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FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE COLUMNWITH LONGITUDINAL HOLE

AMIRHOSSEIN BASRAVI

A project report submitted in partial fulfillment of therequirement for the award of the degree ofMaster of Engineering (Civil Structure)

Faculty of Civil EngineeringUniversiti Teknologi Malaysia

DECEMBER 2010


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To my beloved family

Love you forever


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ACKNOWLEDGEMENT

I have a host of people to grace of their involvement in this major work. The

order I mentioned below does not necessarily represent the amount of work they did.

I am sincerely grateful to my supervisor, Assoc. Prof. Ir. Dr. Mohd Hanim

Osman, for his continuous support, suggestions and immeasurable contribution to my

project. He always provides me guidance and feedback in this project. I am also very

thankful to Prof. Dr. Jahangir Bakhteri for his advice, guidance and motivation. Without

their help, I would not have completed my project.

I would also like to express my deepest gratitude to Universiti Teknologi

Malaysia (UTM) for providing the necessary facilities and the staff in Faculty of Civil

Engineering for their help in the completion of this project.

Deep appreciation goes to my dear parents and sisters; I would definitely notsucceed in my life without their love and support. I would like to grab this opportunity

to thank my friends who have always provided inspiring ideas on my work.

Lastly, thanks are due to the people that I did not mention their name for their

assistance and encouragement.


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ABSTRACT

A finite element study was carried out to investigate the effect of positioning

hole along reinforced concrete short braced columns in multi-storey buildings. RC

columns having different sizes and reinforcement, with holes positioned at the centers

of their cross-sections were modeled by LUSAS using three-dimensional non-linear

finite element analysis. The ultimate strengths of the columns obtained from the present

study is compared with the results obtained from the laboratory testing of the same

columns as well as with the design strengths recommended by the BS 8110 and ACI

codes of practice. The reduction in the load carrying capacity of columns with holes

was highlighted. In conclusion, the analysis results showed significant reduction in

their load carrying capacities and the safety factors obtained were much less than the

nominal value usually recommended by various codes of practice.


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ABSTRAK

Satu kajian menggunakan kaedah unsur terhingga telah dilakukan untuk

mengetahui kesan membuat kedudukan lubang di dalam tiang konkrit bertetulang pada

bangunan bertingkat. Tiang konkrit tetulang yang memiliki ukuran dan tetulang yang

berbeza, dengan lubang terletak di pusat keratan telah di modelkan dengan perisian

LUSAS menggunakan analisis unsur terhingga tiga-dimensi secara non-linear.

Kekuatan muktamad dari tiang yang diperolehi daripada kajian ini dibandingkan dengan

keputusan yang diperolehi daripada ujian makmal keatas tiang yang sama saiz juga

dengan kekuatan rekabentuk yang disyorkan oleh BS 8110 dan kod amalan ACI. Beban

rintangan telah didapati berkurangan bagi tiang yang mempunyai lubang.Kesimpulannya, hasil analisis menunjukkan penurunan yang ketara pada beban

keupayaan dan faktor keselamatan yang diperolehi jauh kurang dari nilai nominal yang

biasanya disyorkan oleh pelbagai kod amalan.


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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS xiv

1 INTRODUCTION 1

1.1 Background 1

1.2 Problem Statement 4

1.3 Objective of the Study 5

1.4 Scopes of the Study 6

2 LITERATURE REVIEW 7

2.1 Concrete 7

2.1.1 Stress-Strain Relation of Concrete 8

2.1.2 Elastic Modulus of Concrete 9


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2.2 Steel Reinforcement 10

2.3 Reinforced Concrete 12

2.3.1 Affecting Factors on Choosing of

Reinforced Concrete for a Structure 13

2.4 Reinforced Concrete Column 16

2.4.1 Types of Column and Failure Modes 17

2.4.2 Reinforced Concrete Column Capacity 20

2.4.3 Fracture 21

2.4.4 Buckling of Column 22

2.5 Finite Element Method 252.5.1 Brief History 26

2.5.2 Definition of FEM 26

2.5.3 Advantages of FEM 27

2.5.4 Methods of Formulating FE Problems 28

2.5.5 Types of Finite Element 29

2.5.6 Basic Steps of Finite Element Analysis 30

2.5.7 Fundamental Requirements 32

2.5.8 Meshing 32

2.5.9 Verification of Results 33

2.6 LUSAS 34

2.6.1 Characteristic of LUSAS Software 34

2.6.2 Analysis Procedure According to LUSAS 34

2.7 Non-linear Analysis 35

2.8 Studies Done Related to RC Column with Hole 40

2.8.1 A Critical Review of RC Columns andConcealing Rain Water Pipe in Buildings 40

2.8.2 Full Scale Test on Shear Strength and

Retrofit of RC Hollow Columns 46

2.8.3 Slender High Strength Concrete Columns

Subjected to Eccentric Loading 49


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3 RESEARCH METHODOLOGY 53

3.1 Introduction 53

3.2 Finite Element Modeling 54

3.2.1 Geometry 54

3.2.2 Finite Element Meshing 56

3.2.3 Material Properties 58

3.2.4 Boundary Condition 59

3.2.5 Loading 60

3.2.6 Nonlinear Analysis 61

3.3 Experimental Work 633.3.1 Test Models 63

3.3.2 The Test Models Classification 65

3.3.3 Preparation of the Test Specimens 66

3.3.4 Instrumentation and Testing of Models 71

3.4 Flowchart of the Finite Element Analysis 74

4 ANALYSIS, RESULTS AND DISCUSSION 76

4.1 Introduction 76

4.2 The Results of Finite Element Analysis 77

4.2.1 Vertical Stress-Strain Curves of Models

Based on FEA Results 81

4.3 Reduction in Load Carrying Capacity of RC

Columns Concealing Hole 82

4.4 Comparison of the Results 84

4.4.1 Design Strength Requirement of Columns 87

4.5 Discussions 91

5 CONCLUSION AND RECOMMENDATION 92

5.1 Conclusions 92

5.2 Recommendations 93

REFERENCES 94


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LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Details of columns in group A, B and C 49

3.1 The specification and dimension of the column models 55

3.2 Concrete properties 58

3.3 Steel properties 59

3.4 The specification and dimension of the column models 64

3.5 The column models type 66

4.1 Maximum vertical stress and strain in the all columns 77

4.2 The percentages of reduction in load carrying capacity ofcolumns with hole 83

4.3 Comparison of the maximum vertical compressive stress

and strain in the models from experimental work and FEA

84

4.4 Comparison of safety factors from experimental studyand FEA based on BS code 89

4.5 Comparison of factor of safety from experimental studyand FEA based on ACI code 90


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LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Hole (rain water pipe) is positioned inside columns 2

1.2 Typical column with hole (embedded drain pipe) 4

2.1 Stress-strain curve of concrete 8

2.2 Static modulus of concrete 9

2.3 Typical stress-strain curve for reinforcing steel 11

2.4 Simplified stress-strain curve for reinforcing steel 12

2.5 P- effect on slender column 18

2.6 Columns failure modes 19

2.7 Forces act on the column section 20

2.8 Basic modes of fracture 21

2.9 Buckling of column 24

2.10 Bending moment in the column 24

2.11 Flow chart for the basic steps of FEA 31

2.12 P- effect on a column 37


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2.13 Nonlinear boundary condition 38

2.14 Forms of modified Newton-Raphson iteration 39

2.15 Inappropriate positioning of rain water pipe incolumns section 41

2.16 Formation of honeycombs around the drain pipe 42

2.17 Leakage in the lapping parts of the PVC drain pipes 43

2.18 Congest ion and non-uniformity in beams reinforcementsat columns section caused by presence of drain pipe 43

2.19 Elbow part of the drain pipe at the ground level 44

2.20 Configurations of lateral reinforcement inhollow columns 47

2.21 Geometry and details of configurations (a) and (b) 49

2.22 Load arrangement for the test 50

2.23 Instrumentation of slender column 51

3.1 Three dimensional solid hexahedral element (HX8M) 56

3.2 Modeling of bar and meshing of model C1b 57

3.3 Typical model showing generated mesh, loadingand boundary condition

60

3.4 Incremental / iterative nonlinear solution 61

3.5 Modified arc length load incrementation for the onedegree of freedom response 62

3.6 Steel works consist of cutting, bending and tying steel bars 67


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3.7 Positioning of the pipes in center of columns cross-section 68

