mechanical behavior of reinforced concrete beams with … · 2019. 2. 24. · mechanical behavior...

Mechanical Behavior of Reinforced Concrete Beams with Embedded Steel Trusses using Non-

Linear FEM

والمدمجة المسلحة الخرسانیة للكمرات المیكانیكي السلوك دراسة

المحددة العناصر طریقة باستخدام فولاذیة جمالونات مع

By

Ragheb Ibrahim Salim

Supervised by

A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Civil Engineering – Design and Rehabilitation of

Structures

December/2018

Dr. Mohammed Arafa

Dr. Mamoun Al‐Qedra

زةــغ – ةــلامیــــــة الإســـــــــامعـالج

عمادة البحث العلمي والدراسات العلیا

الھنـــــدســــــــــــــةة ــــــــــــــــــــلیـك

قســـــــــــم الھنـدســــــة المدنیـــــــــة

برنامج تصمیـــم وتأھیـــل المنشـــآت

The Islamic University–Gaza

Deanship of Research and Graduate Studies

Faculty of Engineering

Civil Engineering Department

Design and Rehabilitation of Structures

Mechanical Behavior of Reinforced Concrete Beams with

Embedded Steel Trusses using Non-Linear FEM

Declaration

I understand the nature of plagiarism, and I am aware of the University’s policy on this.

The work provided in this thesis, unless otherwise referenced, is the researcher's own

work, and has not been submitted by others elsewhere for any other degree or

qualification.

:Student's name راغب إبراهيم سليم اسم الطالب:

:Signature التوقيع:

17/02/2019 التاريخ:

Date:

I

Abstract

Strengthening of reinforced concrete (RC) beams using embedded steel trusses is a

novel technique to enhance shear and flexural behavior of reinforced concrete beams.

This technique has advantages of being constructed rapidly and easily. Enhancing shear

performance of RC beams using embedded steel trusses is quite unknown within the

engineering community.

The main purpose of this research is to study the mechanical behavior of reinforced

concrete beams with embedded steel trusses using non-Linear FEM and investigate the

effect of different parameters on the behavior of these beams.

The behavior of RC beams was simulated using finite element method. The analyses

were conducted using the finite element computer program ABAQUS. From the

analyses the load-deflection relationships until failure, failure modes and crack patterns

were obtained and compared to the experimental results. The FEM results agreed well

with the experiments regarding failure mode and load capacity.

The validation models were used to investigate the influence of the shear span-to-depth

ratios, shear reinforcement, different shape of embedded truss and longitudinal

reinforcement. To verify the numerical results, a reference analytical model is

employed to calculate the ultimate shear strength of RC control beams and RC beams

with embedded steel trusses at different (a/d) ratios. The numerical results showed well

agreement with the analytical results.

The analysis indicates that the shear capacity of reinforced concrete beams using

embedded steel trusses is inversely dependent on the shear span-to-depth ratio. It also

shows that the shear reinforcement (stirrups) has almost small effect on shear capacity

of reinforcement concrete beams with embedded steel trusses.

The numerical results further demonstrate that longitudinal reinforcement have

significant effect on the shear capacity of reinforced concrete beams using embedded

steel trusses. It is also shows that reinforcement concrete beam using embedded steel

truss with diagonal steel angles in critical shear span only have almost the same failure

load and shear behavior of reinforcement concrete beam using embedded steel truss

with diagonal steel angles in full span.

II

لملخصا

المدمجة ھي تقنیة جدیدة الفولاذیة إن تقویة الكمرات الخرسانیة المسلحة باستخدام الجمالونات

. نفیذتتمیز ھذه التقنیة بسرعة وسھولة الت. لتحسین قوى القص والعزوم للكمرات الخرسانیة المسلحة

المدمجة ةالفولاذیإن تقنیة تحسین قوى القص للكمرات الخراسانیة المسلحة باستخدام الجمالونات

.معروفة لدى كثیر من المھندسین الإنشائیین غیر

ستخدام الأطروحة إلى دراسة السلوك المیكانیكي للكمرات الخرسانیة المسلحة با تھدف ھذه

مجة من خلال طریقة العناصر المحددة، وكذلك دراسة تأثیر بعض الجمالونات الفولاذیة المد

.العوامل على سلوك ھذه الكمرات

مج من خلال برنا تم محاكاة سلوك الكمرات الخرسانیة المسلحة باستخدام نظریة العناصر المحددة

)ABAQUS( وتم التأكد من دقة النموذج عن طریق مقارنة نتائج التحلیل مع النتائج المخبریة .

لدراسات سابقة من خلال مقارنة الحمل الذي یحدث عنده فشل العینة وكذلك شكل الفشل للعینة.

ة الكمرات الخراسانیة المسلحفاعلیة ) على a/dبعد التأكد من دقة النموذج، ثم دراسة تأثیر نسبة (

باستخدام الجمالونات الفولاذیة المدمجة. وكذلك تم دراسة تأثیر حدید التسلیح الطولي والعرضي

تم ولتأكید النتائج وتأثیر استخدام نماذج أخرى من الجمالونات المدمجة على فاعلیة ھذه التقنیة.

یل لدراسات السابقة، أظھرت نتائج التحلحساب قوى القص باستخدام النموذج الریاضي الموثق في ا

باستخدام نظریة العناصر المحددة توافق جید مع نتائج النموذج الریاضي.

ما ، حیث أنھ كلفي ھذه التقنیة) لھا تأثیر عكسي على تحمل قوى القص a/dأن نسبة ( بینت النتائج

ھلذلك أن الحدید العرضي ) قلت قوة تحمل الكمرة لقوى القص. وأثبتت النتائج كa/dزادت نسبة (

. على تحمل قوى القص، أما الحدید الطولي فلھ تأثیر كبیر قلیل تأثیر

الزوایاأن استخدام تجربة نماذج أخرى من الجمالونات المدمجة، فقد بینت النتائج خلالومن

المدمجة في منطقة تمركز قوى القص فقط، لھ تقریبا نفس التأثیر الفولاذیة المائلة في الجمالونات

الفولاذیة على كامل الجمالون. الزوایاالناتج عن استخدام

III

Dedication

To my father

To my mother

To my brothers

To my sisters

My wife,

And my daughter

For their endless support

IV

Acknowledgment

First and foremost, I would like to thank my supervisors, Dr. Mohammed Arafa and

Dr. Mamoun Alqedra, without whom this study would not be accomplished. Their

limitless support, encouragement, and valuable suggestions have guided me throughout

the duration of this thesis.

My deepest thanks to my father Mr. Ibrahim M. Salim, for his encouragement and

limitless support.

Finally, I would like to express my thanks to my wife for her emotional support and

understanding during all this time and my lovely kid Dema.

