Initial imperfection influences on the structural behavior ...wseas.us › e-library › conferences › 2010 › TimisoaraP › ... · 3 Case study – 50 m span main frame 3.1 Description

Initial imperfection influences on the structural behavior of steel portal frames with variable cross sections and some sustainability

considerations-Case study

I. MIRCEA CRISTUTIU Department of Architecture

“Politehnica” University of Timisoara Timisoara-300224, Traian Lalescu str., No. 2/602

Romania [email protected]

ZSOLT NAGY

Department of Steel and Concrete Structures “Technical” University of Cluj-Napoca

Cluj-Napoca-400027, Romania [email protected]

Abstract: - Modern light gauge single storey buildings are made by pitched-roof portal frames of class 3 and class 4 tapered steel sections in accordance with stress and stiffness demand. In case of class 3 sections, when they are restrained against lateral torsional buckling, the interaction between sectional plastic buckling and overall elastic buckling of the members in compression and/or in bending is possible. When class 4 sections are used, which generally is the case of the rafter in the hunched part, the sectional buckling (e.g. local buckling of walls or distortion) may occur in elastic domain. If no lateral restrains, or when they are not enough effective, the lateral torsional mode characterizes the global behavior of frame members and, again, interaction with sectional bucking modes may occur. It is well known that the elements with slender class 3 and 4 sections are more sensitive to imperfections than more compact sections as class 1 or 2 are. The paper summarizes a systematic numerical study performed by authors on a relevant series of such type of frames applying different type of initial imperfections. A series of frames of different spans and heights have been analyzed. The frames were designed to withstand the vertical loads and satisfy the ULS and SLS criteria. The frames have pinned base connections, tapered columns, hunched rafters and a pitch roof angle of 80. The length of the rafter hunch is 15% from the span in all the cases. Afterwards a real case of large span portal frame of 50 m, used as structural solution for an ice rink building, will be analyzed accounting for imperfections. For the same building, the present paper gives target values for utilization and operational cost. In order to achieve a viable balance between economic competitiveness, social benefit and environmental impact also some aspect of sustainable construction will be analyzed in the paper. Key-Words: - erection and manufacturing imperfections, steel pitched roof portal frames, large span frame, sustainable construction, life cycle cost. 1 Introduction Pitched roof portal frames usually used in construction industry for industrial steel buildings are currently fabricated by slender welded sections of class 3 and/or 4. Frame members are of variable cross-section, in accordance with stress and stiffness demand. Because rafters carry significant axial compressive loads, the problem of stability is more complex than in case of multi-storey frames [2]. If no adequate restraints are provided, the lateral torsional buckling strength of the members is

generally low. Purlins and side rails supporting the roof deck and cladding introduce some restraining effect, but it is difficult to quantify it for usual design. Actual design codes do not cover the practical design of this kind of structure. There are some provisions for design [3][4], but they are either to pessimistic or not cover all practical applications. Even so, the existing design methods are oriented on isolated elements only. In case of this type of structures the interaction between primary and secondary components, as well as the flexibility of

Selected Topics in Energy, Environment, Sustainable Development and Landscaping

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connections (sometimes they are of partial-strength, too) may significantly influence their response. The buckling strength of these structures is directly influenced by the lateral restraining. Sensitivity to in-plane second-order effects, the global imperfections, and the possible coupling of local and overall buckling may also influence their behaviour. According to EN1993-1-1[1], there are different imperfection shapes. On this purpose a

preliminary analysis shall be performed in order to emphasize the importance of imperfection shape to be considered in the analysis. In Figure 1 are presented two types of imperfections recorded on site: a) erection imperfections (out of plane rafter displacement); b) manufacturing imperfection (local buckling of the web).

a) b)

Fig. 1: Imperfections recorded on site: a) erection imperfection (er); b) manufacturing imperfection (man).