3.8 Column form work was positioned horizontally andready for casting

69

3.9 The fresh reinforced concrete columns after casting 70

3.10 Test setup 74

3.11 Flowchart of finite element analysis 75

4.1 Deformed shape of model C7b 78

4.2 Vertical stress contour of model C7b 78

4.3 Vertical strain contour of model C7b in 2D 79

4.4 Vertical strain contour of model C7b in 3D 79

4.5 Vertical stress contour of model C7a 80

4.6 Vertical strain contour of model C7a 80

4.7 Stress-strain curve of column C1 81




4.11 Vertical stress-strain curve for column C1a 85

4.12 Vertical stress-strain curve for column C3a 86

4.13 Vertical stress-strain curve for column C5b 86

4.14 Vertical stress-strain curve for column C7b 87


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LIST OF SYMBOLS

A g - Gross area of the column section

Anc - Net concrete area of the cross-section of the model

A sc - Area of the longitudinal reinforcement

A st - Total area of longitudinal reinforcement

b - Width of column

d - Effective depth

e - Eccentricity of load

E - Youngs Modulus

f cu - Characteristic compressive strength of concrete

f y - Characteristic yield strength of steel

h - Gross area of the column section

l e

- Net concrete area of the cross-section of the model

M - Ultimate moment

N - Column design load

P - Vertical load to the column


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- Modulus ratio

- Coefficient dependant on the bar type

- Strength reduction factor

- Compressive strain

- Compressive stress


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CHAPTER 1

INTRODUCTION

1.1 Background

A column is the vertical structural member supporting axial compressive loads,

with or with-out moments. Columns support vertical loads from the floors and roof and

transmit these loads to the foundations. The load carrying capacity of a column depends

on the materials used in its construction, its length, the shape of its cross-section, and

the restraints applied to its ends. Failure of a column in a critical location can cause the

progressive collapse of the adjoining floors and the ultimate total collapse of the entire

structure.

For design purposes, columns are divided into two types namely, short columns

and slender columns. Considering lateral load action, columns are divided into two

groups which are braced columns and unbraced columns.


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In the construction of modern multistory buildings, holes (pipes) are positioned

vertically inside the reinforced concrete columns to accommodate the essential services

such as drainage of roof top rain water, electric wiring from floor to floor etc. The holes

(pipes) are placed inside the columns, based on pretext to maintain the aesthetic of the

buildings. The practice of embedding rain water down pipes (holes) inside reinforced

concrete columns is followed particularly in those multistory buildings which have flat

roofs and glass front views. The diameters of holes (pipes) vary, depending on the

amount of drained water.

Tropical countries such as Malaysia are having rainfall throughout the year,

which require an effective and appropriate drainage system for rain water in the

construction of any new building project. Therefore, the practice of positioning hole

(Poly Vinyl Chloride (PVC) pipes) inside reinforced concrete (RC) columns to drain the

rain water from the roof top of the multi-storey buildings and discharge it at the ground

level has become a usual practice nowadays (Figure 1.1). The practice has been adopted

under the impression that, exposing the pipes (holes) outside the columns will affect the

appearance of the buildings.

Figure 1.1 Hole (rain water pipe) is positioned inside columns


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However, this method of drainage could cause serious damage to the safety of

the structure. Columns constructed with holes (embedded PVC drain pipes), not only

have reduced load carrying capacities but also, could be very dangerous to the safety of

the entire building structure and can reduce its useful life significantly.

Some of the problems caused by the practice of positioning hole (PVC rain

water down pipe) inside the column are as follows:

i. Positioning the hole in the corner or edge of the columns section will reduce the

effective cross-sectional area of the column significantly and also will affect to

its shear capacity.

ii. Even in case the hole (rain water pipe) is positioned at the central part of the

columns cross-section, the assessment of the effective depth of the column

section might become inaccurate and hence, load carrying capacity of the

columns is further reduced.

iii. There is a chance of formation of honeycombs around the hole (drain pipe).

iv. Leakage from the joint lapping part of the pipe (hole) can cause corrosion and

rusting in the reinforcement of the column, and hence loss of bond and reduct ion

in the strength of the structural element.

v. The huge reduction in the columns strength at ground level, where elbow part

is used to discharge rainwater.

Therefore, the present study has been carried out to investigate the reduction in

load carrying capacity of rectangular and square reinforced concrete short columns with

hole (embedded PVC drain pipe).


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The hysteric performance of the columns is evaluated using various cross

sections with different amount of reinforcement. Figure 1.2 shows a typical column

with hole positioned at the center of column cross-section. The cross section dimensions

of the column are represented by h and b, where its height is l .

Figure 1.2 Typical column with hole (embedded drain pipe)

1.2 Problem Statement

The practice of positioning hole (PVC pipe) inside reinforced concrete (RC)

columns to drain the rain water common nowadays, however this method of drainage

could cause serious damage to the safety of the structure.


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1.4 Scope of the Study

The study includes 3-D finite element analyses of RC braced short columns with

holes (embedded drain pipes) representing lower level (i.e. ground floor columns). The

investigation concentrate on the modeling of axially loaded columns with hole (PVC

drain pipes) positioned at the center of the columns cross-sections. The LUSAS finite

element program was used to model the columns. The analysis covers material non-

linearity. The dimensions of the columns were the same as the dimensions of the model

tested in the laboratory. The half scale laboratory test was carried out and the finite

element analysis results were compared with them as part of the study.


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CHAPTER 2

LITERATURE REVIEW

2.1 Concrete

Concrete materials have a sufficient compressive strength, so are widely used in

civil engineering, reactor buildings, bridges, irrigation works and blast resistant

structures, etc.

Concrete is a construction material consisting of coarse aggregate, fine

aggregate, cement, water and other chemical and pozzolanic admixtures

(superplasticizer, air entraining, retarder, fly ash and etc.) It has a very wide variety of

strength, and its mechanical behavior is varying with respect to its strength, quality andmaterials. The strength and the durability are two important factors in concrete.


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2.1.1 Stress-Strain Relation of Concrete

Concrete has an inconsistent stress-strain relation, depending on its respective

strength. Compressive strength of concrete depends on the cement content, the cement-

water ratio, the age of concrete and the type of aggregate. However, there is a typical

patent of stress-strain relation for the concrete regardless the concrete strength, as

shown in Figure 2.1.

Figure 2.1 Stress-strain curve of concrete [1]

The behavior of concrete is almost elastically when the load is applied to the

concrete. So according to the stress, the strain of the concrete is increasing

approximately in a linear manner. Finally, the relation will be no longer linear and the

concrete tends to behave more and more as a plastic material. So the displacement


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cannot complete after the removal of the loadings, therefore permanent deformation

incurred.

Generally, the strength of concrete depends on the age, the cement-water ratio,

type of cement and aggregate, and the admixture added to the concrete, an increment in

any of these factors producing an increase in strength. Assumption the concrete can

reach its strength at the age of 28-day because usually the increment of concrete

strength is insignificant after the age of 28-day.

2.1.2 Elastic Modulus of Concrete

The stress-strain relationship for concrete is almost linear provided that the

stress applied is not greater than one third of the ultimate compressive strength. A

number of alternative definitions are able to describe the elasticity of the concrete, but

the most commonly accepted is E = E c, where E c is known as secant or static modulus

(see Figure 2.2).

Figure 2.2 Static modulus of concrete [1]


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The modulus of elasticity of concrete is not constant and highly depends on the

compressive strength of concrete.

BS 1881 has recommended a series of procedure to acquire the static modulus.

In brief, concrete samples in standard cylindrical shape will be loaded just above one

third of its compressive strength, and then cycled back to zero stress in order to remove

the effect of initial bedding-in and minor redistribution of stress in the concrete under

the load. Eventually the concrete strain will react almost linearly to the stress and the

average slope of the graph will be the static modulus of elasticity [2].