V

Table of Contents

Abstract ....................................................................................................................... I

Abstract in Arabic ......................................................................................................... II

Dedication .................................................................................................................. III

Acknowledgment ........................................................................................................ IV

Table of Contents ....................................................................................................... V

List of Tables ............................................................................................................ VIII

List of Figures ............................................................................................................. IX

List of abbreviations .................................................................................................... XI

Chapter 1 Introduction ................................................................................................... 1

1.1 General ............................................................................................................... 2

1.2 Problem Statement ............................................................................................... 3

1.3 Research Aim and Objectives ................................................................................ 3

1.4 Methodology ....................................................................................................... 4

1.5 Layout of the thesis .............................................................................................. 4

Chapter 2 Literature Review ....................................................................................... 5

2.1 Introduction ........................................................................................................ 6

2.2 Modes of failure of RC beams ............................................................................... 6

2.3 Shear behavior of RC beams ................................................................................. 7

2.3.1 Behavior of beams without web reinforcement .................................................. 7

2.3.1.1 Internal forces in a beam without stirrups ....................................................... 9

2.3.1.2 Factors affecting the shear strength of beams without web reinforcement ........... 9

2.3.2 Behavior of beams with web reinforcement..................................................... 11

2.4 Shear strengthening of RC beams ........................................................................ 11

2.4.1 Shear strengthening of RC beams with FRP Composites .................................. 11

2.4.2 Shear strengthening of RC beams using high strength concrete .......................... 12

2.4.3 Shear strengthening of RC beams using prestressed concrete ............................ 13

2.4.4 Shear strengthening of RC beams using high-strength steel ............................... 14

2.5 Shear strengthening of RC beams using embedded steel truss .................................. 14

Chapter 3 Mechanical Behavior and Finite Element Modeling of Materials................. 18

3.1 Introduction ...................................................................................................... 19

3.2 Crack models for concrete ................................................................................... 19

3.2.1 Discrete crack model .................................................................................... 19

3.2.2 Smeared crack models .................................................................................. 20

3.2.3 Concrete Damage Plasticity .......................................................................... 20

VI

3.3 FE modeling of reinforcement ............................................................................. 22

3.4 Modeling of the embedded truss - concrete interface .............................................. 22

3.5 Element Types ................................................................................................... 23

3.5.1 Concrete ..................................................................................................... 23

3.5.2 Reinforcement ............................................................................................. 23

3.5.3 Embedded truss elements .............................................................................. 23

3.6 Material Properties ............................................................................................. 23

3.6.1 Concrete ..................................................................................................... 23

3.6.2 Reinforcement ............................................................................................. 25

3.7 Geometry .......................................................................................................... 25

3.8 Meshing............................................................................................................ 28

3.9 Number of Load Increments ................................................................................ 29

3.10 Description of the adopted study ........................................................................ 29

3.11 Summary ........................................................................................................ 32

Chapter 4 Verification of Finite Element Models and Parametric Study ............................. 33

4.1 Introduction ...................................................................................................... 34

4.2 RC beam with conventional reinforcement ............................................................ 34

4.3 RC beam with flat plate steel embedded truss ........................................................ 36

4.4 RC beam with steel angle embedded truss ............................................................. 37

4.5 Parametric Study ............................................................................................... 40

4.6 Effect of Shear Span-To-Depth Ratios (a/d) .......................................................... 40

4.6.1Failure loads and Load-Deflection Response .................................................... 40

4.6.1.1 Von Mises Stress of embedded steel truss at failure load ................................ 42

4.6.1.2 Comparison between numerical and analytical models ................................... 42

4.6.2 Crack pattern and failure modes .................................................................... 44

4.6.2.1 RC beams with conventional reinforcement .................................................. 44

4.6.2.2 RC beams with embedded steel truss ........................................................... 46

4.7 Effect of shear reinforcement .............................................................................. 49

4.7.1 Failure loads and Load-Deflection Response ................................................... 49


4.8 Effect of longitudinal reinforcement ..................................................................... 53



4.9 Effect of shape of the embedded steel truss ........................................................... 55



VII

4.10 Summary ........................................................................................................ 57

Chapter 5 Conclusion and Recommendations............................................................. 59

5.1 Introduction ...................................................................................................... 60

5.2 Conclusion ........................................................................................................ 60

5.3 Recommendations .............................................................................................. 61

The Reference List ...................................................................................................... 63

VIII

List of Tables Table (3.1): Material properties of steel........................................................................ 31

Table (3.2): Material properties of concrete ………………………………………………. 31

Table (3.3): Descriptions of tested specimens……………………………………………... 31

Table (4.1): Ultimate failure loads for RC beams with conventional reinforcement and RC beams with embedded steel truss …………………………………………………………………………………….. 41

Table (4.2): Comparison between the calculated and numerical ultimate load carrying capacity of RC beams ............................................................................................................. 43

Table (4.3): Comparison of ultimate loads carrying capacity of HSTC beams with and without shear reinforcement (stirrups)................................................................................................ 50

IX

List of Figures Figure (3.1): Drucker–Prager boundary surface (Drucker and Prager 1952) ........................ 20

Figure (3.2): Concrete damage plasticity deviatoric plane (Systèmes 2014) ........................ 21

Figure (3.3): Compression hardening relationship for RC beam models 3 .......................... 24

Figure (3.4): Tension stiffening (displacement) for RC beam models ................................ 25

Figure (3.5): 3-D View of the RC beam modeled in ABAQUS ........................................ 26

Figure (3.6): 3-D View of the embedded conventional steel reinforcement modeled in

ABAQUS .................................................................................................................. 26

Figure (3.7): 3-D View of the embedded flat plate steel truss modeled in ABAQUS ........... 27

Figure (3.8): 3-D View of the embedded steel angle truss modeled in ABAQUS ................ 27

Figure (3.9): 3-D View of the concrete meshed model of RC beam. ................................. 28

Figure (3.10): Meshed model of the embedded flat plate steel truss. .................................. 28

Figure (3.11): Meshed model of the embedded steel angle truss. ....................................... 29

Figure (3.12): Profile and cross section detail of SRCB-1 and SRCB-2 (Zhang, Fu et al. 2016)

................................................................................................................................. 30

Figure(3.13): Profile and cross section detail of SRCB-3 (Zhang, Fu et al. 2016) ................ 30

Figure (3.14) : Profile and cross section detail of SRCB-4 (Zhang, Fu et al. 2016) .............. 31

Figure (4.1): Deflected shape for RC beam with conventional reinforcement. .................... 34

Figure (4.2) : load-deflection curve RC beam with conventional reinforcement .................. 35

Figure (4.3): crack pattern at failure for RC beam with conventional reinforcement ............ 35

Figure (4.4): Deflected shape for RC beam with flat plate steel embedded truss.................. 36

Figure (4.5): load-deflection curve for RC beam with flat plate embedded truss ................. 36

Figure (4.6): crack pattern at failure for RC beam with flat plate steel embedded truss ........ 37

Figure (4.7): Deflected shape for RC beam with steel angle embedded truss ...................... 37

Figure (4.8): load-deflection curve for RC beam with steel angle embedded truss ............... 38

Figure (4.9): Strain curve (strain gauge 1) of steel truss rod. ............................................. 38

Figure (4.10): Strain curve (strain gauge 2) of steel truss rod. ........................................... 39

Figure (4.11): crack pattern at failure for RC beam with steel angle embedded truss ........... 39

Figure (4.12): Shear span to depth ratio (a/d) .................................................................. 40

Figure (4.13): load-deflection relationship for RC beams with embedded steel truss at

different (a/d) ............................................................................................................. 41

Figure (4.14): Von Mises Stress of embedded steel truss at failure load ............................. 42

Figure (4.15): crack pattern at failure for RC beam with conventional reinforcement at (a/d) =

1 ............................................................................................................................... 44


1.25........................................................................................................................... 44


1.5 ............................................................................................................................ 45


1.75........................................................................................................................... 45


2 ............................................................................................................................... 45


2.25........................................................................................................................... 46


2.5 ............................................................................................................................ 46

Figure (4.22): crack pattern at failure for RC beam with embedded steel truss at (a/d)

= 1.25 ........................................................................................................................ 47

X

Figure(4.23): crack pattern at failure for RC beam with embedded steel truss at (a/d) =

1.5 ............................................................................................................................ 47


= 1.75 ........................................................................................................................ 47

Figure (4.25): crack pattern at failure for RC beam with embedded steel truss at (a/d) = 2 ... 48


= 2.25 ........................................................................................................................ 48

Figure (4.27): crack pattern at failure for RC beam with embedded steel truss at (a/d) =

1 ............................................................................................................................... 48


