PERPUSTAKAAN UMP

111111111 110111111 0000092464

FINITE ELEMENT CONCRETE BEAM

USING SYNTHETIC LIGHTWEIGHT COARSE AGGREGATE (SYLCAG) OF

OFFSHORE SAND

MOHAMAD HASRUL BIN JAMALUDIN

Report submitted in partial fulfilment of the requirement

for the award of the degree of

B.ENG (HONS.) CIVIL ENGINEERING

Faculty of Civil Engineering & Earth Resources

UN! VERSITI MALAYSIA PAHANG

JUNE 2014

VII

ABSTRACT

Computer analysis can be used as an effectives tool to analyse structures and components without need to build the structures first. The analysis can be carried out in various condition and time with the verification of the actual condition under laboratory testing too. This study use a computer analysis program called ANSYS to verify what is actually occur to the structure such as beam during laboratory test. The research of lightweight concrete using SYLCAG that used for beam structure has been conducted and the result has been covered based on the theoretical and laboratory test. This study was conducted to analyse the flexural behaviour of the beams using ANSYS The manipulated variable of the beams are the concrete strength and beam density. The objectives that want to be achieved in this study are to understand the advantages of finite element method. Then, the result is compare between theoretical and experimental results. Besides that, the flexural behaviour of reinforced concrete and SYLCAG beam using ANSYS were studied. After the modeling and analysis were complete, the result proved that ANSYS manage to produce accurate result that similar to theoretical within 1% different for deflection for Beam A (Control) even though the experimental result was out of track. For other beams show the flexure behaviour within the manipulation of beam density and concrete strength. Somehow, ultimate moment capacity gives the closest result upon theoretical calculation for ACI 318 and Eurocode 2. This study concludes that the advantages of Finite Element Modeling (FEM) were discovering upon the accuracy of the result. Next is the comparison between theoretical and experimental gives relevant values and lastly the differences properties of the beams show the flexure behaviour.

VIII

ABSTRAK

Analisis komputer boleh digunakan sebagai media yang berkesan untuk menganalisis struktur dan komponennya tanpa perlu untuk membina struktur terlebih dahulu. Analisis mi boleh dijalankan dalam pelbagai keadaan dan masa mengikut situasi sebenar seperti mana ujian di makmal. Kajian mi menggunakan perisian komputer iaitu ANSYS yang mampu mengesahkan keadaan strukturr seperti rasuk sebagaimana ujian di makmal. Penyelidikan ke atas konkrit ringan menggunakan SYLCAG untuk struktur rasuk telah dijalankan dan hasilnya telah di bincang berdasarkan kefahaman teori dan ujian makmal. Kajian mi dijalankan untuk menganalisis kelakuan lenturan rasuk menggunakan ANSYS. Terdapat tiga jenis rasuk yang di model menggunakan ANSYS menggunakan keratan rentas yang sama iaitu 200mm x 150mm x 1500mm. Pemboleh ubah di manipulasi bagi kajian mi adalah gred konkrit dan ketumpatan rasuk. Objektif yang ingin dicapai dalam kajian mi adalah untuk memahami kelebihan kaedah unsur tak terhingga. Kemudian, hasilnya akan dibandingkan bersama hasil kiraan teori dan keputusan ujian makmal. Di samping itu, kajian mi juga bertujuan untuk mengkaji kelakuan lenturan rasuk konkrit bertetulang dan campuran SYLCAG menggunakan ANSYS. Setelah selesai struktur dimodelkan dan analisa telah di siap di lakukan, hasilnya telah membuktikan bahawa ANSYS mampu memberikan keputusan yang hampir sama dengan kiraan teori dalam lingkungan 1% perbezaan bagi lenturan untuk Beam A (Control) walaupun keputusan bagi ujian makmal agak tersasar jauh. Bagi rasuk lain, ia berjaya menunjukkan kelakuan lenturan berdasarkan pemboleh ubah manipulasi iaitu gred konkrit dan ketumpatan rasuk. Selain itu, keputusan bagi keupayaan momen muktamad memberikan hasil yang paling hampir dengan pengiraan teori untuk ACI 318 dan Eurocode 2. Melalui kajian ini, rumusan telah di buat bahawa kelebihan model menggunakan unsur tak terhingga telah memberi ketepatan dalam keputusan yang diperoleh. Seterusnya, perbandingan antara kiraan teori dan ujian makmal telah memberikan nilai-nilai yang saling berkait dan akhir sekali sifat-sifat perbezaan lenturan rasuk telah berjaya di tunjukkan.