2.2 Steel Reinforcement

Steel has great tensile strength and use in the concrete because concrete does not

act in tension well alone; also there is good bond between concrete and reinforcement.

The reinforcing steel has a wide range of strength. It has more consistent properties and

quality compared to the concrete, because it is manufactured in a controlled

environment. There are many types of steel reinforcement. The most common are plain

round mild steel bars and high-yield stress deformed bars.

The typical stress-strain relations of the reinforcing steel can be described in the

stress-strain curve as shown in Figure 2.3.


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Figure 2.3 Typical stress-strain curve for reinforcing steel [1]

From the Figure 2.3, the mild steel behaves as an elastic material until it reaches

its yield point, finally it will have a sudden increase in strain with minute changes in

stress until it reaches the failure point. On the other hand, the high yield steel does nothave a limited yield point but has a more gradual change from elastic to plastic

behavior.

Reinforcing steels have a similar slope in the elastic region with E s = 200

kN/mm 2. The specific strength taken for the mild steel is the yield stress. For the high

yield steel, the specific strength is taken as the 0.2% proof stress. BS 8110 has

recommended an elastic-plastic model for stress-strain relationship, which the

hardening effect is neglected [3]. The stress-strain curve may be simplified bilinear as

shown in Figure 2.4.


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Tensile strength of concrete is neglected in the design of reinforced concrete

because the tensile strength of concrete is just about 10% of its compressive strength.

Therefore the tensile force is assumed to be resisted by the reinforcing steel completely.

The tensile stress is transferred to reinforcing steel through bonding between concrete

and steel, thus insufficient bond will cause the reinforcement to slip within the concrete.

Reinforcing steel can only develop its strength in concrete on the condition that it is

anchored well to the concrete.

2.3.1 Affecting Factors on Choosing of Reinforced Concrete for a Structure

The choice of whether a structure should be built of reinforced concrete, steel,

masonry, or timber depends on the availability of materials and on a number of value

decisions.

i. Economy

Frequently, the foremost consideration is the overall cost of the structure. This

is, of course, a function of the costs of the materials and of the labor and time

necessary to erect the structure. Frequently, however, the overall cost is affected

as much or more by the overall construction time, because the contractor and the

owner must allocate money to carry out the construction and will not receive a

return on their investment until the building is ready for occupancy. S a result,

financial savings due to rapid construction may more than offset increased

material and forming costs. The materials for reinforced concrete structures are

widely available and can be produced as they are needed in the construction,

whereas structural steel must be ordered and partially paid for in advance to

schedule the job in a steel-fabricating yard.


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ii. Suitability of material for architectural and structural function

Concrete has the advantage that it is placed in a plastic condition and is given

the desired shape and texture by means of the forms and the finishing

techniques. This allows such elements as flat plates or other types of slabs to

serve as load-bearing elements while providing the finished floor and ceiling

surfaces. Finally, the choice of size or shape is governed by the designer and not

by the availability of standard manufacture members.

iii. Fire resistance

The structure in a building must withstand the effects of a fire and remain

standing while the building is being evacuated and the fire extinguished. A

concrete building inherently has a 1 to 3 hours first rating without special

fireproofing or other details. Structural steel or timber buildings must be

fireproofed to attain similar fire rating.

iv. Rigidity

The occupants of a building maybe disturbed if their building oscillates in the

wind or if the floors vibrate as people walk by. Due to the greater stiffness and

mass of a concrete structure, vibrations are seldom a problem.

v. Low maintenance

Concrete members inherently require less maintenance than do structural steel or

timber members. This is particularly true if dense, air-entrained concrete has

been used for surfaces exposed to the atmosphere and if care has been taken in


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the design to provide adequate drainage form the structure.

vi. Availability of materials

Sand, gravel or crushed rock, water, cement, and concrete mixing facilities are

very widely available, and reinforcing steel can be transported to most

construction sites more easily than can structural steel.

On the other hand, there are a number of factor that may cause one to select a

material other than reinforced concrete. Those include:

1. Low tensile strength

As stated earlier, the tensile strength of concrete is much lower than its

compressive strength (about 1/10); hence, concrete is subject to cracking when

subjected to tensile stresses.

2. Forms and shoring

The construction of a cast-in-place structure involves three steps not

encountered in the construction of steel or timber structures. These are (a) theconstruction of the forms, (b) the removal of these forms, and (c) the propping

or shoring of the new concrete to support is weight until its strength is adequate.

Each of these steps involves labor and/or materials that are not necessary with

other forms of construction.


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3. Relatively low strength per unit of weight or volume

The compressive strength of concrete is roughly 5 to 10 percent that of steel,

while its unit density is toughly 30 percent that of steel. As a result, a concrete

structure requires a larger volume and a greater weight of material than does a

comparable steel structure. As a result, long-span structures are often built from

steel.

4. Time-dependent volume changes

Both concrete and steel undergo approximately the same amount of thermal

expansion and contraction. Because there is less mass of steel to be heated or

cooled, and because steel is better conductor than concrete, steel structure is

generally affected by temperature changes to a greater extent than is a concrete

structure. On other hand, concrete undergoes during shrinkage, which, if

restrained, may cause deflections or cracking. Furthermore, deflection will tend

to increase with time, possibly doubling, due to creep of the concrete under

sustained compression stress.

2.4 Reinforced Concrete Column

Columns are compression members, although they may have to resist bending

forces due to the eccentricity. A column in a structure transfers loads from beams and

slabs down to foundations. Design of the column is governed by the ultimate limit state,

and the service limit state is seldom to be considered [1].


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2.4.1 Types of Column and Failure Modes

For considering lateral load action, columns are divided into two types which

are braced and unbraced. A column is a braced column when the load is resisted by the

bracing members like shear wall. In this case, the column does not resist lateral load. An

unbraced column is the column that is subjected to lateral loads.

For design purposes, column can be classified as short or slender by a ratio of

effective height (l e) in the bending axis considered to the column depth in the respective

axis (h). BS 8110 has recommended that a slender column can be determined by

Equation 2.1 (for braced structure) or equation 2.2 (for unbraced structure) [3].

The column failure mode can be predicted when knowing the column is short or

slender,

Braced columns:

15 (2.1)

Unbraced columns:

10 (2.2)

Lateral loading acts on a building can cause lateral deflection ( ) to the column.

Consequently, gravity load (P) in the column with eccentricity ( ) will induce additional

moment (M=P ), and increase the column moment.


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Buckling unlikely occurs to a short column. So when the axial load exceeded its

material strength, it will fail. This will cause the column to bulge and eventually to

crush. Buckling may cause a slender column to deflect sideways and therefore induces

an additional moment (M=P ), as illustrated (P- effect) in Figure 2.5.

Figure 2.5 P- effect on slender column [1]

In heavily clad low and medium rise buildings, the P- effects may be small.

However for lightly clad tall buildings with greater lateral flexibility, the P- effects

may become significant. The P- effects may be large enough and require an increase in

the column size.


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There are three modes of column failure, crushing, intermediate and buckling.

Crushing usually occurs in short columns when there is material failure with

negligible lateral deflection. When there are large end moments acted on a

column with an intermediate slenderness ratio, it is possible to occur. Figure 2.6

(a) illustrates the column failure mode in crushing.

Intermediate is typical of intermediate columns and occurs when material failure

intensified by the additional moment and the lateral deflection.

In buckling, there is instability failure which occurs with slender columns.

Figure 2.6 (b) illustrates the failure mode of column in buckling.

(a) (b)

Figure 2.6 Columns failure modes


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2.4.2 Reinforced Concrete Column Capacity

There is a small moment in the short column when cast in-situ concrete structure

in the practical case. This moment supports an approximately symmetrical arrangement

of beams. BS 8110 expresses the capacity of the column (N) as [3],

= 0.35 +0.70 0.35 (2.3)

The columns capacity can be acquired by performing analysis on its cross

section that is subjected to moments and axial forces (see Figure 2.7).