= 2.5 ......................................................................................................................... 49

Figure (4.29): load-deflection relationship for RC beams using embedded steel angle truss

without stirrups .......................................................................................................... 50

Figure (4.30): crack pattern at failure for the beam using embedded steel truss without stirrups

at (a/d) =1 .................................................................................................................. 51


at (a/d) =1.25 .............................................................................................................. 51


at (a/d) =1.5 ............................................................................................................... 52


at (a/d) =1.75 .............................................................................................................. 52


at (a/d) =2 .................................................................................................................. 52


at (a/d)=2.25 .............................................................................................................. 53


at (a/d) =2.5 ............................................................................................................... 53

Figure (4.37): load-deflection relationship for RC beam using embedded steel truss with

reduction in the long. reinf. Ratio and RC beam with conventional reinf. ........................... 54

Figure (4.38): load-deflection relationship for RC beams using embedded steel truss with and

without reduction in the long. reinf. ratio ....................................................................... 54

Figure (4.39): crack pattern at failure for RC beams using embedded steel angle truss with

reduction in the longitudinal reinforcement ratio ............................................................. 55

Figure (4.40): embedded steel truss with diagonal steel angles in critical shear span only .... 55

Figure (4.41): load-deflection relationship for RC beam using embedded steel truss with

diagonal steel angles in critical shear span only and RC beam with conventional reinf. ....... 56

Figure (4.42): load-deflection relationship for RC beam using embedded steel truss and RC

beam using embedded steel truss with diagonal steel angles in critical shear span only ........ 56

Figure (4.43): pattern of crack at failure for RC beam using embedded steel truss with

diagonal steel angles in critical shear span only .............................................................. 57

XI

List of abbreviations RC: Reinforced Concrete.

GFRP: Glass Fiber Reinforced Polymer.

FRP: Fiber Reinforced Polymer.

NSM: Near Surface Mounted.

CFRP: Carbon Fiber Reinforced Polymer.

HSRC: High Strength Reinforced Concrete.

HSTCB: Hybrid Steel Trussed Concrete Beam.

CDP: Concrete Damage Plasticity.

1

Chapter 1 Introduction

2

Chapter 1

Introduction

1.1 General

When principal tensile stresses within the shear region of a reinforced concrete beam

exceed the tensile strength of concrete, diagonal cracks develop in the beam, eventually

causing failure. The brittle nature of concrete causes the collapse to occur shortly after

the formation of the first crack, (Lim and Oh 1999). So, the shear failure pattern of

reinforced concrete beam is more critical and unsafe than the flexural failure pattern of

the same beam. Thus, in order to enhance the shear capacity of concrete beams, the

improvement of the brittle and poor performance of concrete in tension has been

proposed and studied in the last few decades.

Many researches have been conducted to enhance the shear strength of reinforced

concrete beams through using pre-stressed concrete, high strength concrete, steel fiber

concrete, ultra-high performance concrete, and high-strength steel. Nevertheless, these

enhancing measures need complex construction technology and special materials.

Another technique to enhance shear and flexure strength of reinforced concrete beams

is to adopt prefabricated steel trusses embedded in cast-in-place concrete beams, which

has advantages of being constructed rapidly and easily,(Zhang, Fu et al. 2016).

Shear strengthening of reinforced concrete beams using embedded steel trusses

technique is quite unknown within the engineering community. Moreover, it has been

used for three decades in Italy. Through this technique, the steel trusses can bear their

own weight and the weight of slab and fresh concrete without any provisional support

during a first assembly stage. Then, when the concrete become hard, the embedded

trusses can collaborate with the cast in place concrete. Although, interest for this

technique is growing up in many countries because of its advantages, there are not

specific regulations for this technique in American or European codes.

While experimental methods of investigation are extremely useful in obtaining

information about the mechanical behavior of reinforced concrete beams using

embedded steel trusses, the use of numerical models helps in developing a good

understanding of the behavior at lower cost.

3

In this research, non‐linear finite element analysis models for strengthening of

reinforced concrete beams with embedded steel trusses was presented. A finite element

software package ABAQUS was utilized to study the mechanical behavior of reinforced

concrete beams of small shear span-depth ratio with embedded steel trusses. The effect

of the following parameters on the behavior of strengthened beams namely, shear-span

to depth ratios, shear reinforcement at different shear-span to depth ratios, truss shape,

and longitudinal reinforcement were obtained.

1.2 Problem Statement

Shear strengthening of reinforced concrete beams using embedded steel trusses

technique has been used for three decades in Italy; in addition, the interest of this

technique is growing up in many countries. However, there are not specific regulations

for this technique in American and European codes and this technique is quite unknown

in engineering community, (Monaco 2016). Therefore, this study is to address this

problem and study the mechanical behavior of reinforced concrete beams with

embedded steel trusses and the influences of the shear span-to-depth ratios, shear

reinforcement, different shape of embedded truss and longitudinal on the shear behavior

of these beams.

Because of the high cost and large equipment required for full-scale tests, and small-

scale tests; development of a reliable analytical software model is desirable. The finite

element method computer software, ABAQUS, will be used to produce a model, which

closely resembles the experimental available data.

1.3 Research Aim and Objectives

The main aim of this research is to study the mechanical behavior of reinforced concrete

beams with embedded steel trusses using non-Linear FEM. The following are the

objectives of this study:

1. Determine the most capable methods that can be used for modeling and simulation

of reinforced concrete beams with embedded steel trusses.

2. Develop a 3D model reinforced concrete beams with embedded profile steel trusses

in ABAQUS software.

3. Validate the numerical model with respect to the experimental database available in

the literature.

4

4. Study the effect of selected parameters such as: shear span-depth ratio, shear

reinforcement at different shear-span to depth ratios, shape of truss and longitudinal

reinforcement.

1.4 Methodology

To achieve the stated objectives of this research, the following tasks will be

conducted:

1. Review of available literature for the finite element modeling and experimental

works related to the subject.

2. Utilize the finite element software ABAQUS to develop a 3-D non-linear model of

reinforced concrete beams of small shear span-depth ratio with embedded steel trusses.

3. Validate the developed model by means of experimental and numerical results from

a previous studies.

4. Evaluate the sensitivity of critical modeling parameters.

5. Draw conclusions and suggest recommendations.

1.5 Layout of the thesis

The contents of the chapters are presented below to give an overview of the structure

of the master thesis. This thesis consists of five chapters.

Chapter 1 discusses the plan of this thesis.

Chapter 2 presents more details on the literature review of modes of failure in RC

beams, as well as on the shear behavior in RC beams and its background. It also presents

many different techniques to increase the shear strength of reinforced concrete beams.

Chapter 3 presents a finite element analysis of reinforced concrete beams with

embedded steel trusses using ABAQUS based on the experimental results.

Chapter 4 presents a verification of ABAQUS finite element models and the effect

of the following parameters on the behavior of verified strengthened beams: shear-span

to depth ratios, shear reinforcement, truss shape, and longitudinal reinforcement.

Chapter 5 summarizes the main conclusions, and the overall findings of this project

with recommendations for further actions to be taken.

5

Chapter 2

Literature Review

6

Chapter 2

Literature Review

2.1 Introduction

In this chapter, modes of failure in RC beams are initially reviewed. Subsequently a

study of shear behavior in RC beams and its background has been discussed. Finally,

many different techniques to increase the shear strength of reinforced concrete beams

have been presented.

The research, performed throughout this project involves the use of prefabricated steel

trusses embedded in cast-in-place concrete beams that is a novel technique to enhance

shear and flexure strength of reinforced concrete beams. There has been limited

research work performed using of prefabricated steel trusses embedded in cast-in-place

concrete beams as a shear strengthening technique and hence, only a small number of

publications are available for reference work in this regard. The few literatures

pertaining to use of this technique as a shear strengthening technique which been

published till date has been reviewed in this chapter.