TABLE OF CONTENTS

Page

SUPERVISOR DECLARATION

STUDENT DECLARATION

ACKNOWLEDGEMENTS

ABSTRACT

ABSTRAK

TABLE OF CONTENT ix

LIST OF FIGURES

LIST OF TABLESS

LIST OF SYMBOLS xvi

LIST OF ABBREVIATIONS xvii

CHAPTER 1 INTRODUCTION

1.1 Introduction 1

1.2 Background of the Study 2

1.3 Problem Statement 3

1.4 Objectives 3

1.5 Scope of Research 4

1.6 Research Significance 4

1.7 Expected Outcome 5

1.8 Conclusion 5

CHAPTER 2 LITERATURE REVIEW

2.1 Introduction 6

2.2 Laboratorial Analysis 6

2.2.1 Design Based On Flexural Analysis 6 2.2.1.1 Shear & bending 7 2.2.1.2 Deflection 9 2.2.1.3 Crack 11

2.3 Finite Element Modelling (FEM) 14

ix

X

2.3.1 Design Based On Flexural Analysis 15

2.3.1.1 Shear & bending 16

2.3.1.2 Deflection 1.7

2.3.1.3 Crack 20

2.3.2 Stiffness Matrix 21

2.4 Conclusion 23

CHAPTER 3: RESEARCH METHODOLOGY

3.1 Introduction 24

3.2 ANSYS 24

3.2.1 Pre-processor 27 3.2.1.1 Element 29 3.2.1.2 Material 30 3.2.1.3 Cross-section 31 3.2.1.4 Shell & beam properties 33 3.2.1.5 Density 33 3.2.1.6 Modeling 34 3.2.1.7 Automatic meshing 36

3.2.2 Solution 37

3.2.2.1 Structural displacement constrained 38

3.2.2.2 Structural force 39

3.2.2.3 Solve 40

3.3 Conclusion 41

CHAPTER 4: RESULT AND ANALYSIS

4.1 Introduction 42

4.2 Post-processor 42

4.2.1 Read By Load Step Number 43

4.2.2 Plot Results 43

4.3 Deflection

4.3.1 Comparison On Beam A (Control) Based Theoretical, Experimental & ANSYS 46 4.3.2 Comparison On Beam B.Using ANSYS 51 4.3.3 Comparison On Beam B & C Using ANSYS 53

XI

4.3.4 Comparison On Beam A (Control), B & C Using ANSYS 54

4.4 Moment 56

4.4.1 Bending Moment On Beam A (Control), B & C 57

4.4.2 Ultimate Moment Capacity On Beam A (Control), B & C 59

4.5 Conclusion 61

CHAPTER 5: CONCLUSION

5.1 Introduction 62

5.2 Conclusion 62

5.3 Recommendations 64

REFERENCES 65

APPENDICES

Al Ultimate Moment Capacity Theoretical Design by EUROCODE 2 67

A2 Ultimate Moment Capacity Theoretical Design by ACI 318 68

LIST OF FIGURES

XII

FIGURE NO TITLE

2.1 Typical Cracking of Control Beam at Failure

2.2 Shear & Bending Moment diagram based on the

Simply Supported Beam as defined in the Mechanics

of Materials

2.3 Behavior of concrete beams in bending

2.4 Fundamental of deflection consists of type of

restriction, curve and tends direction as defined in the

Structural Analysis

2.5 Load - deflection data and curve from flexural test

conducted in laboratory. (a) Control beam deflection

data based on experimental and theoretical, (b) Load-

Deflection curve of control beam, (c) Lightweight

beam deflection data based on experimental and

theoretical

2.6 Behavior of reinforced concrete beam with increasing

bending moment

2.7 Cracks pattern on reinforced concrete beam

2.8 Failure for beams of Groups 1 & 2

2.9 Crack width versus applied shear

2.10 Reinforced Concrete Beam with Loading

2.11 (i) Calibration model of reinforced concrete beam, (ii)

Models for reinforcement in reinforced concrete

2.12 Beam deformation due to loading & the simplified

equation used as defined in First Course in the Finite

Element Method

2.13 Load-deflection reponse of partially prestressed high

strength concrete T-beams

2.14 Contour plot & deflection curves of uniformly loaded

simply supported deep beam resting on Winkler

foundation

PAGE

7

8

9

10

11

12

12

13

13

15

16

17

18

18

2.15 Derivation of matrix equation for deflected curve of 19

beam as defined in the First Course in the Finite

Element Method

2.16 Typical Cracking Signs in Finite Elements Models: (a) 21

Flexural Cracks, (b) Compressive Cracks, (c)

