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Author’s full name : AMIRHOSSEIN BASRAVI Date of birth : 25 MAY 1986 Title : FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE COLUMN WITH LONGITUDINAL HOLE Academic Session : 2010/2011________________________________________________ I declare that this thesis is classified as : I acknowledged that Universiti Teknologi Malaysia reserves the right as follows:

1. The thesis is the property of Universiti Teknologi Malaysia. 2. The Library of Universiti Teknologi Malaysia has the right to make copies for the purpose

of research only. 3. The Library has the right to make copies of the thesis for academic exchange.

Certified by :

SIGNATURE SIGNATURE OF SUPERVISOR J14909892 ASSOC. PROF. IR. DR. HANIM OSMAN (NEW IC NO. /PASSPORT NO.) NAME OF SUPERVISOR

NOTES : * If the thesis is CONFIDENTAL or RESTRICTED, please attach with the letter from the organization with period and reasons for confidentiality or restriction.

UNIVERSITI TEKNOLOGI MALAYSIA

√

CONFIDENTIAL (Contains confidential information under the Official Secret Act 1972)*

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organization where research was done)* OPEN ACCESS I agree that my thesis to be published as online open access

(full text)

“I hereby declare that I have read this project report and in my

opinion this project report is sufficient in terms of scope and quality for the

award of the degree of Master of Engineering (Civil – Structure)”

Signature : _______________________

Name of Supervisor : ASSOC.PROF. IR. DR. MOHD. HANIM OSMAN

Date :

3 DECEMBER 2010

FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE COLUMN WITH LONGITUDINAL HOLE

AMIRHOSSEIN BASRAVI

A project report submitted in partial fulfillment of the requirement for the award of the degree of Master of Engineering (Civil – Structure)

Faculty of Civil Engineering Universiti Teknologi Malaysia

DECEMBER 2010

ii

I declare that this project report entitled “Finite Element Analysis of Reinforced

Concrete Column with Longitudinal Hole” is the result of my own research except as

cited in the references. The report has not been accepted for any degree and is not

concurrently submitted in candidature of any degree.

Signature : _______________________

Name : AMIRHOSSEIN BASRAVI

Date : 3 DECEMBER 2010

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To my beloved family

Love you forever

iv

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 not

succeed 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.

v

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.

vi

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.

vii

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 25

2.5.1 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 and

Concealing 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 63

3.3.1 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

x

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 of columns 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 study and FEA based on BS code

89

4.5 Comparison of factor of safety from experimental study and FEA based on ACI code

90

xi

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-δ 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-δ effect on a column 37

xii

2.13 Nonlinear boundary condition 38

2.14 Forms of modified Newton-Raphson iteration 39

2.15 Inappropriate positioning of rain water pipe in column’s 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 Congestion and non-uniformity in beams reinforcements at column’s 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 in hollow 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, loading and boundary condition

60

3.4 Incremental / iterative nonlinear solution 61

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

62

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

xiii

3.7 Positioning of the pipes in center of column’s cross-section 68

3.8 Column form work was positioned horizontally and ready 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

4.8 Stress-strain curve of column C3 81

4.9 Stress-strain curve of column C9 82

4.10 Stress-strain curve of column C11 82

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

xiv

LIST OF SYMBOLS

Ag - Gross area of the column section

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

Asc - Area of the longitudinal reinforcement

Ast - Total area of longitudinal reinforcement

b - Width of column

d - Effective depth

e - Eccentricity of load

E - Young’s Modulus

fcu - Characteristic compressive strength of concrete

fy - Characteristic yield strength of steel

h - Gross area of the column section

le

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

M - Ultimate moment

N - Column design load

P - Vertical load to the column

xv

α - Modulus ratio

β - Coefficient dependant on the bar type

Ø - Strength reduction factor

ε - Compressive strain

σ - Compressive stress

1

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.

2

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

3

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 column’s 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

column’s 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 reduction

in the strength of the structural element.

v. The huge reduction in the column’s 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).

4

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.

5

To the best of the knowledge of the author, no significant investigations have

been carried out to study the load carrying capacity of these types of columns. Most of

the previous works in this regard have been limited to the study of the effects of

constant axial load and eccentric load on the behavior of rectangular and circular hollow

reinforced concrete columns and also no information and guidelines in codes of practice

(ACI 318-05, BS 8110-97) on this problem are available and no other significant

investigations have been carried out.

1.3 Objective of the Study

The objectives of the study are listed below:

1. To investigate the reduction in load carrying capacity of the reinforced concrete

short braced columns having rectangular and square cross-sections with hole

(embedded drain pipe).

2. To model the RC columns using three-dimensional non-linear finite element

analysis.

3. To study the compressive strength of the columns subjected to axial

compressive loads only and to compare the research findings with the results of

half scale laboratory tests and the design strengths recommended by the BS

8110 and ACI codes of practice.

6

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.

7

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 and

materials. The strength and the durability are two important factors in concrete.

8

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

9

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 = Ec, where Ec is known as secant or static modulus

(see Figure 2.2).

Figure 2.2 Static modulus of concrete [1]

10

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.