2.2 Modes of failure of RC beams

Several types of failure modes may occur when RC beams are subjected to either

uniformly distributed load or a concentrated load. There are four possible modes of

failure: anchorage failure, crushing failure, flexural failure and shear failure as

explained below:

Anchorage failure: for RC beam, the tensile force in the reinforcement at the end of

the beam must be transferred to the surrounding concrete by bond action between the

two materials; this anchorage requires a certain transmission length. When cracks

develop closer to support, the transmission length gets shorter, and then the beam fails

due to in-sufficient anchorage capacity.

Crushing failure: in compression zone, when the stresses caused by the increasing

load exceed the compressive strength of concrete, crushing of concrete may lead to

brittle failure of the beam. In the tensile zone, if the stresses in the reinforcement exceed

the yielding strength of the reinforcement before crushing failure happens, the beam

could fail for bending.

7

Flexural failure: the first crack would form in the region of maximum bending

moment, where the maximum principal stress attains the material tensile strength. As

the amount of reinforcement increased, several cracks are formed along the beam. In

early stages, these cracks are approximately normal to the beam axis and, as cracking

progresses, they grow in the presence of combined normal and shear stress as mixed-

mode flexural shear cracks.

Shear failure: this mode of failure is discussed in detail in the following subsection.

2.3 Shear behavior of RC beams

The study of shear behavior in concrete structures has been going on since a century

and the foundations of knowledge on shear were provided by Mörch in 1909. Until the

year 1955, researchers were of the view that shear was a simple problem to deal with.

Afterwards, researchers realized that shear in concrete beams cannot be designed as

traditionally as it was done earlier. It is only since the last six decades, researchers have

been focusing their work to develop a common and an efficient consensus on design

for shear which could be internationally acceptable. As a result, many theories have

been developed to explain the shear behavior in beams and to estimate its shear

capacity.

It is well known that shear failures are inherently more dangerous than flexural failures,

since shear failures normally exhibit fewer significant signs of distress and warnings

than flexural failures. The determination of shear strength of RC members is based on

several assumptions, all of which are not yet proved to be correct. It is important to

realize that there is a considerable disagreement in the research community about the

factors that most influence shear capacity.

The behavior of RC beams under shear may be categorized into two types; these types

of behavior are briefly discussed in the following subsections.

2.3.1 Behavior of beams without web reinforcement

The mechanism of the brittle-type diagonal tensile failure of RC beams with no shear

reinforcement (stirrups) is complex and not yet fully understood. The behavior of beams

failing in shear may vary widely, depending on the (a/d) ratio (shear span to effective

depth ratio) and the amount of web reinforcement. (Kani 1966)

8

According to Kani (1966) the shear spans can be divided into three types: short, slender,

and very slender shear spans. The term deep beam is also used to describe beams with

short shear spans.

Very short shear spans, with (a/d) from 0 to 1, develop inclined cracks joining the load

and the support. These cracks, in effect, destroy the horizontal shear flow from the

longitudinal steel to the compression zone, and the behavior changes from beam action

to arch action. Here, the reinforcement serves as the tension ties of a tied arch and has

a uniform tensile force from support to support. The most common mode of failure in

such a beam is an anchorage failure at the ends of the tension tie, (Kani 1966).

Beams with (a/d) ranging from 1 to 2.5 develop inclined cracks and, after some internal

redistribution of forces, carry some additional loads due to arch action. These beams

may fail by splitting failure, bond failure, shear tension, or shear compression failure,

(Kani 1966).

In slender shear spans, those having (a/d) from about 2.5 to about 6, the inclined cracks

disrupt equilibrium to such an extent that the beam fails at the inclined cracking load.

When the load is applied and gradually increased, flexural cracks appear in the mid-

span of the beams, which are more or less vertical in nature. With further increase of

load, inclined shear cracks develop in the beams, at about 1.5d– 2d distance from the

support, which are sometimes called primary shear cracks. The typical cracking in the

slender beams without transverse reinforcement, leading to the failure, involves two

branches. The first branch is the slightly inclined shear crack, with the typical height of

the flexural crack. The second branch of the crack, also called secondary shear crack or

critical crack, initiates from the tip of the first crack at a relatively flatter angle, splitting

the concrete in the compression zone. The failure is by shear compression due to the

crushing of concrete, without ample warning and at comparatively small deflection.

The nominal shear stress at the diagonal tension cracking at the development of the

second branch of inclined crack is taken as the shear capacity of the beam, (Kani 1966).

Very slender beams, with (a/d) greater than about 6, will fail in flexure prior to the

formation of inclined cracks, (Kani 1966).

9

2.3.1.1 Internal forces in a beam without stirrups

According to Fenwick and Pauley (1968) The factors assumed to be carrying shear

force in cracked concrete to the supports when no shear reinforcement are listed below:

1. Shear resistance of uncraked concrete (Vc).

2. Interlocking action of aggregates (Va).

3. Dowel Action of steel reinforcement (Vd).

Before cracking, a reinforced concrete beam acts like a homogeneous beam. After

bending cracks appear, shear displacement occurs along an inclined crack and dowel

action in reinforcements gets mobilized. When the two faces of a bending crack of

moderate width are given a shear displacement relative to each other, a number of

coarse aggregate particles projecting across the crack interlock with each other generate

significant shear resistance. As the applied shear force is increased, the dowel action is

the first to reach the capacity after which a proportionally large shear force is transferred

through aggregate interlock. The aggregate interlock mechanism is probably the next

to fail, necessitating a rapid transfer of a large shear force to the concrete compression

zone, which as a result of this sudden shear transfer, the beam often fails abruptly and

explosively, ( Fenwick and Pauley 1968).

2.3.1.2 Factors affecting the shear strength of beams without web reinforcement

Shear behavior of a beam without shear reinforcement is largely determined by six

factors: the tensile strength of the concrete, the longitudinal reinforcement ratio, the

ratio of shear span to effective depth, size of beam, and the presence of axial forces,

(Wright and MacGregor 2012).

These factors will be discussed below: -

1. Shear span to effective depth ratio. The shear span-to-depth ratio (a/d) is one of

the major parameters that affect the shear strength of reinforcement concrete beams.

All studies showed that shear strength of reinforcement concrete beams decreases with

the increase of the shear span-to-depth ratio (a/d), (Michael 1984, Shah and Ahmad

2008, Alhamad, Al Banna et al. 2017, Hu and Wu 2018). However, (Kani 1966) found

that the shear span-to-depth ratio (a/d) affects the inclined cracking shears and ultimate

shears of portions of members with a/d less than 2. For longer shear spans, (a/d) has

little effect on the inclined cracking shear and can be neglected.

2. Longitudinal reinforcement ratio. According to Lee and Kim (2008) the shear

strength of the RC beams drops significantly if the longitudinal reinforcement ratio

10

decreases below (1.2–1.5) percent. When the steel ratio, is small, flexural cracks extend

higher into the beam and open wider than would be the case for large values of steel

ratio. An increase in crack width causes a decrease in the maximum values of the

components of shear - the aggregate interlock and the dowel action - that are transferred

across the inclined cracks by dowel action or by shear stresses on the crack surfaces.

Similar, (Yu, Che et al. 2011) conducted seven experiments on reinforcement concrete

beams and commented that, there is a decreasing trend of shear strength as the

longitudinal reinforcement ratio decreases. Hamid, Ibrahim et al. (2016) showed that,

the shear capacity of concrete beams longitudinally reinforced with glass fiber-

reinforced polymer (GFRP) bars were affected by high reinforcement ratio of

longitudinal GFRP bars.