2 Numerical simulation 2.1 Analyzed frame A series of frames of different spans and heights have been analyzed. The frames were designed to withstand the vertical loads and satisfy the ULS and SLS criteria. The frames have pinned base connections, tapered columns, hunched rafters and a pitch roof angle of 80 (Figure 2). The length of the rafter hunch is 15% from the span in all the cases. The main dimensions of characteristic sections of frames are presented Figure 2. The chosen dimensions are quite common in practical applications. Both eigen-buckling (LEA) and nonlinear elastic-plastic (GMNIA) analyses have been applied. The computation was performed with Ansys v 8.0 using Shell 43 elements enabling for large strain plastic analysis. Joints were modeled using contact

elements (Ansys Conta 52) in order to introduce in the global analysis the real behavior of connections. The material behavior was introduced by a bilinear elastic-perfectly plastic model, while S235 yield strength was considered in the analysis. Lateral restrains by purlins and side rails were considered. Moreover, in all the cases, it was simulated the restraining effect induced by longitudinal beams located at eaves and ridges. The lateral restraints are of 4 different types, as shown in Figure 3 [5]. Types 2 and 3 simulate the purlin/sheeting effect, when the purlin can be connected with one or two bolts, respectively. Type 4 is type 2 with an additional fly brace. Type 1, the reference case, actually means no lateral restrains introduced by purlins and side rails. To simplify the computation model, in the analysis the lateral restrains have been considered axially rigid.


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L

HvarHxLpin

Fig. 2: Geometry of the analyzed frames

(a) restrain type 1 (b) restrain type 2 (c) restrain type 3 (d) restrain type 4

Fig. 3: Types of lateral restrains

Table 1: Main dimensions of the analyzed frame Dimensions h*b*tf*tw [mm] Frame

type H

[m] L

[m] column hunch rafter

var4x24pin(3) 4 24 (450…900)*280*15*10 (500…900)*250*15*12 500*250*12*10 var4x30pin(3) 4 30 (500…1200)*350*15*12 (550…1200)*300*15*12 550*300*15*10 var8x24pin(3) 8 24 (450…900)*280*15*10 (500…900)*250*15*12 500*250*12*10 var8x30pin(3) 8 30 (500…1200)*350*15*12 (550…1200)*300*15*12 550*300*15*10

(3)-class 3 web cross section for rafter

Erection imperfections

(asymmetric out of plane column displacement)

Manufacturing imperfections

(asymmetric out of plane bending and

twisting of the rafter)

Fig. 4: Imperfections considered in the FEM analyses


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Rafter-to-column and rafter-to-rafter connections are bolted as shown in Figure 2. Vertical loads from permanent and snow actions were introduced at the purlin location (e.g 1.2 m along the rafter). Initial sway imperfection was considered in all models. Both erection and manufacturing imperfections [5] were considered separately in analyses. The applied imperfections are presented in Figure 4.

2.2 Result of numerical simulation Nonlinear 3D elastic-plastic analysis and 3D eigen-value analysis have been conducted to identify the critical and failure modes of frames. Correspondingly, critical and ultimate load multipliers were recorded and the results are presented, for all analyzed frames and LT restraining types. These results are summarized in Fig. 5.

0 1 2 3 4 5 6

var4x24pin(3)

var4x30pin(3)

var8x24pin(3)

var8x30pin(3),

Fig. 5: Load multiplier

where: uλ is the ultimate load multiplier; ,cr iλ is the elastic critical load multiplier corresponding for restrain type i.

Analyzing these results one observes the effectiveness of lateral restrains influences the sequence in which the local and overall buckling occur. When the structure is well laterally restrained, in almost all the cases the local buckling (Fig. 6b ) occurs prior to lateral-torsional mode ( Fig. 6a ). The local buckling is elastic for Class 4 sections, and plastic for Class 3. The critical local buckling load

in cases of restrains types 3 and 4, and Class 4 sections is higher then ultimate load obtained from elastic-plastic analysis, uλ . Also, in these cases, the coupling of local elastic buckling with overall elastic buckling of the rafter occurred ( Fig. 6c).

a) Overal LT buckling b) Local Buckling c) Coupling LT+L Buckling

Fig. 6: Coupling of local elastic buckling with overall elastic buckling

For the case of frames described in Table 1, imperfections of EC3 were taken into account. In Figure 7, a comparison between perfect structure, initial bow (out of plane) imperfection and initial sway imperfection is presented. The applied lateral restraints are type 2 from figure 3. The values of the applied imperfection are as follows:

• 80 mm (24 m span frames), 100 mm (30 m span frame) for initial bow imperfection

(er), l/150 corresponding to curve c, for plastic analysis, according to clause 5.3.2 (3)-a) of EN1993-1.1

