829
406
152.
418
.26
-0.1
0208
3-0
.308
453
-0.4
1053
60.
0032
56-0
.021
685
-0.7
6-0
.375
5230
750
681
3P
oncL
inS
-212
1-4
0.2
6.04
-572
5-5
068
9135
.25
2981
315
2.4
18.2
60.
1292
412
-0.5
9843
6-0
.469
195
0.00
3256
-0.0
2168
5-0
.76
-0.3
7552
307
Max
594.
232
7010
93.9
2684
677
693
9914
890
838
152.
415
2.4
14.0
2712
49.
1736
9323
.200
820.
5896
191.
7627
760.
214
1.76
1066
931
Min
-267
3-3
270
-109
4-2
6694
-1E
+05
-419
644
00
18.2
618
.26
-5.9
3692
8-1
4.84
911
-17.
9771
5-0
.589
559
-1.7
6277
6-0
.96
-1.7
5110
912
26.5
0.7
5.3
10.8
0.7
241
Table II - 6. Element joint forces –Links for configuration (c) sofa frame under medium-service acceptance level load TABLE: Element Joint Forces - LinksLinkLinkElemJoint utputCaCaseType F1 F2 F3 M1 M2 M3Text Text Text Text Text N N N N-mm N-mm N-mm
1 5 405 PonctuLinStatic 476 1 5 -34 12082 -21 5 5 PonctuLinStatic -476 -1 -5 0 0 23 6 346 PonctuLinStatic 0 -25 0 -27 1 23 6 9 PonctuLinStatic 0 25 0 -1 -1 -24 7 286 PonctuLinStatic 336 -1 -5 34 8547 04 7 312 PonctuLinStatic -336 1 5 0 0 05 8 285 PonctuLinStatic -336 -1 -5 34 -8547 05 8 313 PonctuLinStatic 336 1 5 0 0 06 9 406 PonctuLinStatic -476 1 5 -34 -12082 26 9 6 PonctuLinStatic 476 -1 -5 0 0 -27 10 379 PonctuLinStatic 0 -25 0 11 -1 -27 10 8 PonctuLinStatic 0 25 0 -1 1 28 11 225 PonctuLinStatic 0 -171 0 1 -1 -28 11 4 PonctuLinStatic 0 171 0 -1 1 29 12 159 PonctuLinStatic 0 1199 0 1 -1 -29 12 36 PonctuLinStatic 0 -1199 0 -1 1 210 1 2 PonctuLinStatic 0 0 0 0 0 010 1 21 PonctuLinStatic 0 0 0 0 0 011 2 1 PonctuLinStatic 0 0 0 0 0 011 2 56 PonctuLinStatic 0 0 0 0 0 012 3 35 PonctuLinStatic 0 0 0 0 0 012 3 3 PonctuLinStatic 0 0 0 0 0 013 4 36 PonctuLinStatic 0 0 0 0 0 013 4 4 PonctuLinStatic 0 0 0 0 0 016 13 160 PonctuLinStatic 0 -171 0 1 1 216 13 1 PonctuLinStatic 0 171 0 -1 -1 -217 14 126 PonctuLinStatic 0 1199 0 1 1 217 14 56 PonctuLinStatic 0 -1199 0 -1 -1 -218 15 464 PonctuLinStatic 0 2307 0 2 0 018 15 10 PonctuLinStatic 0 -2307 0 -2 0 019 16 431 PonctuLinStatic 0 2307 0 2 0 019 16 7 PonctuLinStatic 0 -2307 0 -2 0 020 17 2 PonctuLinStatic 0 -171 0 -1 1 220 17 192 PonctuLinStatic 0 171 0 1 -1 -221 18 21 PonctuLinStatic 0 1199 0 -1 1 221 18 94 PonctuLinStatic 0 -1199 0 1 -1 -222 19 35 PonctuLinStatic 0 1199 0 -1 -1 -222 19 127 PonctuLinStatic 0 -1199 0 1 1 223 20 3 PonctuLinStatic 0 -171 0 -1 -1 -223 20 193 PonctuLinStatic 0 171 0 1 1 224 21 11 PonctuLinStatic 0 2307 0 -1 0 024 21 463 PonctuLinStatic 0 -2307 0 1 0 025 22 12 PonctuLinStatic 0 2307 0 -1 0 025 22 496 PonctuLinStatic 0 -2307 0 1 0 026 23 242 PonctuLinStatic 0 -25 0 641 1 126 23 13 PonctuLinStatic 0 25 0 1 -1 -127 24 259 PonctuLinStatic 0 -25 0 641 -1 -127 24 15 PonctuLinStatic 0 25 0 1 1 1
Max. 476 2307 5 641 12082 2Min. -476 -2307 -5 -34 -12082 -2
242
T
able
II -
7. E
lem
ent f
orce
s –fr
ames
for
conf
igur
atio
n (c
) sof
a fr
ame
unde
r he
avy-
serv
ice
acce
ptan
ce le
vel l
oad
243
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CaseT
yP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
220
0Po
nLi
nS-3
269.
31.
6E-1
1-5
2.2
00
1.6E
-09
10
152.
418
.26
2.27
E-1
40
2.27
E-1
4-0
.028
137
8.52
E-1
5-1
.175
020
38.1
Pon
LinS
-326
9.3
1.6E
-11
-52.
20
1988
.81E
-09
138
.115
2.4
18.2
61.
42E
-14
0.23
4832
0.23
4832
-0.0
2813
78.
52E
-15
-1.1
750
2076
.2Po
nLi
nS-3
269.
31.
6E-1
1-5
2.2
039
77.6
4E-1
01
76.2
152.
418
.26
5.68
E-1
50.
4696
640.
4696
64-0
.028
137
8.52
E-1
5-1
.175
021
0Po
nLi
nS-3
269.
6-2
E-11
-52.
20
0-5
E-0
92
015
2.4
18.2
6-6
.81E
-14
0-6
.8E
-14
-0.0
2813
7-8
.52E
-15
-1.1
750
2138
.1Po
nLi
nS-3
269.
6-2
E-11
-52.
20
1988
.7-4
E-0
92
38.1
152.