3. Size of beam. According to ACI specifications, the shear capacity is proportional to

the depth of the member. T. Shioya and Okada (1990) tested reinforced concrete beams

with depths ranging from 100 to 3000 mm. The results show that the shear stress at

failure decreases when the depth of the member increases. Similarly, Ghannoum

(1998) performed twelve experiments on nominal strength and high strength concrete

beams and commented that, the size effect is very evident in both nominal strength and

high strength concrete series. Furthermore, he found that the shallower specimens were

consistently able to resist higher shear stress than the deeper ones.

4. Compressive strength of concrete. The shear strength is the function of the

compressive strength. Yaseen (2016) showed that, the shear strength increases by

approximately 55 % and 72% when the compressive strength of concrete increased

from 434 MPa to 61 MPa and then to 119 MPa. On the other hand, Kong (1996) showed

that the concrete compressive strength within the range of 60 to 90 MPa had a little

influence on the shear strength of the beams.

5. Tensile strength of concrete. According to Angelakos, Bentz, and Collins (2001),

concrete tensile strength influence the shear failure process. The concrete tensile

strength mainly affects the shear failure modes. Abdul-Zaher, Abdul-Hafez et al.

(2016), showed that the shear strength increased by 11.43% and 28.57% when tensile

strength increased by 12.5 and 31.25 respectively.

6. Axial forces. Bhide and Collins (1989) researched the effect of axial tension on the

shear behavior of reinforcement concrete beams, he found that the axial tension

increases the inclined crack width and reduces the aggregate interlock, and hence, the

shear strength provided by the concrete is reduced. Shaaban (2004) conducted an

11

experimental and analytical investigation on the shear behavior of high strength fiber

reinforced concrete beams and found that, increasing the axial compression stress level

to 0.2 led to an increase in the first crack load, ultimate load by 24% and 10%, a

reduction in the deflection by (19-30%).

2.3.2 Behavior of beams with web reinforcement

The purpose of web reinforcement is to ensure that the full flexural capacity can be

developed. Prior to inclined crack, the strain in the stirrups is equal to the corresponding

strain of the concrete. Because concrete cracks at a very small strain, the stress in the

stirrups prior to inclined cracking will not exceed the compressive strength of the

concrete. Thus, stirrups do not prevent inclined cracks from forming; they work after

the cracks have formed, (Wright and MacGregor 2012).

After the first inclined crack, redistribution of shear stresses occurs, with some parts of

the shear being carried by the concrete and the rest by the stirrups, Vs. Further loading

will result in the shear stirrups carrying increasing shear, with the concrete contribution

remaining constant. The presence of shear reinforcements restricts the growth of

diagonal cracks and reduces their penetration into the compression zone. This leaves

more uncracked concrete in the compression zone for resisting the combined action of

shear and flexure. The stirrups also counteract the widening of cracks, making available

significant interface shear between the cracks. They also provide some measure of

restraint against the splitting of concrete along the longitudinal reinforcement, also

increasing the dowel action. With further loading and opening of cracks, the interface

shear decreases, forcing of (shear resistance of uncracked concrete and dowel action)

to increase at an accelerated rate the stirrups also start to yield. Soon, the failure of the

beam follows either by splitting (dowel) failure or by compression zone failure due to

the combined shear and compression, (Subramanian 2013).

2.4 Shear strengthening of RC beams

Various techniques have been used to increase shear strength for reinforced concrete

beams in the past decades. These techniques will be discussed below.

2.4.1 Shear strengthening of RC beams with Fiber Reinforced Polymer (FRP)

Composites

Thanasis (1998) studied the shear performance of strengthening of reinforced concrete

beams using epoxy - bonded composite materials in the form of laminates or fabrics

12

through experimentation research. The test results indicate that using epoxy - bonded

composite materials appears to be a highly effective technique. The experimental

results further demonstrated that, the effectiveness of FRP increases as the fibers’

direction becomes closer to the perpendicular to the diagonal crack.

Diagana et al. (2002) studied the shear performance of strengthening reinforced

concrete beams using bonded carbon fiber through experimentation research. The test

results indicate the shear capacity of strengthened beam affected by the applied

composite fabric area, the spacing between the steel stirrups, and the longitudinal steel

bars diameter of reinforced beam.

Al-Mahaidi et al. (2006) studied the bond characteristic between carbon fiber reinforced

polymer (CFRP) and concrete though numerical research. Twelve shear-lap specimens

were modeled using a combination of smeared and discrete cracks to investigate their

ultimate loads, and crack patterns. The numerical results indicated that, transverse

cracks have a significant influence on the bond stress distributions.

Rahal and Rumaih (2011) studied the shear performance of reinforced concrete T-

beams strengthened in shear using near surface mounted (NSM) carbon fiber reinforced

polymer (CFRP) bars and conventional steel reinforcing bars through experimentation

research. Four large scale reinforced concrete T-beams were tested to investigate their

structural performance and ultimate shear strength. Comparing with the common

reinforced concrete T-beams, the test results indicate that using of CFRP increased the

ultimate shear capacity 37% - 92%, reduced the width of the diagonal cracks, and

improve the flexural ductility. The experimental results further demonstrated that

orienting the NSM bars at 45°and extending their anchorage into the flange concrete

improved the efficiency of strengthening.

2.4.2 Shear strengthening of RC beams using high strength concrete

Ashour and Faisal (1992) presented test results of eighteen high strength reinforced

concrete beams without stirrups which were tested to investigate their flexural and shear

strength and behavior under loading. The results indicated that addition of fibers

increased the ultimate shear strength and improved flexural ductility, depending upon

the shear-span/depth ratio and transformed the mode of failure into a more ductile one.

13

Cladera and Marí (2005) studied the shear performance of reinforced concrete beams

that had a compressive strength ranged from 50 to 87 MPa through experimental

research. Eighteen reinforced concrete beams with and without shear reinforcement

were tested to investigate their structural behavior and ultimate shear strength. The test

results indicated, for beams without web reinforcement, the failure shear strength

increased as the concrete compressive strength increased in condition of beams without

web reinforcement. Fragile response for high-strength concrete beams with stirrups is

less than similar beams without web reinforcement.

Perera and Hiroshi (2013) studied the shear performance reinforced high-strength

concrete beams without shear reinforcement though experimental research. The

concrete beams which had compressive strength more than 100 MPa were tested to

investigate their structural performance and ultimate shear strength. It is found that

shear strength started to decrease due to the smooth fracture surface and brittleness.

Saeed and Abubaker (2016) studied the shear performance of high strength reinforced

concrete (HSRC) beams without stirrups through experimental research. Twelve

specimens were tested to investigate their structural performance and ultimate shear

strength. The test results indicated that, the ultimate shear strength of high strength

reinforced concrete (HSRC) beams without stirrups didn't increase significantly when

each of compressive strength and (a/d) ratio increased.

2.4.3 Shear strengthening of RC beams using prestressed concrete

Mikata, Inoue et al. (2001) studied the effects of prestress level and the distribution of

prestress over the section on shear capacity used the test results of prestressed concrete

beams without shear reinforcement and prestressed reinforced concrete beams. Test

results showed that the measured shear cracking load increases as the amount of

introduced prestress increase and when the stress distribution over the section changes

from triangular to rectangular, and the measured inclination of diagonal cracks

decreases with increasing the introduced prestress and decreases when the stress

distribution over the section is changed from triangular distribution to rectangular

distribution.