Figure 2.7 Forces act on the column section [1]

The basic equation for axial force capacity (N) and moment capacity (M) can be

derived from Figure 2.7 as follows,

= + + = 0.405 + + (2.4)


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= 20.92 + 2 2 (2.5)

2.4.3 Fracture

Fracture is the separation of material into two or more pieces under the action of

stress. It is a complex process to predict the occurrence of crack on the concrete that

involves the growth of micro and macro voids or cracks, the geometry of the concrete,

and mechanisms of dislocations. So the understanding on fracture is important to know

the crack.

Concrete will suffer from microscopic damage at high stresses regions, and

forming microcracks. Therefore, a zone will be formed in the concrete where theinteraction of microcracks taking place, and finally leads to localization of a

macroscopic discontinuity. Hence, with the classical linear elastic fracture mechanics

cannot get the process zone forming in the concrete. Over the past few decades,

theoretical approaches that are both physically and practically applicable have been

developed for fracture analysis in concrete structures. Figure 2.8 shows three basic

modes of fracture.

Mode I: Opening Mode II: In-plane shear Mode III: Out-of-plane shear

Figure 2.8 Basic modes of fracture


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The mode I fracture is called as the opening mode. In this mode, the forces are

perpendicular to the crack, pulling it to open. An example of this fracture mode is

flexural crack at the bottom of beams at mid-span.

In mode II, the forces are parallel to the crack. In the same direction, one force is

pushing the top half of the crack backward and the other is pulling the bottom half of

the crack forward. Hence, the crack is sliding along itself and a shear crack is formed.

The mode III fracture is called as out-of-plane shear. The material will be

separate and slide along itself, moving out of its original plane, because the forces are

perpendicular to the crack, and are moving in opposite directions of left and right, in

order to grow the crack in front-back direction.

2.4.4 Buckling of Column

Buckling is a failure mode characterized by a sudden failure of a structural

member subjected to high compressive stresses, where the actual compressive stress is

less than the ultimate compressive stresses at the point of failure that the material is

capable of withstanding.

A short column will fail under the action of an axial load by direct compression

before it buckles, but a slender column will fail by buckling in the same manner. When

a compression member becomes longer, the role of the geometry and stiffness (Young's

modulus) becomes more and more important.


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When axial load applies at the column, the critical load for a slender column can

be determined by the Euler Buckling Load,

= 2 2 (2.6)

In reality, loads are seldom loaded on the column centric, and the moment mayreact due to the small eccentricity. The initial column shape can be approximated before

the application of load by the sine function, suggested by Meyer [4],

0= 0sin (2.7)

0 is the maximum deviation from the straightness at mid-height (see

Figure 2.9).

Also the maximum displacement due to buckling at the mid-height can be

expressed as,

= 01 (2.8)


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Figure 2.9 Buckling of column [4]

It is important that consider the effect of P- in the buckling. Hence, the bending

moment taking place in the column, when the column reaches its instability state, as

illustrated in Figure 2.10.

Figure 2.10 Bending moment in the column [4]


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Therefore, the maximum moment is,

= 11 0 (2.9)

Where M 0 = P.e is the moment due to the load eccentricity (e), and also the

factor 1/ [1-(P/P c)] is the moment magnification factor. When the column load reaches

the buckling load, the buckling moment will grow unbounded.

2.5 Finite Element Method

The Finite Element Method (FEM) of analysis is a very powerful, modern

computational tool. This method has been used successfully to solve very complex

structural engineering problems. FEM has also been widely used in other fields such as

thermal analysis, fluid mechanics, and electromagnetic fields.

Since the method involves a large number of computations, therefore it requires

computer to solve a problem.

The finite element method represents the extension of matrix method for skeletal

structures to the analysis of continuum structures. In finite element method, the

continuum is idealized as a structure consisting of a number of individual elements

connected only at nodal points.


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2.5.1 Brief History

Courant has been credited with being the first person to develop the finite

element method in 1943. He used piecewise polynomial interpolation over triangular

subregions to investigate torsion problems.

The next significant step in the utilization of finite element method was taken by

Boeing in the 1950s, in which Boeing used triangular stress elements to model airplanewings. At 1956, Turner et al. had presented their findings on the stiffness matrices for

beam, truss and other elements. Also at 1960, Clough made the term Finite Element

popular.

During 1960s, investigators began to apply the finite element method to other

areas of engineering, such as heat transfer and seepage flow problems.

The very first attempt to analyze the reinforced concrete by finite element was

done by Ngo and Scordelis in 1967. And finally, Zienkiewicz and Cheung wrote the

first book entirely devoted to the finite element method in 1967 [5].

2.5.2 Definition of FEM

The finite element method (FEM) is a general numerical technique for

approximating the behavior of continua by assembly of small parts (elements). Each


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element is of simple geometry and therefore is much easier to analyze than the actual

structure. In essence approximate a complicated solution by a model that consists of

piecewise continuous simple solutions. The elements are called Finite to distinguish

them from differential elements used in calculus.

2.5.3 Advantages of FEM

When numerical analyses were first introduced in engineering practice in the

1960s, many analysis methods such as boundary element method and finite difference

method, were in use. Over time, these methods were dominated by the FEM because of

its inherent generality and numerical efficiency. Although other methods retain

advantages in certain niche applications, they are difficult or impossible to employ to

other types of analyses. At the same time, the FEM has wider applicability. The

versatile analysis tool can be applied to almost any types of engineering problems. For

this reason, the FEM has widespread adoption for increasingly diverse problems and

dominated the market of commercial analysis software.

One of the main advantages of FEM over most other analysis methods is the fact

that FEM can handle irregular geometries routinely and implement higher order

elements with relative ease. Besides, very little extra effort is required in the FEformulation when anisotropic or heterogeneous are to be modeled. In FE modeling,

elements with different properties and geometries are used to cater for structures with

different types and behaviors. Another advantage of FEM is the ease to handle mixed

boundary condition. All the various types of boundary conditions that may encounter in

problem can be included in the formulation of FE.


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2.5.4 Methods of Formulating Finite Element Problems

The finite element method consists primarily of replacing a set of differential

equations in terms of unknown variables with an equivalent but approximate set of

algebraic equations where each of the unknown variables is evaluated at a nodal point.

Generally there are three approaches to formulate the finite element problems:

1. Direct Method

In direct method individual structural members, such as bars, are analyzed with

techniques similar to those used in analysis of simple trusses and frames. The

displacement caused by applied forces is expressed by a set of equations

convertible into a stiffness matrix for each of the structural member. The

assembly of the element stiffness matrices together will form a large (global)

matrix, which represents the stiffness of the entire structure. Direct method is

difficult to apply to two-and three dimensional problems.

2. The Minimum Total Potential Energy Method

The minimum total potential energy method is a common approach in

generating finite element model in solid mechanics. External load applied to the

body will cause the body to deform. During deformation, the work alone by

external forces is stored in the material in the form of elastic energy, called

Strain Energy. The minimum total potential energy principal states that for a

stable system, the displacement at the equilibrium position occurs such that the

value of the systems total potential energy is a minimum.


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3. Weighted Residual Method

The weighted residual methods are based on assuming an approximate solution

for the governing differential equations. The assumed solution must satisfy the

initial and boundary conditions of the given problem, because the assumed

solution is not exact, substitution of the solution into the differential equation

will lead to some residual or error. Simply stated, each residual method requires

the error to vanish over some selected intervals or at some points.

2.5.5 Types of Finite Element

Classification according to the way the element represents the displacement field

in three dimensions distinguishes among solid, shell, membrane and beam elements.

a) Solid element

The solid element fully represents all three dimensions. The solid element

models the 3-D displacement field with three variables.

b) Shell element

The shell elements are used when the thickness of the shell is considered small

relative to the other dimensions. Stresses normal to the shell cross section are

usually assumed to have linear distribution; consequently the shell element can

model bending. The shell element models the displacement field with two

variables.


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c) Membrane element

The membrane element is visually similar to the shell element, but stresses

normal to the shell cross section are usually assumed to be constant. The

membrane element can model only membrane stresses but not bending stresses.

d) Beam element

The cross section is small in comparison with the length. The beam elementmodels the 3-D displacement field with one variable.