418
.26
-5.9
6E-1
40.
2348
230.
2348
23-0
.028
137
-8.5
2E-1
5-1
.175
021
76.2
Pon
LinS
-326
9.6
-2E-
11-5
2.2
039
77.5
-4E
-09
276
.215
2.4
18.2
6-5
.11E
-14
0.46
9645
0.46
9645
-0.0
2813
7-8
.52E
-15
-1.1
750
220
Pon
LinS
-326
9.3
4904
.99
52.2
02E
-12
03
015
2.4
18.2
60
1.85
E-1
61.
85E
-16
0.02
8137
2.64
3892
-1.1
750
2238
.1Po
nLi
nS-3
269.
349
04.9
952
.20
-198
8.7
-186
880
338
.115
2.4
18.2
6-2
.643
89-0
.234
823
-2.8
7871
0.02
8137
2.64
3892
-1.1
750
2276
.2Po
nLi
nS-3
269.
349
04.9
952
.20
-397
7.5
-373
760
376
.215
2.4
18.2
6-5
.287
779
-0.4
6964
5-5
.757
420.
0281
372.
6438
92-1
.175
023
0Po
nLi
nS-3
269.
6-4
905
52.2
03E
-12
4E-1
04
015
2.4
18.2
65.
68E
-15
3.7E
-16
6.05
E-1
50.
0281
37-2
.643
892
-1.1
750
2338
.1Po
nLi
nS-3
269.
6-4
905
52.2
0-1
988.
818
6880
438
.115
2.4
18.2
62.
6438
9-0
.234
832
2.40
9057
0.02
8137
-2.6
4389
2-1
.175
023
76.2
Pon
LinS
-326
9.6
-490
552
.20
-397
7.6
3737
604
76.2
152.
418
.26
5.28
7779
-0.4
6966
44.
8181
160.
0281
37-2
.643
892
-1.1
750
650
Pon
LinS
-400
8.9
-323
4-1
517
-150
38-1
5295
0-6
2938
35
015
2.4
18.2
6-8
.904
216
-18.
0598
6-2
6.96
41-0
.817
695
-1.7
4321
5-1
.441
-0.9
8648
8165
88.9
Pon
LinS
-400
8.9
-323
4-1
517
-150
38-1
8061
-341
820
588
.92
152.
418
.26
-4.8
3590
5-2
.132
632
-6.9
6854
-0.8
1769
5-1
.743
215
-1.4
41-0
.986
4881
6588
.9Po
nLi
nS-4
008.
9-2
967.
1-9
74.3
-150
38-1
8066
-341
822
588
.92
152.
418
.26
-4.8
3593
8-2
.133
201
-6.9
6914
-0.5
2517
9-1
.599
35-1
.441
-0.9
8648
8165
178
Pon
LinS
-400
8.9
-296
7.1
-974
.3-1
5038
6851
6-7
8149
517
7.8
152.
418
.26
-1.1
0560
98.
0901
916.
9845
82-0
.525
179
-1.5
9935
-1.4
41-0
.986
4881
6517
8Po
nLi
nS-4
008.
9-2
433.
4-2
98.2
-150
3868
516
-781
445
177.
815
2.4
18.2
6-1
.105
542
8.09
0191
6.98
4649
-0.1
6073
1-1
.311
632
-1.4
41-0
.986
4881
6526
7Po
nLi
nS-4
008.
9-2
433.
4-2
98.2
-150
3895
031
1382
255
266.
715
2.4
18.2
61.
9555
4111
.220
9413
.176
48-0
.160
731
-1.3
1163
2-1
.441
-0.9
8648
8165
267
Pon
LinS
-400
8.9
-185
5.1
422.
42-1
5038
9503
113
8225
526
6.7
152.
418
.26
1.95
5541
11.2
2094
13.1
7648
0.22
7693
-0.9
9993
2-1
.441
-0.9
8648
8165
356
Pon
LinS
-400
8.9
-185
5.1
422.
42-1
5038
5747
030
3175
535
5.6
152.
418
.26
4.28
918
6.78
5899
11.0
7508
0.22
7693
-0.9
9993
2-1
.441
-0.9
8648
8165
356
Pon
LinS
-400
8.9
-132
1.3
1098
.6-1
5038
5747
030
3171
535
5.6
152.
418
.26
4.28
9113
6.78
5899
11.0
7501
0.59
2141
-0.7
1220
8-1
.441
-0.9
8648
8165
444
Pon
LinS
-400
8.9
-132
1.3
1098
.6-1
5038
-401
5242
0587
544
4.5
152.
418
.26
5.95
027
-4.7
4100
31.
2092
670.
5921
41-0
.712
208
-1.4
41-0
.986
4881
6544
4Po
nLi
nS-4
008.
9-1
054.
416
41.2
-150
38-4
0147
4205
905
444.
515
2.4
18.2
65.
9503
03-4
.740
433
1.20
987
0.88
4657
-0.5
6834
9-1
.441
-0.9
8648
8165
533
Pon
LinS
-400
8.9
-105
4.4
1641
.2-1
5038
-186
082
5143
455
533.
415
2.4
18.2
67.
2767
14-2
1.97
195
-14.
6952
0.88
4657
-0.5
6834
9-1
.441
-0.9
8648
8172
0Po
nLi
nS-3
399.
7-1
089.
8-1
579
-0.1
6-1
8865
214
1765
60
152.
418
.26
2.00
5626
-22.
2754
9-2
0.26
99-0
.851
146
-0.5
8740
9-1
.222
-1.0
5E-0
572
102
Pon
LinS
-339
9.7
-108
9.8
-157
9-0
.16
-281
8825
2508
610
1.6
152.
418
.26
3.57
2365
-3.3
2829
30.
2440
71-0
.851
146
-0.5
8740
9-1
.222
-1.0
5E-0
572
102
Pon
LinS
-339
9.7
-822
.88
-103
6-0
.16
-281
9325
2505
610
1.6
152.
418
.26
3.57
2326
-3.3
2894
40.
2433
82-0
.558
63-0
.443
549
-1.2
22-1
.05E
-05
7220
3Po
nLi
nS-3
399.