Hou, Nakamura et al. (2017) studied the shear resistance mechanism of reinforced

concrete and prestressed concrete tapered beams without stirrups. Three series of seven

beams with different parameters (a/d) ratios and prestress levels were tested. The results

14

indicated that when the prestress level increased, the inclination of the shear stress flow

decreased while the effective depth of the critical section became larger, and the shear

capacity of prestressed concrete tapered slender beam without stirrups became higher

than that of prestressed concrete constant depth beam without stirrups because of the

larger critical section.

2.4.4 Shear strengthening of RC beams using high-strength steel

Hassan and Paul (2008) studied the effects of high-strength steel on shear performance

using test results of concrete beams reinforced with either conventional- or high-

strength steel and tested up to failure. Six large-size beams were tested to study the

effect of the shear span depth ratio, concrete compressive strength, as well as the type

and the amount of longitudinal steel reinforcement. The experimental results showed

that using high-strength steel affected significantly the shear behavior of the concrete

beams. The experimental results further demonstrated that, using high-strength steel

improve the mode of failure to shear compression failure.

Lee and Sang-Woo (2011) studied the effects of high-strength stirrups shear capacity

using the test results of thirty-two simply supported RC beams. The results indicated all

the beams with stirrups with a yield strength ≤ 700 MPa (101,500 psi) failed after

reaching their yield strains, unrelatedly to the compressive strength of the concrete,

whereas the shear failure mode of the beams with a yield strength > 700 MPa (101,500

psi) was affected by the compressive strength of the concrete.

2.5 Shear strengthening of RC beams using embedded steel truss

Strengthening of reinforced concrete beam using embedded steel truss is a novel

technique to enhance shear and flexural behavior of reinforced concrete beam. In this

technique the steel truss is embedded in concrete core. The truss is usually made up of

steel angles that represent the bottom and the top chords, a system of steel angles or

steel plates welded in order to form the diagonals of the truss. The web elements work

as struts and ties, which can be inclined or according to different geometries.

The RC beams with embedded steel trusses represent a structural solution to improve

the shear performances and ultimate shear strength for RC beams with small shear span

to depth ratios, also frequently introduced within seismic frame structure.

15

The main advantages in their use are higher construction speed with the minimum site

labor and economical convenience. There has been limited research work performed

using of prefabricated steel trusses embedded in cast-in-place concrete beams as a shear

strengthening technique and hence, only a small number of publications are available

for reference work in this regard. The few literatures pertaining to use of this technique

as a shear strengthening technique, which been published until date, will be discussed

below.

Tesser and Scotta (2013) studied the shear and flexural behavior of composite steel

truss and concrete beams with inferior precast concrete base. Twenty-four beam

specimens with different depth were tested to investigate their shear and flexural

behavior. The results of flexural test indicated that, all the beams suffered yielding of

the steel bottom chord. The results of shear test showed that, all the beams were affected

by inclined cracks in the portion between the load application point closer to the support

and the support itself. The experimental results further demonstrated that, the specimens

which are characterized by shear span to depth ratio lower than 4.6, failed in shear.

Tullini and Minghini (2013) studied the bending moment capacity and shear connection

strength of composite beams with concrete – encased steel truss through finite element

formulation based on Newark's classical models. Simply supported beams subjected to

uniformly distributed load are considered. Test results indicated that, for medium spans,

the bending strength turns out to be proportional to the beam span length and the

ultimate conditions are in fluenced by the shear connections. In the other region,

including medium up to long spans, the bending strength is constant with the beam span

length and the ultimate conditions are essentially governed by the concrete com-

pressive strength at midspan. The numerical results demonstrate that, in the presence of

a brittle shear connection, the ultimate limit state is governed by the ultimate slip at the

supports. Whereas, in the presence of a ductile shear connection, the beam ductility is

limited by premature compression failure of concrete.

Colajanni, La Mendola et al. (2014) studied the transformation mechanism of stress in

hybrid steel trussed-concrete beams through experimentation research. Push-out tests

were used to investigate the tensile strength of beam specimens. The results of push-

out tests indicated, the specimens exhibit almost brittle failures due to the collapse of

the concrete in tension with the steel tensile web rebar that developed large inelastic

deformations, mainly concentrated at the ends close to the bottom steel plate.

16

Monti and Petrone (2015) developed shear capacity equations for composite steel truss

beam. These equations were obtained from developed mechanics-based shear models.

In the study two different equations were proposed: the first one was derived from an

analytical method that considered the contribution of the concrete whereas the second

equation obtained from a simplified method which does not consider the contribution

of the concrete. The results of both quotations showed significant agreement with

experimental and numerical results.

Campione, Colajanni et al. (2016) developed a calculation method for the pridiction of

the shear resistance of the hyprid steel trussed concrete beams. These beams are

prefabricated steel truss embedded within a concrete cast in palce. The analytical model

was developed based on the results of previous experimental three-point bending test.

Furthermore the analytical results were supported by the results of previous finit

element modeling.

Zhang, Fu et al. (2016) studied the effects of shear embedded steel trusses on shear

performance of reinforced concrete beams using the test results of five beam specimens

characterized by small shear span to depth ratio. The experimental results showed that,

using steel angle truss adding horizontal reinforcement increased the ultimate shear

strength compared with the common reinforced concrete beams. The experimental

results further confirmed that embedding the steel trusses in reinforced concrete beams

is indeed a promising novel technique that can significantly improve the structural

behavior of reinforced concrete beams in shear failure.

Monaco (2016) studied the shear performance of hybrid steel trussed concrete beams

(HSTCB) through finite element method. Numerical simulation of experimental three-

point bending test was developed for the aim. The numerical results indicated that,

detailing model with cohesive interaction is more accurate than simplified finite

element model with perfect bond hypothesis.

Kareemi, Petrone et al. (2016) studied the shear performance of composite beams made

of prefabricated steel trusses encase in structural concrete through experimentation

research. Eight beam specimens subjected to uniformly distributed load were tested to

investigate their ultimate shear strength. The experimental results demonstrate that

composite truss beams have an effective performance in shear.

17

Colajanni, La Mendola et al. (2017) investigated the mechanical response of hybrid

steel trussed-concrete beams under shear through experimentation research. Two series

of beams subjected to positive and negative moment respectively were tested to

investigate their ultimate shear strength and structural performance. The results

indicated that in almost all cases fragile shear failure occurred mainly because of the

crisis of the compressed concrete strut involved in the mechanism.

Ballarini, La Mendola et al. (2017) used finite element method to study the failure

behavior of hybrid steel trussed-concrete beams under three-point bending test. The

numerical model was compared with previous experimental data, and showed well

agreement to the experimental results. The numerical results indicated that, the small-

size beam exhibited shear failure, while the large-size beam experienced flexural

failure.

Colajanni, La Mendola et al. (2018)studied the failure mode and the stress transfer

mechanism of semi precast hybrid trussed-concrete beams through experimentation

research. Six beams specimens subjected to four-point bending with deferent (a/d)

ratios were tested. The experimental results showed that the flexural failure load and

the connection failure load are almost coincident for (a/d) ratios in the range 3.6 < (a/d)

< 4.8.

18

Chapter 3

Mechanical Behavior and

Finite Element Modeling

of Materials

19

Chapter 3

Mechanical Behavior and Finite Element Modeling of Materials

3.1 Introduction

Finite element method is a numerical procedure for finding estimated solutions to

boundary element problems for partial differential equations, which incorporates for

connecting numerous simple element equation over a large domain. Furthermore, it

subdivides the whole problem into smaller and simple parts called finite elements.

Nowadays, finite element analysis is an important tool for studying the structural

response of concrete. Experiments are the most accurate method to study the behavior

of reinforced concrete members, but it is expensive and cannot be counted on to give

all the information needed.