2.5.6 Basic Steps of Finite Element Analysis

In general, there are several approaches to formulating finite element problems:

1. Direct formulation

2. The minimum total potential energy formulation

3. Weighted residual formulation

Again, it is important to note that the basic steps involved in any finite element

analysis, regardless of how generate the finite element model, will be the same as those

listed in Figure 2.11. Basic steps for the finite element analyses are illustrated as a flow

chart in Figure 2.11.


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Figure 2.11 Flow chart for the basic steps of FEA [6]

1. Create and discrete the solution domain into finite elements; that is,

subdivide the problem into nodes and elements.

Pre-processing Phase

2. Assume a shape function to represent the physical behavior of an

element; that is, a continuous function is assumed to represent the

approximate solution of an element.

3. Develop equations for an element.

4. Assemble the elements to present the entire problem. Construct the

global stiffness matrix.

5. Apply boundary conditions, initial conditions and loading.

Solution Phase

6. Solve a set of linear or non-linear algebraic equations simultaneously

to obtain nodal results, such as displacement values at different

nodes.

Post-processing Phase

7. Obtain other important information. (i.e. principle stresses)


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2.5.7 Fundamental Requirements

Three basic conditions must be observed, which are:

1) The equilibrium of forces

2) The compatibility of displacements

3) The material behavior law

The first condition requires that the internal forces balance the external applied

loads. Compatibility condition requires that the deformed structure fits together that the

deformations of the member are compatible.

It is also necessary to know the relationship between load and deformation for

each component of the structure (material behavior law). This relationship in linear

elasticity is the Hooks law.

2.5.8 Meshing

The most important requirement of the FEM is the need to split the solution

domain (model geometry) into simply shaped subdomains called finite elements. This

is a discretization process commonly called meshing and elements are called finite

because of their finite, rather than infinitesimally small size having infinite number of

degrees of freedom. Thus the continuous model with an infinite number of degrees of


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freedom (DOF) is approximated by a discretized FE model with a finite DOF. This

allows for reasonably simple polynomial functions to be used to approximate the field

variables in each element. Meshing the model geometry also discretizes the original

continuous boundary condition. The loads and restraints are represented by discrete

loads and supports applied to element nodes [7].

There are many ways in turning a mathematical model into an FE model by

meshing. The three major factors which define the choice of discretization are element

size, element order (order of the element shape function) and element mapping (elementshape may distort from the ideal shape after mapped to the actual shape in the FE

mesh).

2.5.9 Verification of Results

Finite element analysis software has become a common tool in the hands of

design engineers. The results of the finite element analysis have to be verified so that it

does not contain errors such as applying wrong boundary conditions and loads, poor

element shape and size after meshing, wrong input data, selecting inappropriate types of

elements.

Experimental testing of the model is one of the best ways for checking the

results, but it may be time consuming and expensive. Hence, it is always a good practice

to start by applying equilibrium conditions and energy balance to different portions of a

model to ensure that the physical laws are not violated.


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a) Pre-processing phase

Pre-processing involves creating a geometric representation of the structure,

then assigning properties, then outputting the information as a formatted data

file (.dat) suitable for processing by LUSAS [8].

b) Finite Element Solver

Sets of linear or nonlinear algebra equations are solved simultaneously to obtainnodal results, such as displacement values at different nodes or temperature

values at different nodes in heat transfer problems.

c) Result-Processing

In this process, the results can be processed to show the contour of

displacements, stresses, strains, reactions and other important information.

Graphs as well as the deformed shapes of a model can be plotted.

2.7 Non-linear Analysis

In a linear finite element analysis, all materials are assumed to have linear elastic

behavior and deformations are small enough not to significantly affect the overall

behavior of the structure. However, nonlinear finite element analysis is required in

situations such as gross changes in structural geometry, permanent deformations and

structural cracks.


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The nonlinear analysis generally can be divided into three types:

1. Material nonlinearity

2. Geometric nonlinearity

3. Boundary nonlinearity

1. Material nonlinearity

Material nonlinearity effects occur from a nonlinear constitutive model which

has disproportionate stresses and strains. A nonlinear material model is one that

does not follow a linear relation between strain and stress and thus does not have

a constant modulus of elasticity. Using such a material, model stiffness changes

during the loading process and the stiffness matrix must be recalculated during

the solution process. The nonlinear material properties require more complex

definition, which depends on what stress-strain relationship is assumed in the

model [7]. Common examples of nonlinear material behavior are the plasticyielding of metals, the ductile fracture of granular composites such as concrete

or time-dependant behavior such as creep.

2. Geometric nonlinearity

Geometric nonlinearity occurs when there is significant change in the structural

configuration during loading. In nonlinear geometry analysis, the shape

deformation (rather than the change in material properties, as was the case in the

nonlinear material model) changes the structure matrix. Consequently, stiffness

does not remain constant throughout the process of deformation due to the

applied load, and the stiffness matrix must be recalculated during the process of

load application. Common examples of geometric nonlinearity are plate

structures which develop membrane behavior, and the geometric split of truss or


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previous stiffness matrix. This reduces the number of iteration as the factorization of the

tangent stiffness matrix is not required for every iteration.

Three common forms of modified Newton-Raphson iteration are illustrated in

Figure 2.14.

Figure 2.14 Forms of modified Newton-Raphson iteration [8]


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2.8 Studies Done Related to Reinforced Concrete Column with Hole

There are few studies conducted by researchers to comprehend the behavior of

the reinforced concrete column with hole. The literature study on the problems shows

that no information and guidelines in codes of practice (ACI 318-05, BS 8110-97) on

this problem are available and also no other significant investigations have been

carried out. Reviews are done by studying the article and material from the reliable

sources.

2.8.1 A Critical Review of the Reinforced Concrete Columns and Walls

Concealing Rain Water Pipe in Multistory Buildings

Jahangir Bakhteri, Wahid Omar and Ahmad Mahir Makhtar [9], presented a

critical review of the reinforced concrete columns and walls concealing rain water pipe

in multistory building. This paper showed that using drain pipe inside columns not only

reduces the load carrying capacity of the columns, also cause several dangerous to the

buildings safety which are as follow:

i. Positioning the drain pipe in the corner or at the edge of the columns sectionand will virtually reduce the effective cross-sectional area of the column as

shown in Figure 2.15 (a), (b) and (c). The pipe may not be held at central

position in the column/wall, because during casting and vibrating of the concrete

there are chances that the pipe may get an inclined position which will cause

further decrease in load carrying capacity of the column /wall.( Figure 2.15 (d)).


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(a), (b) & (c): Column section in plan showing probable effective area

(d): vertical section of column showing inclined position of the drain pipe

Figure 2.11 Inappropriate positioning of rain water pipe in columns section [9]


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ii. There are chances of honeycomb formation around the drain pipe in the column

as shown Figure 2.16.

Figure 2.12 Formation of honeycombs around the drain pipe [9]

iii. Rusting of reinforcement in the structure will occur because the pipes may have

leakage at their lapping parts or joints as shown in Figure 2.17, which is cause

loss of bond and reduction in the strength of the structural elements by

corrosion.


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Figure 2.13 Leakage in the lapping parts of the PVC drain pipes [9]

iv. Due to the presence of drain pipe in beam-column joints, the beams

reinforcement has to be bent as shown in Figure 2.18, which causes irregularity

and non-uniformity in the beams reinforcement and hence a reduction in

strength and functioning of the beam. The problem will be much critical in

beams with higher percentage of reinforcement.

Figure 2.14 Congestion and non-uniformity in beams reinforcements at columns

section caused by the presence of drain pipe [9]


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v. The columns strength at base level is reduced by elbow part of the pipe, which

is used to drain the rain water at ground level. In case the drain pipe has not been

taken out at ground level i.e. the positioning of the elbow part of the pipe has

been forgotten. To rectify this mistake, the concrete of the columns section at

ground level has been hacked severely and then the elbow part of the pipe has

been installed followed by grouting of fresh concrete as shown in Figure 2.19.

Figure 2.15 Elbow part of the drain pipe at the ground level [9]


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The columns concealing drain pipes are usually designed by the Malaysian

practicing engineers on the basis of their reduced cross-sectional areas A r which is

calculated as follows:

Ar = A g - A p (2.10)

Where, A r is reduced area of the section of the column, A g is gross area of the

columns section, and A p is cross-sectional area of the drain pipe.