Diagonal Tensile Cracks

2.17 Stiffness matrix development from bending moment, 22

shear & displacement nodal as defined in the First

Course in the Finite Element Method

3.1 Flowchart of Pre-processor phase 25

3.2 Flowchart of Solution phase 25

3.3 Flowchart of Post-processor phase 26

3.4 Beam specification 26

3.5 Pre-processor menu - 28

3.6 Define Code and unit 28

3.7 2D Elastic Beam 3 29

3.8 Selection of elements types for code checking 30

3.9 Concrete and reinforcing steel selection based on 31

strength class in Eurocode 2

3.10 Dimension of rectangular beam 32

3.11 Reinforcement group properties requirement of 32

rectangular beam

3.12 Shell & beam properties 33

3.13 Verify density in the Material Properties Section 34

3.14 Create the key points using Coordinate System (CS) 35

3.15 Six keypoints were plotted 35

3.16 The straight lines connected to every keypoint 36

3.17 The line were meshed automatically 37

3.18 Type of analysis selection 38

3.19 At keypoint (2), the displacement are constrained at 39

both X (UX) and Y (UY) direction as pin, at keypoint

(4) the displacement is constrained at only Y (UY) as

direction roller

XIII

3.20 At keypoint (3) & (4), the applied forces are concave 40

in Y (FY) direction

3.21 Solution command box told that the solution is done 41

by ANSYS

4.1 Read Results by Load Step Number 43

4.2 The components of displacement or deflection under 44

Degree Of Freedom (DOF) Solution category

4.3 Deflection diagram that shows the various deflection 45

values from minimum to maximum

4.4 Different view control of deflection diagram 46

4.5 Load - deflection curve on Beam A (Control) 47

4.6 Enlarged of load - deflection curve on Beam A 48

(Control)

4.7 Deflections of Control Beam (Buckhouse 1997) vs. 50

Finite Element Model at Ultimate Load

4.8 Load - Deflection curve on Beam B using ANSYS 52

4.9 Load - Deflection curve on Beam A (Control), B & C 55

using ANSYS

4.10 Bending moment diagram 57

4.11 Interaction diagram that consists of ultimate strength 59

xiv

LIST OF TABLES

TABLE TITLE PAGE

NO

3.1 The properties of Beam A (Control), B & C 27

4.1 Beam A (CONTROL) deflection results based on 47

theoretical, experimental and ANSYS

4.2 Beam A deflection results comparison among 49

theoretical, experimental and ANSYS

4.3 Beam B ANSYS deflection results based on concrete 51

strength grade C16 & C20

4.4 Beam B deflection results comparison between on two 52

concrete strengths

4.5 Deflection result between Beam B & C 53

4.6 Deflection result on Beam A, B & C using ANSYS 54

4.7 Deflection result comparison among Beams A 56

(Control), B & C using ANSYS

4.8 Bending moment for Beam A (Control), B & C 58

4.9 Small-Scale Flexure Results Comparison 58

4.10 Ultimate moment capacity for Beam A (Control), B & 60

C

xv

LIST OF SYMBOL

V Shear force

M Moment

Degree

d Displacement

Y Yield

P Force

CL Control

% Percentagi

kN Kilo Newton

mm milimeter

kg/m' Kilogram per meter cube

MPa Mega Pascal

N/mm 2 Newton per milimeter square

xvi

LIST OF ABBREBIATIONS

SYLCAG Synthetic Lightweight Coarse Aggregate

UMP Universiti Malaysia Pahang

BS British Standard

ACI American Concrete Institute

FEM Finite Element Modeling

DOF Degree Of Freedom

CS Coordinate System

XVII

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

Computer analysis can be used as an effectives tool to analyze structures and

components without need to build the structures first. The analysis can be carried out in

various condition and time with the verification of the actual condition under laboratory

testing too. This study use a computer analysis program called ANSYS to verify what is

actually occur to the structure such as beam during laboratory test. In the scope of

structural analysis solution, ANSYS provide the ability to simulate every structural

aspect including linear static analysis that simply provides stresses or deformations,

nodal analysis that determines vibration characteristics, through to advanced transient

nonlinear phenomena involving dynamic effects and complex behaviors. For the initial

step of this study, we will look at the background of the study that will brief about what

the material is used to build lightweight beam structures and some explanation on uses

of ANSYS. Then, the problem statement that explain about the disadvantages of

laboratorial test. Next, there are three objectives to be achieved with the following of

the scope of study that will brief the limitation in this study. Lastly, the significance that

can be found in this study is that in the future it can be enhanced further.