In recent years many finite element analysis packages has been developed, one of these

packages is ABAQUS\CAE, which is used in this study. ABAQUS/CAE is a software

tool for analysis a wide variety of finite element models, is divided in to different

modules: part, property, assembly, step, interaction, mesh, job and visualization for

defining geometry and material properties, applying boundary conditions and load,

generating mesh and analysis the model.(Systèmes 2014)

In this chapter, a finite element analysis of reinforced concrete beams using embedded

steel trusses has been performed to develop models based on the experimental results.

The models were created using ABAQUS/CAE. Three categories of beam are

considered in this research and the test data is taken from the experiment conducted by

Zhang, Fu et al. (2016).

3.2 Crack models for concrete

According to Bazant and Planas (1998), concrete cracking may be modelled using

discrete crack models, smeared crack models or concrete damage plasticity models. The

following sections present further details of these models.

3.2.1 Discrete crack model

In this approach, the crack is treated as a geometrical entity. This method implies a

continuous change in nodal connectivity, which consider serious drawback of the

approach, due to the nature of the finite element displacement method. The other

drawback of this approach that, the crack is constrained to follow a predefined path

20

along the element edges. It means that, to decide where and how the cracks may arise

a great amount of work is required, (ACI 2004).

3.2.2 Smeared crack models

The smeared crack concept is the counterpart of the discrete crack concept. In this

approach a cracked solid is imagined to be a continuum. Accordingly, the cracked

material can be described with a stress-strain relation. As this means that, the smeared

crack approach is a more attractive procedure than the discrete crack approach, because

it does not impose restrictions with respect to the orientation of the crack planes.

According to Rots and Blaauwendraad (1989), the smeared crack models can be

subdivided into fixed and rotating smeared crack. In the first kind of model, the

orientation of the crack is fixed during the entire computational process, whereas in the

second kind of model the orientation of the crack can rotate with the axes of principal

strain. The smeared crack model is most effective for use with concrete shell elements,

so that will not be used for this model.

3.2.3 Concrete Damage Plasticity (CDP)

According to the hypothesis of Drucker and Prager (1952), failure is determined by

non-dilatational strain energy and the boundary surface. The shape of energy and the

boundary surface in the stress space assumed to be the shape of a cone. The advantage

of this assumption is no complication in numerical applications due to surface

smoothness.

1 Figure (3.1): Drucker–Prager boundary surface (Drucker and Prager 1952)

21

Concrete damage plasticity model available in ABAQUS software is a modification of

Drucker–Prager hypothesis. According to the modification, the failure surface is

governed by parametric Kc, (Systèmes 2014).

Parametric Kc is a ratio of distances between the hydrostatic axis and the compression

and the tension meridian respectively in the deviatoric cross section. This ratio is always

higher than 0.5 and less than 1. The CDP model recommends to assume Kc = 2/3,

(Systèmes 2014).

Experimental results show that, the shapes of the plane’s meridians are curved. On the

other hand, CDP model assumes the plastic potential surface in the meridional plane is

formed of a hyperbola, so that the shape is adjusted through eccentricity. Parameter

eccentricity can be calculated as a ratio of tensile strength to compressive strength

(Kmiecik and Kamiński 2011). The CDP model recommends to assume eccentricity =

0.1, (Systèmes 2014).

Another parameter describing the state of the material is a ratio of the strength in the

biaxial state to the strength in the uniaxial state. The recommended value by Systèmes

(2014) for this ratio is 1.12. The last parameter describing the performance of concrete

under compound stress is dilation angle. In modeling dilation angle = 31 degree

recommended by (Systèmes 2014).

Figure (3.22): Concrete damage plasticity deviatoric plane (Systèmes 2014)

22

In this study, concrete damaged plasticity method was used to simulate the concrete

behavior. This method was used by (Salh 2014, Yosef Nezhad Arya 2015), and showed

well agreement with experimental results.

3.3 FE modeling of reinforcement

There are three approaches to model steel reinforcement in finite element models for

reinforcement concrete: the discrete model, the smeared model, and the embedded

model, (Tavárez 2001).

The reinforcement in the discrete model is connected to the nodes of the concrete mesh.

Therefore, the concrete will share same nodes and the steel meshed and the concrete

and the reinforcement will occupy the same regions. This approach suffers from the

drawback that the location of reinforcement restricts the mesh of the concrete and the

steel volume is not deducted from the volume of concrete. The smeared model assumes

that the reinforcement is uniformly distributed in the concrete element in defined region

of the finite element mesh.

In the embedded model the displacement of the reinforcement steel is compatible with

the surrounding concrete element. In this approach the restriction of the concrete mesh

is overcome because the stiffness of the reinforcement steel is evaluated separately from

the concrete. The embedded model, models reinforced steel efficiently specially, when

the reinforcement is complex, but it increases the run time and computational cost due

to the increasing of the number of nodes and the degree of freedom.

In this study, the embedded method has been used to model the reinforcement in the

reinforced concrete beams. (Salh 2014, Yosef Nezhad Arya 2015) applied this method

to model the reinforced steel and gave acceptable results compared to the experimental

evidence.

3.4 Modeling of the embedded truss - concrete interface

There are two models which deal with the case of reinforced concrete beams with

embedded steel truss. The first one provides a simplified modeling of the concrete-truss

elements interaction by tying the nodes of the two surfaces in contact; the second one

provides the insertion of cohesive contact elements between the truss elements and the

surrounding concrete. The simplified approach, which is used in this study is very easy

to apply in practice and generates a constraint between the nodes and the meshes of the

23

elements that rigidly connected each other. (Monaco 2016, Ballarini, La Mendola et al.

2017) used this method to model the reinforced steel and gave acceptable results

compared to the experimental evidence.

3.5 Element Types ABAQUS provides an extensive element library that helps efficiently to solve different

problems. Each element in ABAQUS has a unique name, such as B22, B23H, SC6R,

or C3D8R.

3.5.1 Concrete

To model the concrete in 3D models, an eight node linear brick, reduced integration

element which called C3D8R was used. This element has 8-nodes with three degree of

freedom at each node. These elements can predict cracking, plastic deformation and

crushing.

3.5.2 Reinforcement

The reinforcement bars were modelled by using 3D beam element. A 2-node beam

element in three-dimensional with linear interpolation formulations which called B31

was used. The steel bars were embedded into the concrete element, so that no interface

element was needed and perfect bond between concrete and reinforcement was

assumed.

3.5.3 Embedded truss elements

To model the elements of the embedded truss in 3D models, the simplest element type

C3D8R was used to develop favorite convergence and to reduce the computational

times. Monaco (2016) used this element to model truss elements, and showed well

agreement with experimental results.

3.6 Material Properties

3.6.1 Concrete

The ABAQUS program requires the uniaxial stress-strain relationship of concrete in

tension and compression in order to be able to model concrete. In this study for concrete

under compression a relationship proposed by Kabaila, Saenz et al. (1964) was adopted

as shown in equation (3.1). See Figure (3.3) for compression hardening relationship for

RC beam models.

(3.1)

24

In which δ is the compressive stress and δp is the experimentally determined maximum

compressive stress (41 MPa), ε is the strain and εp is the corresponding strain (0.0035),

and α is an experimentally determined coefficient representing the elastic modulus of

the concrete.

Figure (3.3): Compression hardening relationship for RC beam models 3

For concrete under uniaxial tension, the tension softening curve of Hordijk (1991) was

used as follows:

Where fc' = 41 MPa, ft = 4 MPa, wt and wcr are respectively the crack opening

displacement and the crack opening displacement at the complete release of stress, GF

is the required fracture energy, and C1=3 and C2=6.93 are constants obtained from

tensile test of concrete. In equation (3.4) da is the maximum aggregate size and it was

assumed to be 20 mm. See Figure (3.4) for tension stiffening (displacement) for RC

beam models.