• 14 mm (4 m height frame), 28 mm (8 m height frame) for initial equivalent sway imperfection, according to clause 5.3.2 (3) b) of EN1993-1.1

λuλcr,4λcr,3λcr,2λcr,1


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1.00

0.91

0.99

0.00 0.20 0.40 0.60 0.80 1.00

λu,imp/λo

var4x24pin(3)-no

var4x24pin(3)-man

var4x24pin(3)-er

1.00

0.88

0.98

0.00 0.20 0.40 0.60 0.80 1.00

λu,imp/λo

var4x30pin(3)-no

var4x30pin(3)-man

var4x30pin(3)-er

1.00

0.90

0.97

0.00 0.20 0.40 0.60 0.80 1.00

λu,imp/λo

var8x24pin(3)-no

var8x24pin(3)-man

var8x24pin(3)-er


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1.00

0.89

0.97

0.00 0.20 0.40 0.60 0.80 1.00

λu,imp/λo

var8x30pin(3)-no

var8x30pin(3)-man

var8x30pin(3)-er

Fig. 7: Ultimate load multiplier for different type of EC 3 imperfections

3 Case study – 50 m span main frame 3.1 Description of the frame The primary load-bearing structure of the building uses a simple steel portal frame shape based on a 6.00 m grid (Figure 8), combined with a king post truss rafter. The clear span of the frame is 50 m, with additional 4 m extension on both sides. The frames have fixed base connections, tapered columns, hunched and king-post truss rafters and a pitch roof angle of 30. The rafter was extended over the two lateral extensions and fixed at the top level of the columns from the extremities. In that way instead of having a simple frame, we have transformed the rafter in a continuous beam, increasing both its strength and stiffness. The

supporting structure of the tribune is fixed to the frame column in the transverse plane, increasing in that way the lateral stiffness of the whole transverse frame. In order to prevent lateral-torsional buckling of the rafter, its lower flange was braced laterally to the roof purlins (see Figure 9 a&b). Supplementary lateral restraints were provided by means of longitudinal beams, stiffened together by the roof bracings. At the mid span, king post truss was laterally restrained in order to prevent its lateral displacement in case of horizontal actions (e.g. seismic action-see Figure 9a). All the assemblies (excluding longitudinal beam, bracings) are made from welded steel sections. A structural steel with S355 steel grade (fy=355 N/mm2) have been used. In Figure 10 are presented the structural model of the building and the actual stage of the constructed building.

Fig. 8. Characteristic section of the structure


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a) lateral restraining of the king post truss b) rafter-to-column detail

Fig. 9. Connections detail

Fig. 10. The whole structural model and the actual stage of the building

3.2 Design of the main frame-linear elastic

analysis (LEA) In order to evaluate the structural response, in the design process were considered the following loads (characteristic values):

• Roof loads (EN1991-1-1): dead load + technological load qk = 1.0 kN / m2

• Live loads on floors (EN1991-1-1) uk= 5.0 kN / m2

• Snow loads on the roof according to CR 1-1-3-2005 (EN1991-1-3), s0,k=1.5 kN/m2

• Wind loads on building envelope according to NP-082-04 (EN1991-1-4), qref=0.4 kN/m2

• Fire loads of 120 MJ/m2 • Seismic action according to P100-

2006 (EN1998-1), with peak ground acceleration ag=0.12g and control period of seismic motion Tc=0.7 sec

The design of the steel structure was performed following the Romanian code STAS 10108/0-78 [13]. For strength, stability and stiffness requirements of the structural elements the prescription of SR-EN1993-1-1[8], SR-EN1993-1-8[9] and P100/2006 [10] were also used.

In the case of large spanned structures, the vertical deflection under gravitational loads represents one of the major constraints in the design process. In order to keep under control the deformations of the frames, fixed base connections, tapered columns and hunched king-post truss rafter solution were chosen [10]. The rafters were extended on both sides over the annexes, increasing both the vertical and horizontal stiffness of the frame. A suitable horizontal and vertical bracing system were provided in order to control structural flexibility, eigen values and deflections of the main structure. Fly braces were provided at the inner flange of the rafter in order to improve the flexural-torsional buckling resistance of these elements (Fig. 9b). Having class 3 section of the structural elements, linear elastic structural analysis was performed, using a seismic behavior factor of q=1 according to P100-2006 [10]. Even with q=1, the combinations of actions for seismic design situations were not the dominant load combinations. The design checks of the structural elements for ULS include persistent or transient design situations (fundamental combinations) where snow loads play the key role. For SLS design checks of the structural elements fundamental and exceptional load combinations


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were used. Performing a dynamic 3D analysis of the structure, with the structural masses concentrated on joints, first longitudinal eigen period of Tlong=0.588

sec and first transversal eigen period of Ttransv=0.448 sec were obtained (see Figure 11).