I

z

1.2 BACKGROUND OF STUDY

Concrete has become a key ingredient in the construction field in the world,

especially in Malaysia. The mixture consists of coarse aggregate and fine aggregate that

bonded with cement and water. For common type of concrete mixture usually normal to

become high or moderate with permeability, resistance to freezing, corrosion and

chemicals reaction therefore it is can be controlled. But, these characteristic can be

upgraded with lightweight concrete that can expand the increase of volume and qualities

in sustaining and lessened to the dead weight. In lightweight concrete mix ingredient,

the coarse aggregates were replaced with artificial offshore sand coarse aggregates.

Offshore sand is one alternative after river sand that widely used. Offshore sand should

extract from 15m ocean depth (Dias, 2007). The study of offshore sand that mixed with

concrete to become lightweight concrete has been made and named as Synthetic

Lightweight Coarse Aggregate (SYLCAG).

A beam is a one of the structural element that capable to sustain dead and live

load with bending resisting. In terms of bending moment, it is kind of force that induced

into the material of the beam from external loads, self-weight and external reaction.

Within the study of lightweight concrete using SYLCAG, to see more accurate result of

strengthen and flexural behavior, the real structure as beam were made to been analyze

in the laboratory. This paper presents the test results of 3 beams consist of 1 beam with

common sand mixture as control parameter and 2 lightweight beams using SYLCAG

that will be compare with computer analysis using software call ANSYS.

Experimental based on testing has been commonly used to analyze individual or

combination elements and its effects under loading. To further analyze these lightweight

beams and compare with laboratory testing results, the modeling of finite element

method using ANSYS software were create. The finite element model was creating to

be tested again in the software to show flexural behavior and failure from load-

deflection response. The Finite Element Modeling (FEM) analysis and laboratory

testing produced close or similar results. With computer analysis, the analysis can be

done frequently without having to concrete mixing repeatedly to build a beam. It can

also verify the condition of the beam under laboratory testing in daily observation.

1.3 PROBLEM STATEMENT

Recently, the usage of sand in the construction field tu build up lightweight

structures such as beam, column and slab demand a lot of these materials. In this

scenario, over-exploitation of river sand will lead to environmental harm locally. For

solution, offshore sand is the best way to take over the uses of common sand as

alternative material. The study, testing and analyze on structure part that mixed with

offshore sand has been covered in laboratory. But, seems here to run the testing and

analyze some element and parameter on structure part such as beam in laboratory are

time consuming, need men power and costly in uses of materials. Besides that, the

produced data can be not very accurate cause of some error in terms of apparatus or

technical. The analysis with computer software by using Finite Element Modeling

(FEM) to get the graphical result will minimize the time usage, energy and cost.

Furthermore, with computer analysis, the analysis can be run frequently and better in

produce accurate result.

1.4 OBJECTIVES

(i) To understand the advantages of Finite Element Modeling (FEM) for

analysis of simply supported concrete and SYLCAG beams

(ii) To compare the Finite Element Modeling (FEM) results with the

theoretical and laboratory experimental results

(iii) To study the flexural behavior of reinforced concrete and SYLCAG

beams using ANSYS

3

4

1.5 SCOPE OF RESEARCH

This study use computer analysis software called ANSYS to analyze the flexural

behavior of reinforced concrete beam using Synthetic Lightweight Coarse Aggregate

(SYLCAG) from linear response and up to failure. This study simulated by numerical

model the 3 types of beams consist of one control beam with common sand mixture and

another two beams using SYLCAG. The lightweight beam has the strength with grade

16MPa and 20MPa while the control one has the gred 30MPa. The size of beams is

200mm x 150mm X 1500mm. The mixtures are difference in aggregate density that

will come out with the differences beam density which is for I s, lightweight beam is

2030kg/m3, 2' lightweight beam is 1900kg/m3 and the 3rd or control beam is

2300kg/rn3. Flexural tests were performed in the laboratory to gain the load-deflection

curve and has been calculated to get the flexural behavior consists of bending moment,

ultimate moment capacity and deflection. The next action is, by using ANSYS; the

result will be verified with the same properties as the actuals. The results from ANSYS

will be compared with the flexural test result in laboratory and theoretical. The results

from ANSYS also will show the characteristics of the beams that could not be seen

from the laboratory testing immediately and gain understanding on how the beams will

react in actual conditions.