In case of the column with higher flexural stresses (i.e. moment), the assumption

made in the effective depths of the column which contains drain pipe is usually

inappropriate. This is because, for the design purposes, the practicing engineers assume

an approximate effective depth for the columns section and a rational formula for the

calculation of the effective depth of such type of columns is lacking.

An experimental study has been carried out (Jahangir Bakhteri & Ahmad

Iskandar,[10]) to consider the effect of concealing Poly Vinyl Chloride (PVC) pipe

inside reinforced concrete (RC) columns in multistory buildings.

Compressive strength and load carrying capacity of rectangular reinforced

concrete short columns with embedded rain water pipe have been investigated and theresults have been presented. The models have been loaded axially until their failure and

the collapse load and maximum axial strain of samples are recorded.

To summarize this paper all the results show reduction in load carrying

capacities of the columns by positioning drain pipes inside them [10].


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For design of the column with embedded drain pipe , the strength of the columns

should be taken as half of the value obtained in BS 8110 and ACI code, because of the

huge reduction in the load carrying capacity of these type of the columns.

Usage of coated steel pipe instead of PVC pipe positioned at the center of

columns cross-section is suggested in this paper as an alternative solution. It has also

been mentioned that in the case of structure subjected to lateral load, this practice

should not be used because appropriate determination of the effective depth of the

column concealing rain water pipe is difficult.

2.8.2 Full Scale Tests on Ductility, Shear Strength and Retrofit of Reinforced

Concrete Hollow Columns

Y. L. Mo, Y.-K. Yeh, C.-T.Cheng, I. C. Tsai and C. C. Kao [11], worked on

hollow bridge column. To maximize structural efficiency in terms of the strength/mass

and stiffness/mass ratios and to reduce the mass contribution of the column to seismic

response, it is desirable to use a hollow section with high-strength concrete for the

columns. To consider both ductility and workability, the configuration of lateral steel in

the hollow columns used in the high-speed rail project of Taiwan.

The purpose of this integrated project is five points:

1) To study experimentally the flexural, shear, and retrofit performances of hollow

rectangular and circular reinforced concrete bridge columns.


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2) To investigate the constitutive models of confined concrete as affected by the

configuration, spacing and steel ratio of confinement reinforcement, as well as

the compression/shear ratio.

3) To evaluate the reduction of shear strength with increasing ductility factor and

develop a set of guidelines for seismic design, retrofit, and repair of such

columns.

4) To extend the applicability of the truss model for shear element to include such

columns to develop a computer program that can predict the shear stress-shearstrain relationship of hollow bridge columns with confined reinforcement.

5) Find a good method for seismic repair of such columns and develop a computer

program that can perform seismic design, retrofit, and repair of such columns.

The cross-sections used in this integrated research project are shown in Figure

2.20.

(a) hollow bridge columns with (b) hollow bridge columns with

rectangular section circular section

Figure 2.6 Configurations of lateral reinforcement in hollow columns [11]


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The above mentioned investigation shows that, when a specimen with

insufficient shear reinforcement was FRP retrofitted, the failure mode of the specimen

could change from brittle shear failure to ductile flexural failure.

The specimen, with both insufficient lateral reinforcement and lap splice at the

plastic hinge region, should not be used in design because it has much lower ductility

due to premature bond failure.

The specimen, with insufficient lateral reinforcement, has flexure and shear

failures. Its ductility is less than that of specimen failed by flexure because its plastic

hinge could not be fully developed. The ultimate displacements and flexural capacities

of FRP-repaired columns were about 50% to 60% and 10% to 20%, respectively,

greater than those of original columns.

In the column analyses there were three cases, namely, Case 1 with code-

required confinement reinforcement, Case 2 with 50% of code required confinement

reinforcement, and Case 3 with 50% of code required confinement reinforcement and

the remaining 50% replaced by steel plate. In Case 1, the ductility capacity was very

good, and increased with increasing confinement reinforcement. The shear strength was

less than that calculated by Priestleys formula. In Case 2, both the ductility capacity

and the shear strength were reduced dramatically. In Case 3, both the ductility capacity

and the shear strength were not less than those for Case 1.


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2.8.3 Slender High Strength Concrete Columns Subjected to Eccentric Loading

An experimental study is done by Claeson and Gylltoft [12]. The research is

about studying the behavior of slender reinforced concrete columns. In the research, 12

full-scale reinforced concrete columns were tested to failure under the eccentric load.

The research was then followed by performing numerical simulations to verify

with the test results.

The detailing and configuration of the column cross section is as indicated in

Figure 2.21 and as tabulated in Table 2.1.

Figure 2.21 Geometry and details of configurations (a) and (b) [12]

Table 2.1 : Details of columns in group A, B and C [12]

Column group Length (mm) Configuration Eccentricity (mm) Stirrup spacing (mm)

A 2400 a 20 100/180

B 3000 b 20 130/240

C 4000 c 20 130/240


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There were 4 test sample prepared for each group of column. In each group, 2

columns were cast by normal-strength concrete and the other 2 columns were cast by

high-strength concrete. The materials for the columns tested for obtaining the data on its

mechanical properties such as elasticity, strength, etc.

Both the ends of the column were attached to a bearing plate to produce a good

pinned support to the column before the test. Figure 2.22 is illustrating the load

arrangement for the test. It can be seen that the column are supported and loaded with

an eccentricity of 20mm.

Figure 2.22 Load arrangement for the test [12]


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Sensors were attached to the test sample at different height level, as illustrated in

Figure 2.23. Sensors consist of different types of gauges which were used to measure

the lateral displacement of the column, as response to the vertical eccentric load.

Figure 2.23 Instrumentation of slender column [12]

The research is continued with the finite element modeling. The objective was to

develop a non-linear finite element model that could simulate the failure mechanism of

the column. ABAQUS was used to perform the analysis. A 3-noded 3-dimensional


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hybrid beam element was developed for the model of the columns, because it enabled

the analysis to run in a reasonable amount of time. Also, a similar study done by

Claeson [13] has concluded that there is a good agreement between the analysis using

beam elements and one using solid elements.

During the modeling, the program ABAQUS combines the standard elements of

plain concrete with a special option, called the rebar. The option strengthens the

concrete in the direction chosen, thereby simulating the behavior of a reinforcement bar.

By the approach, the material behavior of the plain concrete is taken into accountindependently of the reinforcement.

In order to simulate the behavior of the materials in plastic state, constitutive

models for the concrete and the reinforcement were developed. The concrete model was

developed by the smeared crack approach, and the reinforcement was modeled by a

linear elastic-plastic model.

The research has concluded that the high-strength concrete columns fail in a

brittle manner, and the spacing of the links does not affect the column ultimate strength.

Secondly, the failure mode of the column is depending on the eccentricity of the vertical

load. When the eccentricity of the load is low, the material crushing strength played a

dominant role. When the load eccentricity is increased, the yielding of the compressive

reinforcement determined the column capacity. Thirdly, the maximum lateraldeflections at the mid-height of the columns were almost the same. Finally, the column

strength is very much depending on the eccentricity of the vertical load.


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CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

A number of powerful finite element software packages have become

commercially available. They include ABAQUS, ANSYS, COSMOSM, MARC and

LUSAS. In order to meet the objectives of this research, the reinforced concrete

column with hole was modeled using LUSAS version 14.0. The experimental work

was used to calibrate the finite element model. As the research focused on the accuracy

of finite element analysis, the results of analysis were checked by comparison with the

results of laboratory test.

This chapter explains the process to build the model and the process to run the

non linear analysis using LUSAS software.


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3.2 Finite Element Modeling

The technique of finite element modeling lies in the development of a suitable

mesh arrangement. Thus, many trial models were created during the early stage of the

research. Different element types and different methods of modeling were created

before the final arrangement of mesh and element was determined. In the following

sections, the procedures for the implementation of a FEM for nonlinear analysis are

described.