First longitudinal vibration mode T=0.588 sec First transversal vibration mode T=0.448 sec

Fig. 11. Eigen vibration modes and periods The maximum transversal and longitudinal sway displacement for SLS check under seismic loads according to P100-2006 are:

,,

0,0050.014 112.50.4 1.0

SLSr aSLS

r x

d hd mmqν

⋅= ≤ = =

⋅ ⋅ (1)

,,

0,0050.047 137.50.4 1.0

SLSr aSLS

r y

d hd mmqν

⋅= ≤ = =

⋅ ⋅ (2)

The maximum vertical deflection of the rafter for SLS check under snow load is:

161.4 166.7300aLf mm f mm= ≤ = = (3)

In order to have an overview about the real behavior of the structure, a finite element linear elastic analysis (FEM) of the transverse frame has been performed with Ansys computer program. The elements of the frame were modeled using shell finite elements (Shell 43- see Figure 12). The forces

on the rafter were applied as point loads (points where purlins are fixed on the frame). The connections between structural elements rafter-to-column, beam-to-column, rafter-to-rafter, column base connections were considered fully rigid. The results of the detailed linear-elastic analysis (LEA) confirmed the previously evaluated ULS and SLS results. The recorded vertical displacement in case of FEM linear elastic analysis was 152 mm (instead of 203 mm –linear elastic analysis). It might be emphasized that the resulted structure is more rigid in case of FEM analysis, explained by the shift of the neutral axis along the elements with variable cross sections (i.e. tapered column, and hunched rafter).

Fig. 12. FEM model of the main frame

The resulted maximum stress does not exceed 252 N/mm2. There were many concerns about the

stress distribution in the connection of the king post


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truss with the rafter, but the obtained results does not overpass the limit. 3.3 Design of the main frame - non linear

elastic-plastic analysis (GMNIA) In Figure 14, it is illustrated the way in which the initial bow (out of plane) imperfection is considered in the nonlinear-elastic analysis (GMNIA). Three types of lateral restraints of the rafter were

considered separately in the analyses (see Figure 13 [5],[11]). Types 2 simulate the purlin/sheeting effect, when the purlin can be connected with one or two bolts, respectively. Type 3 is the same with type 2 with an additional fly brace. Type 1, the reference case, actually means no lateral restrains introduced by purlins and side rails.

(a) restraint type 1

(b) restraint type 2

(c) restraint type 3

Fig. 13. Types of lateral restraints considered in the analysis

a) global view b) lateral view

Fig. 14. Manufacturing imperfections considered in non-linear elastic-plastic analysis [6]

Fig. 15. Stress distribution along the transverse frame under gravity load combinations-non

linear elastic-plastic analysis

To simplify the computational model, in the analysis the lateral restraints were considered axially rigid. The values of the applied imperfection is 167 mm (50 m span frame) for initial bow imperfection (er), l/150 corresponding to curve c, for plastic analysis, according to clause 5.3.2 (3)-a) of EN1993-1.1 [1]. The material behavior was introduced by a bilinear elastic-perfectly plastic model, with a yielding limit of 355 N/mm2.In Figure 15 is presented the Von

Missed stress distribution within the elements of the analised frame and in Figure 16 are illustrated the capacity curves for different type of analysis. As it was expected the lateral restrains of the rafter played an important role in the total capacity of the main frame. Also it must be emphasized that there is more than 25% structural capacity reserve.


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Fig. 16. Capacity curves for different type of analyses

4 Sustainability and life cycle cost Sustainable construction is about achieving a viable balance between economic competitiveness, social benefit and environmental impact. Economic competitiveness is defined mainly by the selected materials and designed solutions. Initial cost estimation for the described ice rink solution is presented below (Table 2.). Because the execution

works have been suspended before to finish totally the building, supplementary unforeseen costs appeared. A real cost evaluation received from the general contractor is presented below (Table 3.). It can be seen that supplementary costs double the evaluated initial cost of the building. In terms of economic competitiveness due to unforeseen costs the building lost 17 years of utilization costs, creating in that way a hardly unbalanced degradation in performance of sustainability and life cycle cost.