7-8
22.8
8-1
036
-0.1
677
061
3360
766
203.
215
2.4
18.2
64.
7546
499.
0991
3513
.853
78-0
.558
63-0
.443
549
-1.2
22-1
.05E
-05
7220
3Po
nLi
nS-3
399.
7-2
89.0
9-3
60.3
-0.1
677
061
3360
826
203.
215
2.4
18.2
64.
7547
269.
0991
3513
.853
86-0
.194
182
-0.1
5582
6-1
.222
-1.0
5E-0
572
305
Pon
LinS
-339
9.7
-289
.09
-360
.3-0
.16
1136
7036
5459
630
4.8
152.
418
.26
5.17
0346
13.4
2179
18.5
9213
-0.1
9418
2-0
.155
826
-1.2
22-1
.05E
-05
7230
5Po
nLi
nS-3
399.
728
9.18
360.
36-0
.16
1136
7036
5459
630
4.8
152.
418
.26
5.17
0346
13.4
2179
18.5
9213
0.19
4242
0.15
5874
-1.2
22-1
.05E
-05
7240
6Po
nLi
nS-3
399.
728
9.18
360.
36-0
.16
7705
033
6073
640
6.4
152.
418
.26
4.75
4602
9.09
7814
13.8
5242
0.19
4242
0.15
5874
-1.2
22-1
.05E
-05
7240
6Po
nLi
nS-3
399.
782
2.96
1036
.5-0
.16
7705
033
6068
640
6.4
152.
418
.26
4.75
4525
9.09
7814
13.8
5234
0.55
869
0.44
3593
-1.2
22-1
.05E
-05
7250
8Po
nLi
nS-3
399.
782
2.96
1036
.5-0
.16
-282
1525
2488
650
815
2.4
18.2
63.
5720
79-3
.331
585
0.24
0494
0.55
869
0.44
3593
-1.2
22-1
.05E
-05
7250
8Po
nLi
nS-3
399.
710
89.8
615
79.2
-0.1
6-2
8210
2524
916
508
152.
418
.26
3.57
2118
-3.3
3093
40.
2411
840.
8512
050.
5874
57-1
.222
-1.0
5E-0
572
610
Pon
LinS
-339
9.7
1089
.86
1579
.2-0
.16
-188
686
1417
396
609.
615
2.4
18.2
62.
0052
56-2
2.27
945
-20.
2742
0.85
1205
0.58
7457
-1.2
22-1
.05E
-05
800
Pon
LinS
-400
8.8
1054
.49
-164
115
039
-186
063
5143
717
015
2.4
18.2
67.
2770
81-2
1.96
974
-14.
6927
-0.8
8459
20.
5683
92-1
.441
0.98
6504
4880
88.9
Pon
LinS
-400
8.8
1054
.49
-164
115
039
-401
3942
0608
788
.92
152.
418
.26
5.95
057
-4.7
3949
21.
2110
78-0
.884
592
0.56
8392
-1.4
410.
9865
0448
8088
.9Po
nLi
nS-4
008.
813
21.3
8-1
098
1503
9-4
0144
4206
067
88.9
215
2.4
18.2
65.
9505
36-4
.740
061
1.21
0475
-0.5
9207
70.
7122
51-1
.441
0.98
6504
4880
178
Pon
LinS
-400
8.8
1321
.38
-109
815
039
5746
730
3182
717
7.8
152.
418
.26
4.28
9279
6.78
557
11.0
7485
-0.5
9207
70.
7122
51-1
.441
0.98
6504
4880
178
Pon
LinS
-400
8.8
1855
.17
-422
.315
039
5746
730
3187
717
7.8
152.
418
.26
4.28
9346
6.78
557
11.0
7492
-0.2
2762
80.
9999
75-1
.441
0.98
6504
4880
267
Pon
LinS
-400
8.8
1855
.17
-422
.315
039
9501
713
8230
726
6.7
152.
418
.26
1.95
5606
11.2
1935
13.1
7495
-0.2
2762
80.
9999
75-1
.441
0.98
6504
4880
267
Pon
LinS
-400
8.8
2433
.44
298.
3115
039
9501
713
8230
726
6.7
152.
418
.26
1.95
5606
11.2
1935
13.1
7495
0.16
0795
1.31
1675
-1.4
410.
9865
0448
8035
6Po
nLi
nS-4
008.
824
33.4
429
8.31
1503
968
492
-781
467
355.
615
2.4
18.2
6-1
.105
577
8.08
7323
6.98
1746
0.16
0795
1.31
1675
-1.4
410.
9865
0448
8035
6Po
nLi
nS-4
008.
829
67.2
297
4.44
1503
968
492
-781
517
355.
615
2.4
18.2
6-1
.105
644
8.08
7323
6.98
1679
0.52
5243
1.59
9393
-1.4
410.
9865
0448
8044
4Po
nLi
nS-4
008.
829
67.2
297
4.44
1503
9-1
8101
-341
832
744
4.5
152.
418
.26
-4.8
3607
4-2
.137
338
-6.9
7341
0.52
5243
1.59
9393
-1.4
410.
9865
0448
8044
4Po
nLi
nS-4
008.
832
34.1
215
17.1
1503
9-1
8096
-341
829
744
4.5
152.
418
.26
-4.8
3604
-2.1
3676
8-6
.972
810.
8177
651.
7432
58-1
.441
0.98
6504
48
244
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CaseT
yP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
2
8053
3Po
nLi
nS-4
008.
832
34.1
215
17.1
1503
9-1
5299
6-6
2940
07
533.
415
2.4
18.2
6-8
.904
452
-18.
0652
7-2
6.96
970.
8177
651.
7432
58-1
.441
0.98
6504
4887
0Po
nLi
nS29
.41
-320
9.1
-155
415
234
-164
790
1415
618
015
2.4
18.2
62.
0027
33-1
9.45
793
-17.
4552
-0.8
3790
2-1
.729
745
0.01
060.
9993
2697
8788
.9Po
nLi
nS29
.41
-320
9.1
-155
415
234
-265
9642
6845
888
.915
2.4
18.2
66.