3.2.1 Geometry

The geometry of the models is based on the details of the tested columns. Ten

columns in five sets, having various size and reinforcement were modeled. The hole

was positioned at the centre of cross-section of each one of them. Each set contain two

types of column with same size and reinforcement:

Type (a): Model without hole (control model)

Type (b): Model with hole

The dimensions of the columns cross-section vary from 125125 mm to

300300 mm. All models were placed with 20 mm cover to reinforcement. The holes

having four different diameters (48, 60, 89 and 114 mm) were modeled. The models

specification and dimension of each set are shown in Table 3.1.


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Table 3.1 : The specification and dimension of the column models

One of the biggest changes in the columns geometry design is the geometry of

the reinforcement bars. The reinforcement bars have a circular cross section in reality,

whilst in the model they are modeled with a square cross-section. The square form of

the reinforcement is much easier to model, i.e. design and mesh, in LUSAS, as well as

contributing to minimizing the calculation time for the FE-analyses. It should be noted

that the area of the reinforcements square cross section is equivalent to the area of the

circular reinforcement. The stirrups are not modeled due to the miniscule effect they

have on the studied behavior of the column. Element aspect ratio should be considered

in the FE modeling. In many cases, as the element aspect ratio increases, the inaccuracy

of solution increases. So using partitions can cause low aspect ratio for getting more

accurate solution.

Columnset

h(mm)

b(mm)

Gross Area(mm2 )

Hole Diameter(mm)

Hole Area(mm2 )

BarSize

C1 125 125 15625 48 1809 4Y10

C2 150 150 22500 60 2827 4Y10

C3 200 150 30000 60 2827 6Y10

C4 200 200 40000 60 2827 4Y12

C5 200 200 40000 89 6221. 4Y12

C6 250 200 50000 89 6221 4Y16+2Y12

C7 250 250 62500 89 6221 4Y16

C8 275 275 75625 114 10207 4Y20

C9 300 250 75000 89 6221 4Y16+2Y12

C10 300 300 90000 89 6221 4Y20

C11 300 300 90000 114 10207 4Y20


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The reinforcement is modeled with hexahedral volume features (HX8M three

dimensional continuum solid elements). The reinforcement bars have a circular cross

section in reality, whilst in the model they are modeled with a square cross-section. The

square form of the reinforcement is much easier to model, i.e. design and mesh, in

LUSAS, as well as contributing to minimizing the calculation time for the FE-analyses.

It should be noted that the area of the reinforcements square cross section is equivalent

to the area of the circular reinforcement. Aspect ratio is defined as the ratio of the

longest to the shortest dimension of a quadrilateral element. Element aspect ratio is

considered in the FE modeling. In many cases, as the element aspect ratio increases, the

inaccuracy of solution increases. So using partitions can cause low aspect ratio forgetting more accurate solution, because the best results are obtained when the element

shape is regular and compact. It is tried to maintain low aspect ratio and corner angles

of quadrilateral be 90 degree in the meshing of all models. The modeling of bar and

meshing of model are shown in Figure 3.2.

Figure 3.2 Modeling of bar and meshing of model C1b


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3.2.3 Material Properties

Material nonlinearity occurs when the stress- strain relationship ceases to be

linear by plastic yielding and strain hardening. Materially nonlinear effects arise from a

nonlinear constitutive model (that is, progressively disproportionate stresses and

strains). Common examples of nonlinear material behavior are the plastic yielding of

metals, the ductile fracture of granular composites such as concrete or time-dependent

behavior such as creep. LUSAS incorporates a variety of nonlinear constitutive models,

covering the behavior of the more common engineering materials.

a) Concrete

The concrete is defined as an isotropic material in the modeling. In addition, the

LUSAS concrete (model 94) material model is used to model the concrete in the

plastic stage. For good correlation with experimental results, the plastic material

properties of the concrete were assigned according to the results from the

experimental test. Tabulated in Table 3.2 are the properties of the concrete.

Table 3.2 : Concrete properties

Elastic PropertiesYoungs Modulus = 20130 N/mm

Poissons Ratio = 0.2

Plastic Properties

Compressive Strength = 37.12 N/mm

Tensile Strength = 3.712 N/mm

Strain at end of softening curve = 0.003


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b) Steel Bar

The reinforcing steel is defined as an isotropic material. In the plastic properties,

the stress potential model was selected and Von Mises yield surface was tried

for the plastic behavior of the steel. Table 3.3 below shows the steel properties

for the reinforcement.

Table 3.3 : Steel properties

Elastic PropertiesYoungs Modulus = 200000 N/mm

Poissons Ratio = 0.3

Plastic Properties Yield Stress = 460 N/mm 2

3.2.4 Boundary Condition

The bottom of the column was fully fixed in x, y and z directions. The top of

the column, which was supported by two rollers, allowed movement in vertical z

direction. Thus the restraint at the top of the column was fixed from movement in x and

y directions.


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3.2.5 Loading

The axial compression load was assigned at the top face of the column. The

results of the experimental test were showed that the amount of loading is variable in

each column. However, LUSAS would apply the load in the incremental manner until

the analysis stopped. The generated mesh, applied load and boundary condition of the

model are shown in Figure 3.3.

Figure 3.3 Typical model showing generated mesh, loading and boundary condition


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3.2.6 Nonlinear Analysis

Nonlinear analysis control properties were defined as properties of a loadcase. In

LUSAS, the nonlinear analysis is based on the Newton-Raphson procedure by which

the stiffness matrix (K T) is updated after each iteration. The procedure is an increment

iterative method, in which the total load is applied in a number of increments. A linear

prediction of nonlinear response is made with each increment, and subsequent iterative

corrections are performed to restore equilibrium by the elimination of the residual or

out of balance forces. The load incrementation procedures in this analysis were set foreach model in order to reduce the elapsed time of the analysis [8].

LUSAS incorporates two groups of the Newton-Raphson method, which are

standard Newton-Raphson and modified Newton-Raphson. The standard Newton-

Raphson was employed. Automatic load incrementation was adopted in the analysis.

The incremental / iterative nonlinear solution is shown in Figure 3.4.

Figure 3.4 Incremental / iterative nonlinear solution [8]


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Fine integration was used in this analysis as recommended by the LUSAS

modeler user manual. Alternatively, the Rheinbolts arc-length control was set to

improve the convergence characteristics and the ability to detect and negotiate limit

points according to LUSAS theory manual [8].

Figure 3.5 below shows the Rheinbolts arc-length load incrementation method

for the midspan displacement of the model in this study.

Figure 3.5 Modified arc length load incrementation for the one degree of freedom

response [8]


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3.3 Experimental Work

The results of the half scale laboratory test were used as comparison with the

results from the finite element analysis. Hence, the finite element model was

implemented based on the parameters and conditions in the laboratory test [14].

3.3.1 Test Models

Twenty two columns in eleven sets, having various size and reinforcement were

constructed. The PVC pipes were positioned at the centre of cross-section of each one

of them. Each set contain two types of column with same size and reinforcement:

Type (a): specimen without pipe (control model)

Type (b): specimen with PVC pipe

The dimensions of the columns cross-section vary from 125125 mm to

300300 mm. The models specification and dimension of each set are shown in Table

3.4. All models were placed with 20 mm cover to reinforcement based on BS 81110requirement i.e bar size, maximum aggregate size and to meet 1.5 hours period of fire

resistance. The PVC pipes having four different diameters (48, 60, 89 and 114 mm)

were used.


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Table 3.4 : The specification and dimension of the column models

High strength deformed steel bars having yield strength of 460 N/mm 2 were

used in the models. After completion of reinforcement details (i.e. bars cutting and

bending), using water proof grade one plywood, appropriate formwork for the models

were prepared.

The concreting of the models has been carried out in the Structures laboratory of

the Faculty of Civil Engineering at UTM, during which, cube samples have been

prepared in random order. This is needed in order to assess the actual strength of the

concrete in the models. The surface of the models has been kept wet for at least three

days. After removal of the formworks, the models were kept undisturbed for 28 days.