1.6 RESEARCH SIGNIFICANCE

The significance of this study is it can be test frequently with differences

material or element such as steel, timber and composite. This study also can be

expanding with various parameters by changing concrete grade, density and size of the

beam. Besides that, this software is potential to produces more result that cannot get by

laboratory test immediately such as linear and non-linear analysis that consists of elastic

and non-elastic structure, stress and strain. Furthermore the study can be much further

with investigation of stiffness of the beam in the Finite Element Modeling (FEM) and

the result can be as guideline to check and fix the lack of existing beam or re-design another beam.

1.7 EXPECTED OUTCOME

Based on the objectives that want to be achieved, the expected Outcome of this

study is firstly, the finite element method will ease the analysis especially for checking

in terms of flexural behavior or other analysis. Then, this method can produce more

accurate data if the ANSYS modeling has the exactly same material properties and

specification with the laboratory sampling (conventional beam). Lastly, based on the

result outcome from ANSYS, the deformed shape of the graph in terms of shear,

bending deflection and cracking, we can study and analyze the data to conduct solution

to strengthen the actual structure by changing the parameter or reduce the failure limit.

1.8 CONCLUSION

Based on this chapter, there are advantages of Finite Element Modeling (FEM)

to analyze the lightweight beam in three ways. Firstly, the analysis will show the

graphical and accuracy result compare to laboratorial test. Secondly, the usage of

ANSYS will verify the various results that cannot obtain from laboratorial testing

immediately. Finally, this study can be run frequently also with further investigation for

very complex data needed. In the next chapter, we will look at the fundamental part of

the flexural analysis including under the laboratorial test and Finite Element Modeling

(FEM) that consist of shear and bending moment, deflection and cracking.

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

This chapter will define at both laboratorial and finite element analysis. The

analysis will explain the design based on flexural that consist of bending moment,

deflection and crack based on theoretical terms, calculation and formula derivation also

with the procedure on both laboratorial and finite element method.

2.2 LABORATORIAL ANALYSIS

Usually, to run the experiment based on structural analysis, basically it involve

mixing of concrete, steel reinforcement installation and running test on the structure

with various load to identify the level of strength, flexibility, shear and lots more

parameter needed before design some structures.

2.2.1 Design Based On Flexural Analysis

Three concrete control beams were cast with flexural and shear reinforcing steel

and shear reinforcement was placed in each beam to force a flexural failure mechanism.

All three beams were loaded with transverse point loads at third points along the beams

until failure occurred (Buckhouse et a!, 1997)

7

Figure 2.1: Typical Cracking of Control Beam at Failure

(Buckhouse et al, 1997)

Because of the concrete in the constant moment region (flexural failure), the

beams was failed in compression and were ductile with significant flexural cracking of

the concrete in the constant moment region. To predict ultimate load, every beams were

plotted the load-deflection curves and compared.

2.2.1.1 Shear & bending

The shear and moment diagrams provide a useful means for determining the

largest shear and moment in a member, and they specify where these maximums occur.

When the load is applied on the beam, it will develop an internal shear force and

bending moment that, in general, vary from point to point along the axis of the beam. In

order to properly design a beam, before that the maximum shear and moment must be

determined as defined in the Mechanics of Materials (Hibbeler R.C, 8th ed, p56 - p57)

II

-, U ;ii1 - - ww :1 B I)

.," -1 -

nm n FITFITITIT

L - - --1 - - Simply SuFcorted Beam Model

Frèbydiagrarn f the left

segment of the beam

—i

L iiL Shear Force, V= r

Maxiinim

Shear and bending moment diagrams

Figure 2.2: Shear & Bending Moment diagram based on the Simply Supported

Beam as defined in the Mechanics of Materials (Hibbeler R.C, 81h ed, p56 -p57)

Bending moment are depends on the loading and the length of the beam. Even

though the materials of the several beams are differences in terms of density and

concrete strength, it is proven that those factors cannot give affect for bending moment.

Furthermore, the material of the beam itself are used to investigate the ultimate strength

in terms of ultimate moment capacity that can be influenced thorough the manipulation

of density and concrete strength.