0388
07-3
.140
412
2.89
8395
-0.8
3790
2-1
.729
745
0.01
060.
9993
2697
8788
.9Po
nLi
nS29
.41
-294
2.2
-101
215
234
-265
9642
6845
888
.915
2.4
18.2
66.
0388
07-3
.140
412
2.89
8395
-0.5
4538
7-1
.585
885
0.01
060.
9993
2697
8717
8Po
nLi
nS29
.41
-294
2.2
-101
215
234
6335
368
8403
817
7.8
152.
418
.26
9.73
9205
7.48
0545
17.2
1975
-0.5
4538
7-1
.585
885
0.01
060.
9993
2697
8717
8Po
nLi
nS29
.41
-240
8.4
-335
.715
234
6334
768
8403
817
7.8
152.
418
.26
9.73
9205
7.47
9835
17.2
1904
-0.1
8093
8-1
.298
162
0.01
060.
9993
2697
8726
7Po
nLi
nS29
.41
-240
8.4
-335
.715
234
9318
990
2508
826
6.7
152.
418
.26
12.7
6825
11.0
0344
23.7
7169
-0.1
8093
8-1
.298
162
0.01
060.
9993
2697
8726
7Po
nLi
nS29
.41
-183
0.1
384.
9415
234
9318
990
2508
826
6.7
152.
418
.26
12.7
6825
11.0
0344
23.7
7169
0.20
7491
-0.9
8646
20.
0106
0.99
9326
9787
356
Pon
LinS
29.4
1-1
830.
138
4.94
1523
458
968
1065
204
835
5.6
152.
418
.26
15.0
76.
9627
5322
.032
750.
2074
91-0
.986
462
0.01
060.
9993
2697
8735
6Po
nLi
nS29
.41
-129
6.3
1061
.115
234
5897
410
6520
48
355.
615
2.4
18.2
615
.07
6.96
3463
22.0
3346
0.57
1939
-0.6
9874
30.
0106
0.99
9326
9787
445
Pon
LinS
29.4
1-1
296.
310
61.1
1523
4-3
5355
1180
446
844
4.5
152.
418
.26
16.7
004
-4.1
7457
712
.525
820.
5719
39-0
.698
743
0.01
060.
9993
2697
8744
5Po
nLi
nS29
.41
-102
9.4
1603
.815
234
-353
5511
8044
68
444.
515
2.4
18.2
616
.700
4-4
.174
577
12.5
2582
0.86
4455
-0.5
5487
90.
0106
0.99
9326
9787
533
Pon
LinS
29.4
1-1
029.
416
03.8
1523
4-1
7792
812
7196
28
533.
415
2.4
18.2
617
.995
12-2
1.00
918
-3.0
1406
0.86
4455
-0.5
5487
90.
0106
0.99
9326
9794
0Po
nLi
nS20
.35
-108
9.8
-157
9-0
.11
-185
760
1263
376
90
152.
418
.26
17.8
7365
-21.
934
-4.0
6035
-0.8
5114
6-0
.587
409
0.00
73-7
.216
E-06
9410
2Po
nLi
nS20
.35
-108
9.8
-157
9-0
.11
-253
2813
7409
69
101.
615
2.4
18.2
619
.440
07-2
.990
657
16.4
4941
-0.8
5114
6-0
.587
409
0.00
73-7
.216
E-06
9410
2Po
nLi
nS20
.35
-822
.87
-103
6-0
.11
-253
2813
7409
69
101.
615
2.4
18.2
619
.440
07-2
.990
657
16.4
4941
-0.5
5862
5-0
.443
544
0.00
73-7
.216
E-06
9420
3Po
nLi
nS20
.35
-822
.87
-103
6-0
.11
7996
814
5770
09
203.
215
2.4
18.2
620
.622
869.
4423
2530
.065
18-0
.558
625
-0.4
4354
40.
0073
-7.2
16E-
0694
203
Pon
LinS
20.3
5-2
89.0
9-3
60.3
-0.1
179
961
1457
700
920
3.2
152.
418
.26
20.6
2286
9.44
1514
30.0
6437
-0.1
9418
2-0
.155
826
0.00
73-7
.216
E-06
9430
5Po
nLi
nS20
.35
-289
.09
-360
.3-0
.11
1165
6214
8707
29
304.
815
2.4
18.2
621
.038
3913
.763
2334
.801
62-0
.194
182
-0.1
5582
60.
0073
-7.2
16E-
0694
305
Pon
LinS
20.3
528
9.18
360.
37-0
.11
1165
6214
8707
29
304.
815
2.4
18.2
621
.038
3913
.763
2334
.801
620.
1942
470.
1558
740.
0073
-7.2
16E-
0694
406
Pon
LinS
20.3
528
9.18
360.
37-0
.11
7994
814
5769
19
406.
415
2.4
18.2
620
.622
729.
4400
5630
.062
780.
1942
470.
1558
740.
0073
-7.2
16E-
0694
406
Pon
LinS
20.3
582
2.97
1036
.5-0
.11
7995
514
5769
19
406.
415
2.4
18.2
620
.622
729.
4408
6730
.063
590.
5586
950.
4435
980.
0073
-7.2
16E-
0694
508
Pon
LinS
20.3
582
2.97
1036
.5-0
.11
-253
5313
7407
79
508
152.
418
.26
19.4
3979
-2.9
9357
516
.446
220.
5586
950.
4435
980.
0073
-7.2
16E-
0694
508
Pon
LinS
20.3
510
89.8
615
79.2
-0.1
1-2
5353
1374
077
950
815
2.4
18.2
619
.439
79-2
.993
575
16.4
4622
0.85
1211
0.58
7457
0.00
73-7
.216
E-06
9461
0Po
nLi
nS20
.35
1089
.86
1579
.2-0
.11
-185
797
1263
347
960
9.6
152.
418
.26
17.8
7324
-21.
9383
7-4
.065
130.
8512
110.
5874
570.
0073
-7.2
16E-
0610
20
Pon
LinS
29.5
410
29.5
2-1
604
-152
34-1
7790
712
7193
310
015
2.4
18.2
617
.994
71-2
1.00
675
-3.0
1204
-0.8
6438
50.