Column

set

h(mm)

b(mm)

Gross Area(mm2 )

Pipe Diameter(mm)

Pipe Area(mm2 )

Bar

Size

C1 125 125 15625 48 1809 4Y10

C2 150 150 22500 60 2827 4Y10

C3 200 150 30000 60 2827 6Y10

C4 200 200 40000 60 2827 4Y12

C5 200 200 40000 89 6221. 4Y12

C6 250 200 50000 89 6221 4Y16+2Y12C7 250 250 62500 89 6221 4Y16

C8 275 275 75625 114 10207 4Y20

C9 300 250 75000 89 6221 4Y16+2Y12

C10 300 300 90000 89 6221 4Y20

C11 300 300 90000 114 10207 4Y20


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All columns were assumed to be braced column. So they were designed as short

braced column. The

ratios and the type of the models are shown in Table

3.5.

Table 3.5 : The column models type

Column set Column Type

C1 12.0 12.0 shortC2 10.0 10.0 short

C3 7.5 10.0 short

C4 7.5 7.5 short

C5 7.5 7.5 short

C6 6.0 7.5 short

C7 6.0 6.0 short

C8 5.45 5.45 short

C9 5.0 6.0 short

C10 5.0 5.0 short

C11 5.0 5.0 short

3.3.3 Preparation of the Test Specimens

Basically, preparation of specimens consists of steel works and concrete works.

Steel works consist of cutting, bending and tying steel bars. Steel bar tensile test was


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also conducted to obtain the yielding strength of steel bars. Meanwhile, concrete works

involve preparing formworks, casting, compacting and curing.

a) Steel Works

Appropriate reinforcement details are very essential for achieving required

strength in reinforced concrete. Therefore, they should be tied together properly

to ensure greatest quality of work. Steel bars having yield strength of 460

N/mm 2 in different sizes were cut. Mild steel bars with 6 mm diameter as links

were cut and bended carefully. The minimum size of the links was considered as

1 4multiply the size of the largest compression bar but not less than 6 mm.The spacing between links was taken 12 times of the smallest compression bar

size. Figure 3.6 shows the arrangement of reinforcement bar of columns in the

laboratory.

Figure 3.6 Steel works consist of cutting, bending and tying steel bars


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Meanwhile, another important step was the positioning of the pipes. The pipe

was installed in center of cross-section of each column. The pipes were tied to the

longitudinal steel bar by steel wire to ensure no movement during casting. Positioning

of the pipes in the center of columns cross-section is shown in Figure 3.7.

Figure 3.7 Positioning of the pipes in center of columns cross-section

a) Concrete Works

All these column specimens were made with 20 mm clear cover to all

reinforcement according to BS 8110, i.e. based on bar size, maximum aggregate

size and to meet 1.5 hours period of fire resistance. The sets of formwork with

18mm thickness water proof plywood, which was well-cut into desired


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dimensions, were prepared. After the formwork and reinforcement were

completed, casting work was carried out. Ready mixed concrete with Grade 35

was used in this experiment. The columns were casted horizontally because of

ease in casting and compacting, also to prevent construction tolerances. Extra

care has been taken to prepare the columns formworks such that to produce the

exact dimensions of the models and to have the verticality in the models.

Column was positioned horizontally on a leveled ground surface as shown in

Figure 3.8. This was then followed by the pouring of the mix into the formwork.

Figure 3.8 Column form work was positioned horizontally and ready for casting

The concrete mix was compacted using poker vibrator. Before the concrete was

hardened, the top surface of the columns was well-trowel to have smooth surface.

Figure 3.9 shows the fresh concrete after casting. In order to obtain the concrete

strength of the models at certain duration after casting, 9 cubes were prepared for cube

test.


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Figure 3.9 The fresh reinforced concrete columns after casting

b) Curing Techniques

Curing is a technique necessity for the development of desired concrete strength

and hardness. Normally, curing begins after placement of concrete. It helps to

maintain the satisfactory moisture content in the concrete. Temperature and

relative humidity conditions are two important factors in proper curing and they

play a significant role in contribution to the rate of moisture loss from the

concrete. The surface of the models has been kept wet for 7 days. Burlap is used

to cover the specimens and wet with water regularly. This helps to maintain the

concrete surface at continuously wet condition as well as prevent evaporation

from the concrete surfaces.


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3.3.4 Instrumentation and Testing of the Models

In this study, specimens were prepared and tested under axial compressive load

to investigate the load carrying capacity of the short braced reinforced column with

embedded pipe. The models have been tested using a 5000 kN capacity universal testing

machine. The columns were loaded under a monotonically increasing axial compressive

load until their collapse.

a) Strain Gauge

Before the testing of the column specimens the strain gauges were installed on

the models. In order to record the vertical axial strains in each model, two

electric resistance strain gauges on opposite vertical faces of the column at its

mid height and two electric resistance strain gauges at the adjacent faces of the

model near its top end have been installed. The installations of the strain gaugeswere carried out as in the following stage:

Preparation

The following items were required for bonding and lead wire connection: strain

gauge, bonding adhesive, solvent, cleaning tissue for industrial use, abrasive

paper, polyethylene sheet.

Positioning

The location on the test specimen where the strain gauge was to be bonded was

roughly determined.


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Surface preparation

Before bonding, all grease, rust, etc were removed. An area somewhat larger

than the bonding area uniformly and finely was sanded with abrasive paper.

Fine cleaning

The bonding area was cleaned with industrial tissue paper soaked in small

quantity of acetone. Cleaning was continued until a new tissue appearedcompletely free of contamination.

Applying bonding adhesive

The proper amount of adhesive was dropped onto the back of gauge base. The

adhesive was spread over the back surface thinly and uniformly by using

adhesive nozzle.

Curing and pressing

Curing and pressing gauge was placed on guide mark, and then a polyethylene

sheet was placed onto it and pressed down on the gauge constantly by using

thumb. This was done quickly as curing process was completed very fast.

The analysis of strain measurements is not done in the scope of this study. It can

be referred to the experimental work by Hossein Mousavian [14].


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b) Loading Procedure

In order to represent the restraint provided by the beams and slab to the column

in each floor level, in the testing set up, each end of the model were fixed to the

testing machine to simulate the actual condition in the columns.

Before positioning the models in testing machine the center of the columns were

marked, then the center of the columns were positioned in center of testing machine

loading surface to achieve an axial compressive loading condition without eccentricity.In the next stage, the model was checked to be aligned vertically by the spirit level

readings on two opposite face of the column. In order to prevent local failure at the

loaded ends of the columns, two pieces of plywood with 10 mm thickness were located

in top and bottom of the model. In final stage before testing, the strain gauges wires

were connected to the data logger.

The models have been tested using the 5000 kN capacity universal testing

machine. The columns were loaded under a monotonically increasing axial compressive

load until their collapse. The loading and the vertical axial strain readings were recorded

after every increment of 20 kN load. The test setup is shown in Figure 3.10.


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Figure 3.10 Test setup

3.4 Flowchart of the Finite Element Analysis

In order to achieve the stated objectives, this FEA study is carried out in few

stages. The flowchart of all stage is indicated in Figure 3.11 which provides a general

overview about finite element analysis of this research and its completion procedure.


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Figure 3.11 Flowchart of finite element analysis

Draw the Geometry of the Modeland Make the Hole along Model (b)

Using Partition for MaintainLow Aspect Ratio

Assign the Material Properties forConcrete and Reinforcement

Apply Boundary Condition for Topand Bottom of the Model

Apply Loading on the TopFace of the Model

Meshing and Discretization of theModels using 3D Solid Element

Run and Analysis of the Modelsand Presentation of the Results


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CHAPTER 4

ANALYSIS, RESULTS AND DISCUSSIONS

4.1 Introduction

This chapter presents the results of comparative study between numerical

approach using finite element analysis and laboratory test. The comparative study was

undertaken to determine the accuracy of the finite element analysis in predicting the

nonlinear behavior of the reinforced concrete column with hole. Comparison was made

on the aspects of stress-strain curve and mode of failure. With the aid of graphs and

diagrams, the results of the comparative study between finite element analysis and

experiment were highlighted.

Verifications of the finite element analysis results were done during the

modeling, to ensure the results obtained are reliable. In this part of the investigation, a

preliminary study was conducted for having an early understanding on the column

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