Table 2. Cost estimate for the ice rink according to DIN 276 cost groups. _______________________________________________________________________________________________________ Cost group Description Total [Euro] Percentage [%] _______________________________________________________________________________________________________ 100 Site cost 0 0.00% 200 Utilities 0 0.00% 300 Construction costs 2.000.000 60.60% 400 Mechanical and electrical works 600.000 18.20% 500 Site finishing 300.000 9.10% 600 Equipment 300.000 9.10% 700 Design, project management 100.000 3.00% _______________________________________________________________________________________________________ Cost group 100-700 3.300.000 100.00% General project development cost 330.000 Total project cost 3.630.000 _______________________________________________________________________________________________________ Notes: Estimated values based on Romanian price level in year 2007. Table 3. Real cost evaluated by the general contractor according to DIN 276 cost groups. _______________________________________________________________________________________________________ Cost group Description Total [Euro] Percentage [%] _______________________________________________________________________________________________________ 100 Site cost 0 0.00% 200 Utilities 0 0.00% 300 Construction costs 4.200.760 59.20% 400 Mechanical and electrical works 1.346.117 19.00% 500 Site finishing 350.000 4.90% 600 Equipment 974.915 13.70% 700 Design, project management 220.000 3.10% _______________________________________________________________________________________________________ Cost group 100-700 7.091.792 100.00% General project development cost 709.179 Total project cost 7.800.971 _________________________________________________________________________________________ Notes: Values based on 3.2719 euro/lei conversion factor.


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From the point of view of social benefit ice rinks are attractive sports and recreational facilities promoting health and social activity as a key element of “quality of life” [16]. From the point of view of environmental impact - energy consumption is in the key role when speaking of the life cycle costs and above all the environmental load of the facility during its life cycle [17]. The key to the effective utilization of the energy resources is in the consciousness of the energy-sinks and the various parameters affecting the energy consumption. The construction, plant system and operation define the energy consumption of an ice rink. The construction characteristics are the heat and moisture transfer properties of the roof and walls, as well as air infiltration through cracks and openings in the building envelope.

The structure of the floor is also important from the energy point of view [16]. Plant characteristics include the refrigeration, ventilation, dehumidification, heating, lighting and ice maintenance systems. The operational characteristics are the length of the skating season, air temperature and humidity, ice temperature, supply air temperature and fresh air intake of the air-handling unit as well as the control- and adjustment parameters of the appliances. Figure 3.a. shows the estimated energy spectrums and Figure 3.b. illustrates the estimated energy flows of a small sized ice rink. Based on these reference values, Table 4 illustrates the estimated expenses for the life cycle expenses evaluation.

Fig. 17. Spectrum of heating energy need (a) and electric consumption spectrum (b) of a prototype ice rink in Munich (10) Table 4. Estimated expenses for the ice rink utilization phase (main utilization area HNF=5700 m2). _________________________________________________________________________________________ Expenditures –utilization phase Target value [Euro/m2 x HNF x 1year] _________________________________________________________________________________________ Cleaning of the building 4.45 Water sewage 3.90 Heating 2.25 Cooling 8.55 Electricity 6.45 Service / maintenance /inspection 1.10 Miscellaneous 2.25 Building maintenance 4.45 _________________________________________________________________________________________ Utilization subtotals 33.40 _________________________________________________________________________________________

5 Conclusion First part of the paper presets a parametric study performed in order to analyze the influence of two different types of imperfections (e.g. manufacturing imperfections characterized by initial bow imperfections, and erection imperfections characterized by initial sway imperfections). The magnitude of the imperfections was considered as being equal with those prescribed in EN1993-1.