5549
330.
0106
-0.9
9929
5510
288
.9Po
nLi
nS29
.54
1029
.52
-160
4-1
5234
-353
4511
8040
910
88.9
152.
418
.26
16.6
9987
-4.1
7345
12.5
2642
-0.8
6438
50.
5549
330.
0106
-0.9
9929
5510
288
.9Po
nLi
nS29
.54
1296
.41
-106
1-1
5234
-353
4511
8040
910
88.9
152.
418
.26
16.6
9987
-4.1
7345
12.5
2642
-0.5
7186
90.
6987
920.
0106
-0.9
9929
5510
217
8Po
nLi
nS29
.54
1296
.41
-106
1-1
5234
5897
310
6515
910
177.
815
2.4
18.2
615
.069
366.
9632
8722
.032
65-0
.571
869
0.69
8792
0.01
06-0
.999
2955
102
178
Pon
LinS
29.5
418
30.2
-384
.8-1
5234
5896
610
6515
910
177.
815
2.4
18.2
615
.069
366.
9625
7722
.031
94-0
.207
421
0.98
6516
0.01
06-0
.999
2955
102
267
Pon
LinS
29.5
418
30.2
-384
.8-1
5234
9317
690
2454
1026
6.7
152.
418
.26
12.7
675
11.0
0196
23.7
6946
-0.2
0742
10.
9865
160.
0106
-0.9
9929
5510
226
7Po
nLi
nS29
.54
2408
.46
335.
8-1
5234
9317
690
2454
1026
6.7
152.
418
.26
12.7
675
11.0
0196
23.7
6946
0.18
1003
1.29
821
0.01
06-0
.999
2955
102
356
Pon
LinS
29.5
424
08.4
633
5.8
-152
3463
324
6883
4210
355.
615
2.4
18.2
69.
7383
357.
4770
5317
.215
390.
1810
031.
2982
10.
0106
-0.9
9929
5510
235
6Po
nLi
nS29
.54
2942
.25
1011
.9-1
5234
6333
068
8342
1035
5.6
152.
418
.26
9.73
8335
7.47
7764
17.2
161
0.54
5451
1.58
5934
0.01
06-0
.999
2955
102
445
Pon
LinS
29.5
429
42.2
510
11.9
-152
34-2
6631
4267
7610
444.
515
2.4
18.2
66.
0378
21-3
.144
496
2.89
3325
0.54
5451
1.58
5934
0.01
06-0
.999
2955
102
445
Pon
LinS
29.5
432
09.1
415
54.6
-152
34-2
6631
4267
7610
444.
515
2.4
18.2
66.
0378
21-3
.144
496
2.89
3325
0.83
7967
1.72
9793
0.01
06-0
.999
2955
102
533
Pon
LinS
29.5
432
09.1
415
54.6
-152
34-1
6483
614
1483
1053
3.4
152.
418
.26
2.00
1632
-19.
4633
2-1
7.46
170.
8379
671.
7297
930.
0106
-0.9
9929
5511
20
Pon
LinS
-247
4.2
17.2
562
.16
-188
2511
0741
6946
.66
110
18.2
615
2.4
0.82
024
1.56
6715
2.38
6955
0.03
3506
0.00
9298
-0.8
89-1
.234
8581
112
406
Pon
LinS
-247
4.2
17.2
562
.16
-188
2585
481
-65.
1311
406.
418
.26
152.
4-0
.007
691.
2093
491.
2016
590.
0335
060.
0092
98-0
.889
-1.2
3485
8111
281
3Po
nLi
nS-2
474.
217
.25
62.1
6-1
8825
6022
1-7
076.
911
812.
818
.26
152.
4-0
.835
622
0.85
1983
0.01
6361
0.03
3506
0.00
9298
-0.8
89-1
.234
8581
146
0Po
nLi
nS-2
474.
517
.25
-62.
218
824
-110
774
6945
.73
120
18.2
615
2.4
0.82
013
-1.5
6717
8-0
.747
05-0
.033
527
0.00
9298
-0.8
891.
2348
2271
146
406
Pon
LinS
-247
4.5
17.2
5-6
2.2
1882
4-8
5497
-65.
2712
406.
418
.26
152.
4-0
.007
707
-1.2
0957
-1.2
1728
-0.0
3352
70.
0092
98-0
.889
1.23
4822
7114
681
3Po
nLi
nS-2
474.
517
.25
-62.
218
824
-602
20-7
076.
312
812.
818
.26
152.
4-0
.835
542
-0.8
5196
2-1
.687
5-0
.033
527
0.00
9298
-0.8
891.
2348
2271
180
0Po
nLi
nS89
1.16
65.1
60.
99-1
8825
-825
.17
2194
3.6
130
152.
418
.26
0.31
0448
-0.0
9743
30.
2130
140.
0005
340.
0351
230.
3202
-1.2
3485
8118
040
6Po
nLi
nS89
1.16
65.1
60.
99-1
8825
-122
6.8
-453
8.3
1340
6.4
152.
418
.26
-0.0
6420
5-0
.144
86-0
.209
070.
0005
340.
0351
230.
3202
-1.2
3485
8118
081
3Po
nLi
nS89
1.16
65.1
60.
99-1
8825
-162
8.5
-310
2013
812.
815
2.4
18.2
6-0
.438
858
-0.1
9228
8-0
.631
150.
0005
340.
0351
230.
3202
-1.2
3485
8121
40
Pon
LinS
891.
5-6
5.25
-0.9
918
824
-162
9-3
1067
140
152.
418
.26
-0.4
3951
4-0
.192
346
-0.6
3186
-0.0
0053
4-0
.035
171
0.32
041.
2348
2271
245
TAB
LE:
Elem
ent F
orce
s - F
ram
esFr
amSt
atio
nput
CaseT
yP
V2V3
TM
2M
3m
eEem
Stat
ion
6M33
/(bh2
)6M
22/(h
b2)s
umfle
xion
3V33
/(2bh
)3V
22/(2
bh)P
/(bh)
T/(a
lfa*d
l*dc2
)Te
xtm
mTe
xtTe
xtN
NN
N-m
mN
-mm
N-m
mTe
xm
mh
bN
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
2N
/mm
3N
/mm
2
214
406
Pon
LinS
891.