8

9

An increases load that is subjected on simply supported beam causes the bending

and the top surface will shorten under compression and the bottom surface lengthens

under tension. The load also causes the beam to bend downward at mid-span and

upward over the supports. (Yassin, 2012)

Load

ct :::T t Steel reinforcement t

(a). Simply supported beam

crack

Tension crack

Steel reinforcement

reinrorccruent

(b). Continuous beam

Figure 2.3: Behavior of concrete beams in bending (Yassin, 2012)

2.2.1.2 Deflection

Deflection is defined as degree to which the structural element is displaced

under a load. The limit of deflection in design scope must be achieved so that the

structures will have stability and integrity. Structures subjected to a load that will return

to its original undeformed after the load is removed are under condition called linear elastic material response. The causes of deflection are from its internal loadings such as

normal force, shear force or internal bending such as bending moment as defined in the

Structural Analysis (Hibbeler R.C, 8 th ed, p305 - p307)

'U

-9 roller (W forket

Resist force from pin support

A-4L

pm

Restrict displacement

I, - II

fwd support

Resist Moment (fixed wall)

•

pnwth', morwnt. nthc lImini awsm upwvd u,iW 4*nu wd

kani

It n

At

monieni diagram

^A'

I ___ ,inflection lint

kflcrthrn curvc

Figure 2.4: Fundamental of deflection consists of type of restriction, curve and tends

direction as defined in the Structural Analysis (Hibbeler R.C, 8th ed, p305 -p307)

Flexural test of lightweight beam manage to show the flexural behavior upon the

manipulation of the density and concrete strength of every different beam. The increases

of deflection value were discovered during laboratory test to study and investigate about

flexure behavior of lightweight beam that mix with offshore sand.

Table 4.2: MId-span deflection of beam CL

Theory Expermten tal Remarks

D.fkcoloa (m) Deflection (urns)

0.0 000 0.09 004

1632 0.12 0.13

1817 0.14 0.14

Mos 0.15 0.17

22.13 0.17 0.3

24.19 0.18 0.39

26.24 0.20 0.64

27.01 0.21 0.67

27.5 0.21 1.62 First crack observed

28.02 0.21 2.98

29 0.22 4.06

30.02 0.23 6.64

30.99 0.24 7.91

32 0.24 10.14

52.5 0.25 12.16 Ultimate Load

ii

(a) (b) Table 4.3: Mid-span deflection of beam 1300

Load(12N) Theory Experimental Remarks

Deflection (mm) Deflection (mm)

0.00 0.00 0.00

2.06 0.02 0.25

4.01 0.03 0.40

4.99 0.04 0.48 First crack observed

6.01 0.05 1.17

8.06 0.06 3.86

8.88 0.07 4.45 Ultimate Load

(c)

Figure 2.5: Load - deflection data and curve from flexural test conducted in laboratory.

(a) Control beam deflection data based on experimental and theoretical, (b) Load-

Deflection curve of control beam, (c) Lightweight beam deflection data based on

experimental and theoretical (Zawawiv Aziz, 2013)

2.2.1.3 Crack

Flexural cracks are normally expected during the service life of a safely-

designed, ordinary, reinforced concrete structure. The cracks will develop in a

reinforced concrete member under services loads. When concrete dry, it shrinks and if

the shrinkage is restrained, tensile stresses developed and then if the stresses exceed the

tensile strength of the concrete. The progression of flexural cracking as the bending

moment on a reinforced concrete beam is increased due to consideration of three

principal stages of behavior like the beam is un-cracked, the beam is cracked but

12

stresses are within the elastic range and the beam reaches its ultimate strength (Carino

& Clifton, 1995)

(b) Cracked, elastic behavior cross Transformed Strain Stressss a Coss sc

at crack Section Dlstflbutlon Distribution

E) ri

kdjjd

T=A ts nA

Figure 2.6: Behavior of reinforced concrete beam with increasing bending moment

Figure 2.7: Cracks pattern on reinforced concrete beam (Zawawiv Aziz, 2013)

Flexural cracks tended to develop at approximately the location of the stirrups.

Therefore, the spacing of cracks was dominated by the location of the stirrups.

Therefore, the spacing of cracks was dominated by the location of the stirrups. For

beams without transverse reinforcement as shown in figure 6 (Beams GI -MO, G2-MO,

G3-CO and G3-MO) has further increase in load resulted in the formation of a critical

diagonal shear crack and sudden failure. For beams G -MO and G2-MO characterized

by the formation of a single critical diagonal crack spanning from the point of load

application to the support (Munikrjslma, Hosny, Rizkalla & Zia, 2011)