However, it was observed that the considered imperfections do not influence significantly the final capacity of the frame. Moreover, the capacity of the frame when the initial sway imperfections are applied, is influenced mainly by the height of the frame, while when initial bow imperfections were, the capacity is influenced by the span of the frame. The paper illustrates the successful application of the steel structure for a large span using a simple portal frame shape, combined with a king post truss rafter. A wide range of design parameters are briefly summarized. The article also emphasizes the whole


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design process, assisted by FE analysis - in order to perform supplementary stability checks of the framed structure. Case study selected was the main frame of an Ice Rink. Due to the unusual shape of the transverse frame, there were many concerns about its real behavior under gravitational load, the most important ones in this particular case. For this purpose a linear elastic analysis (LEA) followed by a nonlinear elastic-plastic analysis (GMNIA) were performed in order to determine the real behavior of the frames. From structural point of view a good agreement between 3D structural analysis and LEA-FEM has been found. GMNIA analysis confirm at least 25% overstrenght of the structure by applying the chosen structural solution and lateral restraints of the main rafter. Even with behavior factor q=1, the combinations of actions for earthquake design situations were not the dominant load combinations. In the design checks of the structural elements, gravity loads played the key role. Finally it is underlined why the ice rink design and operation are totally unique and differ in many ways from standard buildings. The paper shows the difference between estimated cost and real cost in this particular case, which should change radically the final classification of the building from the point of view of sustainability. This case study is a good example to emphasize the difference between theoretical and practical approach in terms of costs, which highly influenced by particular contractual context and the total duration of the execution time. References: [1] EN 1993-1-1 Eurocode 3: Design of steel

structures Part 1.1: General rules and rules for buildings;

[2] Davies, J.M., In-plane stability in portal frames, The Structural Engineer, Vol. 68, No. 8, p. 141-147, 1990;

[3] C. M. King: Design of steel portal frames for Europe. Technical report SCI publication P164;

[4] N. Balut, E. Cuteanu: Flexural-torsional buckling of portal frame rafters. Proceedings of the 10-th Interantional Conference on metal Structures. ICMS 2003, Timisoara-Romania, 16-17 oct 2003, pp 1-10 (2003);

[5] D. Dubina, I. M. Cristutiu, V. Ungureanu, Zs. Nagy: Stability and ductility performances of light steel industrial building portal frames, 3-rd European Conference of Steel Structures, Eurosteel 2002, Coimbra-Portugal, sept. 2002, pp 635-643 (2002);

[6] CR-0-2005: Cod de proiectare pentru bazele proiectarii structurilor in constructii (Design Code. Basis of design. Romanian design code).

[7] P100-2006: Cod de proiectare seismica P100. Partea I-Prevederi de proiectare pentru cladiri (EN1998-1).

[8] SR-EN 1993-1-1: Eurocod 3: Proiectarea structurilor de oţel Partea 1-1: Reguli generale şi reguli pentru clădiri

[9] SR-EN1993-1-8:Eurocod 3: Proiectarea structurilor de oţel. Partea 1-8: Proiectarea îmbinărilor

[10] H. C. Schulitz, W. Sobek, K. J. Habermann - Steel Construction Manual, Birkhauser Verlag 2000, ISBN no. 3-7643-6181-6

[11] D. Dubina, I. M. Cristutiu: Buckling strength of pitched-roof portal frames of Class 3 and Class 4 tapered sections, International Conference on Steel and Composite Structures - Eurosteel 2005, Maastricth-Holland, 7-11 june 2005, pp 635-643 (2005);

[12] DIN 276-1:2006-11 (2006): Kostenplanung im Hochbau und im Besonderen die einzelnen Stufen der Kostenermittlung basieren im Wesentlichen auf den Vorgaben.

[13] STAS 10108/0-78 :Calculul elementelor din oţel. ASRO-Asociatia de Standardizare din Romania

[14] CR 1-1-3-2005 (2005): Cod de proiectare. Evaluarea Zapezii asupra constructiilor (Actions on structures-Snow loads). Ministerul Transportului Constructiilor si Turismului din Romania

[15] NP-082-04 (2005): Cod de proiectare. Bazele proiectarii si actiuni asupra constructiilor. Actiunea vantului. (Actions on structures-Wind loads). Ministerul Transportului Constructiilor si Turismului din Romania

[16] International Ice Hockey Federation (2006): Recommendation of International Ice Hockey Federation for Ice Rinks

[17] Bundesministerium für Verkehr, Bau- und Wohnungswessen, 2001-Guideline for Sustainable Building – Federal office for N\Building and regional Planning.

[18] Franz Knoll, Thomas Vogel (2009): Design for robustness. Structural engineering documents 11. IABSE Sed Documents, ISBN 978-3-85748-120-8.


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