5-6
5.25
-0.9
918
824
-122
7.1
-454
7.7
1440
6.4
152.
418
.26
-0.0
6433
8-0
.144
887
-0.2
0923
-0.0
0053
4-0
.035
171
0.32
041.
2348
2271
214
813
Pon
LinS
891.
5-6
5.25
-0.9
918
824
-825
.12
2197
1.2
1481
2.8
152.
418
.26
0.31
0838
-0.0
9742
80.
2134
1-0
.000
534
-0.0
3517
10.
3204
1.23
4822
7124
70
Pon
LinS
-12.
34-9
2.55
-23.
6119
268
-607
8.7
-640
0515
015
2.4
18.2
6-0
.905
516
-0.7
1775
5-1
.623
27-0
.012
726
-0.0
4988
6-0
.004
1.26
3976
5424
721
6Po
nLi
nS-1
2.34
-92.
55-2
3.61
1926
8-9
81.3
9-4
4023
1521
5.9
152.
418
.26
-0.6
2282
2-0
.115
879
-0.7
387
-0.0
1272
6-0
.049
886
-0.0
041.
2639
7654
247
432
Pon
LinS
-12.
34-9
2.55
-23.
6119
268
4115
.9-2
4041
1543
1.8
152.
418
.26
-0.3
4012
70.
4859
970.
1458
7-0
.012
726
-0.0
4988
6-0
.004
1.26
3976
5426
50
Pon
LinS
-12.
4492
.73
-23.
8-1
9268
-612
964
091.
416
015
2.4
18.2
60.
9067
35-0
.723
693
0.18
3042
-0.0
1282
90.
0499
83-0
.004
-1.2
6397
9226
521
6Po
nLi
nS-1
2.44
92.7
3-2
3.8
-192
68-9
90.8
244
071.
316
215.
915
2.4
18.2
60.
6234
99-0
.116
993
0.50
6506
-0.0
1282
90.
0499
83-0
.004
-1.2
6397
9226
543
2Po
nLi
nS-1
2.44
92.7
3-2
3.8
-192
6841
47.4
2405
1.1
1643
1.8
152.
418
.26
0.34
0263
0.48
9707
0.82
9971
-0.0
1282
90.
0499
83-0
.004
-1.2
6397
9228
30
Pon
LinS
95.7
159
9.97
37.4
9-2
623
2184
338
1166
170
152.
418
.26
5.39
256
2.57
9206
7.97
1766
0.02
0208
0.32
3396
0.03
44-0
.172
0858
283
330
Pon
LinS
95.7
159
9.97
37.4
9-2
623
9463
.418
3058
1733
0.2
152.
418
.26
2.58
9812
1.11
7407
3.70
722
0.02
0208
0.32
3396
0.03
44-0
.172
0858
283
660
Pon
LinS
95.7
159
9.97
37.4
9-2
623
-291
6.7
-150
5117
660.
415
2.4
18.2
6-0
.212
935
-0.3
4439
1-0
.557
330.
0202
080.
3233
960.
0344
-0.1
7208
5831
10
Pon
LinS
95.7
160
0.05
37.4
826
1729
11.5
1505
518
015
2.4
18.2
60.
2129
90.
3437
830.
5567
730.
0202
020.
3234
390.
0344
0.17
1675
8631
133
0Po
nLi
nS95
.71
600.
0537
.48
2617
-946
4.1
-183
082
1833
0.2
152.
418
.26
-2.5
9015
3-1
.117
495
-3.7
0765
0.02
0202
0.32
3439
0.03
440.
1716
7586
311
660
Pon
LinS
95.7
160
0.05
37.4
826
17-2
1840
-381
218
1866
0.4
152.
418
.26
-5.3
9329
6-2
.578
772
-7.9
7207
0.02
0202
0.32
3439
0.03
440.
1716
7586
337
0Po
nLi
nS-9
25.5
9-9
5.72
37.3
6-3
863
4003
8-2
9718
190
18.2
615
2.4
-3.5
0899
80.
5664
42-2
.942
560.
0201
38-0
.051
595
-0.3
33-0
.253
3739
337
610
Pon
LinS
-925
.59
-95.
7237
.36
-386
317
261
2863
1.1
1960
9.6
18.2
615
2.4
3.38
0669
0.24
4207
3.62
4876
0.02
0138
-0.0
5159
5-0
.333
-0.2
5337
3933
80
Pon
LinS
-152
5.6
-0.0
044
-0.1
20.
9814
644
-166
5.1
200
18.2
615
2.4
-0.1
9661
40.
2071
820.
0105
68-6
.47E
-05
-2.3
8E-0
6-0
.548
6.42
86E-
0533
861
0Po
nLi
nS-1
525.
6-0
.004
4-0
.12
0.98
1471
5-1
662.
520
609.
618
.26
152.
4-0
.196
297
0.20
8181
0.01
1884
-6.4
7E-0
5-2
.38E
-06
-0.5
486.
4286
E-05
339
0Po
nLi
nS-9
25.6
795
.7-3
7.61
3870
1733
828
627.
721
018
.26
152.
43.
3802
710.
2452
953.
6255
66-0
.020
273
0.05
1584
-0.3
330.
2538
6325
339
610
Pon
LinS
-925
.67
95.7
-37.
6138
7040
264
-297
1421
609.
618
.26
152.
4-3
.508
522
0.56
9643
-2.9
3888
-0.0
2027
30.
0515
84-0
.333
0.25
3863
2534
00
Pon
LinS
-23.
61-1
2.34
-92.
55-2
1691
-192
68-4
715.
622
018
.26
152.
4-0
.556
807
-0.2
7260
1-0
.829
41-0
.049
886
-0.0
0665
2-0
.008
-1.4
2286
9934
041
9Po
nLi
nS-2
3.61
-12.
34-9
2.55
-216
9119
520
457.
6122
419.
118
.26
152.
40.
0540
330.
2761
590.
3301
92-0
.049
886
-0.0
0665
2-0
.008
-1.4
2286
9934
083
8Po
nLi
nS-2
3.61
-12.
34-9
2.55
-216
9158
308
5630
.85
2283
8.2
18.2
615
2.4
0.66
4873
0.82
4919
1.48
9792
-0.0
4988
6-0
.006
652
-0.0
08-1
.422
8699
374
0Po
nLi
nS-2
3.8
-12.
4492
.73
2169
619
268
-475
1.9
230
18.2
615
2.4
-0.5
6108
30.
2726
01-0
.288
480.
0499
83-0
.006
705
-0.0
091.
4232
0513
374
419
Pon
LinS
-23.
8-1
2.44
92.7
321
696
-195
9446
0.03
2341
9.1
18.2
615
2.4
0.05
4319
-0.2
7720
9-0
.222
890.
0499
83-0
.006
705
-0.0
091.
4232
0513
374
838
Pon
LinS
-23.
8-1
2.44
92.7
321
696
-584
5756
71.9
123
838.
218
.26
152.
40.
6697
21-0
.827
02-0
.157
30.
0499
83-0
.006
705
-0.0
091.
4232
0513
408
0Po
nLi
nS-8
3.37
-833
.03
-13.
7520
621
-502
2.6
-541
043
240
152.
418
.26
-7.6
5442
7-0
.593
052
-8.2
4748
-0.0
0741
2-0
.449
02-0
.03
1.35
2696
240
833
0Po
nLi
nS-8
3.37
-833
.03
-13.
7520
621
-481
.11
-265
976
2433
0.2
152.
418
.26
-3.7
6289
8-0
.056
808
-3.8
1971
-0.0
0741
2-0
.449
02-0
.03
1.35
2696
240
845
6Po
nLi
nS-8
3.37
-833
.03
-13.
7520
621
1250
-161
127
2445
6.1
152.
418
.26
-2.2
7955
40.
1475
94-2
.131
96-0
.007
412
-0.4
4902
-0.0
31.
3526
962
408
456
Pon
LinS
-95.
72-9
25.5
9-3
7.36
-400
38-4
721.
3-1
8292
325
015
2.4
18.2
6-2
.587
912
-0.5
5747
-3.1
4538
-0.0
2013
8-0
.498
912
-0.0
34-2
.626
4377
408
660
Pon
LinS
-95.
72-9
25.5
9-3
7.36
-400
3829
13.5
6208
.04
2520
4.3
152.
418
.26
0.08
7828
0.34
4015
0.43
1843
-0.0
2013
8-0
.498
912
-0.0
34-2
.626
4377
436
0Po
nLi
nS-9
5.7
-925
.67
-37.
6140
264
-291
4.7
-620
1.9
260
152.
418
.26
-0.0
8774
1-0
.344
16-0
.431
9-0
.020
273
-0.4
9895
5-0
.034
2.64
1278
6443
620
3Po
nLi
nS-9
5.7
-925
.67
-37.
6140
264
4710
.818
1487
2620
2.8
152.
418
.26
2.56
759
0.55
6233
3.12
3823
-0.0
2027
3-0
.498
955
-0.0
342.
6412
7864
436
203
Pon
LinS
-83.
27-8
32.9
4-1
3.81
-205
48-1
266.
515
9832
270
152.
418
.26
2.26
1226
-0.1
4954
92.
1116
77-0
.007
444
-0.4
4897
2-0
.03
-1.3
4789
1843
633
0Po
nLi
nS-8
3.27
-832
.94
-13.
81-2
0548
493.
3626
5982
2712
7.4
152.
418
.26
3.76
299
0.05
8254
3.82
1245
-0.0
0744
4-0
.448
972
-0.0
3-1
.347
8918
436
660
Pon
LinS
-83.
27-8
32.9
4-1
3.81
-205
4850
53.3
5410
1927
457.
615
2.4
18.2
67.
6540
880.
5966
758.
2507
63-0
.007
444
-0.4
4897
2-0
.03
-1.3
4789
1847
20
Pon
LinS
-318
2.8
-60.
35-9
.285
8618
0.94
-353
4928
015
2.4
18.2
6-0
.500
099
0.02
1365
-0.4
7873
-0.0
0495
9-0
.032
53-1
.144
0.56
3233
1147
240
6Po
nLi
nS-3
182.
8-6
0.35
-9.2
8586
3918
.7-1
0824
2840
6.4
152.
418
.26
-0.1
5313
40.
4627
030.
3095
69-0
.004
959
-0.0
3253
-1.1
440.
5632
3311
472
813
Pon
LinS
-318
2.8
-60.
35-9
.285
8676
56.4
1370
0.7
2881
2.8
152.
418
.26
0.19
383
0.90
4041
1.09
7872
-0.0
0495
9-0
.032
53-1
.144
0.56
3233
1150
60
Pon
LinS
-318
2.8
-60.
349.
06-8
586
-236
.04
-353
4629
015
2.4
18.2
6-0
.500
056
-0.0
2787
1-0
.527
930.
0048
84-0
.032
525
-1.1
44-0
.563
2259
506
406
Pon
LinS
-318
2.8
-60.
349.
06-8
586
-391
9.1
-108
2229
406.
415
2.4
18.2
6-0
.153
107
-0.4
6275
5-0
.615
860.
0048
84-0
.032
525
-1.1
44-0
.563
2259
506
813
Pon
LinS
-318
2.8
-60.
349.
06-8
586
-760
2.2
1370
1.4
2981
2.8
152.
418
.26
0.19
3841
-0.8
9763
8-0
.703
80.
0048
84-0
.032
525
-1.1
44-0
.563
2259
Max
891.
549
04.9
916
41.2
4026
411
6562
1487
072
152.
415
2.4
21.0
3839
13.7
6323
34.8
0162
0.88
4657
2.64
3892
0.32
042.
6412
7864
Min
-400
8.9
-490
5-1
641
-400
38-1
8868
6-6
2940
018
.26
18.2
6-8
.904
452
-22.
2794
5-2
6.96
97-0
.884
592
-2.6
4389
2-1
.441
-2.6
2643
7726
.50.
75.
310
.80.
7
246
Table II - 8. Element joint forces –Links for configuration (c) sofa frame under heavy-service acceptance level load TABLE: Element Joint Forces - LinksLink LinkElem Joint tputCaCaseType F1 F2 F3 M1 M2 M3Text Text Text Text Text N N N N-mm N-mm N-mm
1 5 405 PonctuLinStatic 713.46 2.03 7.95 -51.14 18121.38 -2.721 5 5 PonctuLinStatic -713.46 -2.03 -7.95 -0.33 0.43 2.723 6 346 PonctuLinStatic 0.00189 -37.91 0.04684 -40.81 0.88 3.533 6 9 PonctuLinStatic -0.00189 37.91 -0.04684 -1.1 -0.88 -3.584 7 286 PonctuLinStatic 504.69 -2.03 -7.95 51.34 12818.87 0.384 7 312 PonctuLinStatic -504.69 2.03 7.95 0.33 0.22 -0.385 8 285 PonctuLinStatic -504.69 -2.01 -7.95 50.72 -12818.87 -0.375 8 313 PonctuLinStatic 504.69 2.01 7.95 0.33 -0.22 0.376 9 406 PonctuLinStatic -713.46 2.02 7.95 -50.93 -18121.38 2.726 9 6 PonctuLinStatic 713.46 -2.02 -7.95 -0.34 -0.43 -2.727 10 379 PonctuLinStatic -0.001893 -37.95 -0.02239 17.23 -0.88 -3.537 10 8 PonctuLinStatic 0.001893 37.95 0.02239 -1.09 0.88 3.588 11 225 PonctuLinStatic 0.0003477 -256.51 -0.003284 1.58 -0.75 -2.638 11 4 PonctuLinStatic -0.000348 256.51 0.003284 -1.66 0.75 2.629 12 159 PonctuLinStatic 0.0003478 1798.73 -0.003609 1.71 -0.75 -2.639 12 36 PonctuLinStatic -0.000348 -1798.73 0.003609 -1.8 0.75 2.6210 1 2 PonctuLinStatic -6.13E-16 2.921E-12 -4.56E-13 -2.96E-12 -9.236E-11 2.848E-1010 1 21 PonctuLinStatic 6.132E-16 -2.921E-12 4.562E-13 2.964E-12 -7.987E-12 -2.594E-1211 2 1 PonctuLinStatic -6.63E-15 -3.466E-12 -1.49E-13 1.208E-11 -1.529E-11 -7.258E-1111 2 56 PonctuLinStatic 6.631E-15 3.466E-12 1.493E-13 -1.21E-11 2.75E-12 -2.68E-1212 3 35 PonctuLinStatic 6.377E-16 3.572E-12 6.172E-13 1.264E-11 7.414E-11 4.165E-1112 3 3 PonctuLinStatic -6.38E-16 -3.572E-12 -6.17E-13 -1.26E-11 -2.396E-11 2.251E-1213 4 36 PonctuLinStatic 1.014E-13 2.701E-13 -1E-13 3.993E-12 2.572E-11 -7.404E-1113 4 4 PonctuLinStatic -1.01E-13 -2.701E-13 1E-13 -3.99E-12 -6.278E-13 -1.219E-1216 13 160 PonctuLinStatic -0.000347 -256.92 -0.003289 1.58 0.75 2.6316 13 1 PonctuLinStatic 0.0003468 256.92 0.003289 -1.67 -0.75 -2.6217 14 126 PonctuLinStatic -0.000347 1798.54 -0.003614 1.71 0.75 2.6317 14 56 PonctuLinStatic 0.0003468 -1798.54 0.003614 -1.8 -0.75 -2.6218 15 464 PonctuLinStatic -4.25E-05 3460.85 -0.005328 2.42 0.33 -0.3718 15 10 PonctuLinStatic 4.253E-05 -3460.85 0.005328 -2.55 -0.33 0.3719 16 431 PonctuLinStatic 4.356E-05 3460.83 -0.005326 2.42 -0.33 0.3719 16 7 PonctuLinStatic -4.36E-05 -3460.83 0.005326 -2.55 0.33 -0.3720 17 2 PonctuLinStatic -0.000347 -256.92 -0.003289 -1.17 0.75 2.9220 17 192 PonctuLinStatic 0.0003468 256.92 0.003289 1.09 -0.75 -2.9121 18 21 PonctuLinStatic -0.000347 1798.54 -0.003614 -1.32 0.75 2.9221 18 94 PonctuLinStatic 0.0003468 -1798.54 0.003614 1.23 -0.75 -2.9122 19 35 PonctuLinStatic 0.0003478 1798.73 -0.003609 -1.32 -0.75 -2.9222 19 127 PonctuLinStatic -0.000348 -1798.73 0.003609 1.22 0.75 2.9123 20 3 PonctuLinStatic 0.0003477 -256.51 -0.003284 -1.17 -0.75 -2.9223 20 193 PonctuLinStatic -0.000348 256.51 0.003284 1.09 0.75 2.9124 21 11 PonctuLinStatic 4.356E-05 3460.83 -0.005326 -2.05 -0.33 0.3324 21 463 PonctuLinStatic -4.36E-05 -3460.83 0.005326 1.91 0.33 -0.3325 22 12 PonctuLinStatic -4.25E-05 3460.85 -0.005328 -2.05 0.33 -0.3325 22 496 PonctuLinStatic 4.253E-05 -3460.85 0.005328 1.91 -0.33 0.3326 23 242 PonctuLinStatic 0.00189 -37.91 0.04684 961.28 0.93 1.9526 23 13 PonctuLinStatic -0.00189 37.91 -0.04684 1.54 -0.88 -1.9527 24 259 PonctuLinStatic -0.001893 -37.95 -0.02239 962.31 -0.93 -1.9527 24 15 PonctuLinStatic 0.001893 37.95 0.02239 1.54 0.88 1.95
Max 713.46 3460.85 7.95 962.31 18121.38 3.58Min -713.46 -3460.85 -7.95 -51.14 -18121.38 -3.58