0

5

10

15

20

25

30

35

40

45

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004

Stre

ss M

pa

Strain

Compression Hardening

(3.3)

(3.4)

(3.2)

25

3.6.2 Reinforcement

An elastic-plastic constitutive relationship with strain hardening is assumed for

reinforcing steel and embedded steel truss. This model generally yields acceptable

results for the response prediction of RC members, (Neale, Ebead et al. 2005, Khan,

Al-Osta et al. 2017). According to Bǎzant (1982), the Poisson’s ratio was assumed to

be 0.3, and the elastic modulus was assumed to be 200 GPa.

3.7 Geometry

Three models are built to simulate the beam specimens as show in Figures (3.5) to (3.8).

The concrete part and truss part are done as 3D deformable solid elements, but the

reinforcement steel part is done as a two-node linear 3D truss element, then all parts are

merged together in the assembly module. The bond between the embedded truss

elements and the surrounding concrete was considered as perfect bond. Therefore, the

embedded option was used in defining the truss elements inside the host element which

was the concrete beam.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.05 0.1 0.15 0.2 0.25

Stre

ss M

pa

Displacement (mm)

TensionStiffening

4 Figure (3.4): Tension stiffening (displacement) for RC beam models

26

Figure (3.5): 3-D View of the RC beam modeled in ABAQUS 5

Figure (3.6): 3-D View of the embedded conventional steel reinforcement modeled in ABAQUS6

27

Figure (3.7): 3-D View of the embedded flat plate steel truss modeled in ABAQUS7

Figure (3.8): 3-D View of the embedded steel angle truss modeled in ABAQUS8

28

3.8 Meshing

Study of the mesh convergence is very important to determine a suitable mesh density.

ABAQUS/CAE provides different meshing techniques. In this study, for plain concrete

structured mesh is selected, and for the embedded truss multiple meshed are selected.

The mesh element for concrete and embedded truss is three-dimensional solid, which

called C3D8R. A 2-node beam element in three-dimensional with linear interpolation

formulations B31 is used for the rebar elements. According to Systèmes (2014) the best

size of the mesh range from 10% to 15% of the depth, so 40 mm element size had been

used in this model as shown in Figures (3.9) to (3.11).

Figure (3.9): 3-D View of the concrete meshed model of RC beam. 9

Figure (3.10): Meshed model of the embedded flat plate steel truss. 10

29

3.9 Number of Load Increments

The number of load increment may have a major effect on the accuracy of the results.

The structural response at each increment can be calculated by ABAQUS through

dividing the applied load into smaller increments. The increments characteristics are

specified in Step Module. ABAQUS analysis may miss key events in the response if

the increment is too large, such as the beginning of yielding in a member. However,

selecting a smaller step-size also leads to a larger computational expense, due to more

increments being calculated. The large number of increments also leads to larger post-

process files and accompanying post-process times. For the ABAQUS analyses

developed for this study, load increment size was chosen by trial and error to get an

accurate solution with reasonable computation time.

3.10 Description of the adopted study

To verify the finite element models, the test data from the experimental program

conducted by Zhang, Fu et al. (2016) was used. In this experiment, five full-scale beam

specimens were tested, named SRCB-1 to 5. These specimens (1800 mm long and 300

mm high) were designed according to ACI318-14. The specimens had a rectangular

cross section of 200 mm x 300 mm. The specimens had three steel bars with 22 mm

11 Figure (3.11): Meshed model of the embedded steel angle truss.

30

diameter in the bottom and two steel bars with 16 mm diameter in the top of the beam

for longitudinal reinforcement. The stirrups consisted of 8 mm diameter bars spaced at

150 mm were used for shear reinforcement in SRCB-1 and SRCB-3-5 and spaced at 75

mm in SRCB-2.

SRCB-1 and SRCB-2 were the control beams, Figure (3.12). SRCB-3 was a reinforced

concrete beam with embedded longitudinal angle steel and vertical flat steel as the

strengthening steel skeletons, Figure (3.13). SRCB-4 and SRCB-5 were the reinforced

concrete beams with an embedded longitudinal angle steel and diagonal angle steel as

the strengthening steel skeletons, but SRCB-5 had additional horizontal web

reinforcements, Figure (3.14). The material properties are listed in Table (3.1) and (3.2),

and the outline of the tested specimens is listed in Table (3.3).

Figure (3.12): Profile and cross section detail of SRCB-1 and SRCB-2 (Zhang, Fu et al. 2016)

13 Figure(3.13): Profile and cross section detail of SRCB-3 (Zhang, Fu et al. 2016)

31

Type of steel

Diameter,

thickness, (mm)

Yield strength

(MPa)

Ultimate strength

(MPa)

Modulus of

elasticity (GPa)

Reinforcement ɸ 8 363 465 210



Reinforcement ɸ22 393 557 200

Flat steel 30×4 266 363 200

Steel angle 40×40×4 345 519 200

Steel angle 30×30×3 348 522 200

Test specimen SRCB-1 SRCB-2 SRCB-3 SRCB-4 SRCB-5

Shear span to depth ratio (a/d) 1.4 1.4 1.5 1.5 1.5

Type of loading

Two Point

Loads

Two Point

Loads

Two Point

Loads

Two Point

Loads

Two Point

Loads

Figure (3.14) : Profile and cross section detail of SRCB-4 (Zhang, Fu et al. 2016)

Table (3.1): Material properties of steel (Zhang, Fu et al. 2016)

Table (3.2): Material properties of concrete (Zhang, Fu et al. 2016)

Table (3.3): Descriptions of tested specimens (Zhang, Fu et al. 2016)

32

3.11 Summary

This chapter provided an overview of the modeling techniques that are used to analyze

the mechanical behavior of RC beams with embedded steel truss. The analyses were

conducted using the finite element computer program ABAQUS.

The concrete was modelled using a plastic damage model. The embedded steel

reinforcement model has been used to simulate the reinforced steel and embedded truss.

This method of modelling the steel reinforcement solves the mesh restriction problem

that appears in discrete and smeared modelling of reinforcement, by evaluation of

stiffness of reinforcement elements separately from the concrete elements. This method

provides a perfect bond between the host element (concrete) and the slave element (steel

rebar and embedded truss). Moreover, in this method, the displacement of steel bars

and embedded truss will be compatible with the displacement of the surrounding

concrete elements.

A brief discussion was provided to issues related to the selection of mesh size and load

increment size that effected the accuracy of the solution.

Test specimen

SRCB-1 SRCB-2 SRCB-3 SRCB-4 SRCB-5

Compressive strength (MPa)

41.54 41.73 44.11 40.41 42.36

Modulus of elasticity (GPa)

34.11 34.10 34.56 33.72 34.13

33

Chapter 4 Verification of Finite Element Models and

Parametric Study

34

Chapter 4 Verification of Finite Element Models

and Parametric Study

4.1 Introduction

In this chapter, the developed finite element models were verified by comparing results

obtained from the FE analysis with results obtained from the adopted experimental

tests. The verification process was based on the following criteria: load – mid span

deflection curves, strain curves, and loads and deflection at failure. Having the finite

element model validated, a parametric study was performed using the verified model to

evaluate the effect of the following parameters on the behavior of strengthened beams:

shear-span to depth ratios, shear reinforcement, truss shape, and longitudinal

reinforcement.

4.2 RC beam with conventional reinforcement

Results of RC beams models with conventional reinforcement showed that, the load at

failure is 350 kN and the corresponding deflection is 5.6 mm. The deflected shape at

failure for the beam is shown in Figure (4.1)

A comparison of the load-deflection response between the FEM and the test results for

the RC beam with conventional reinforcement is shown in Figure (4.2). The failure load

predicted by FE model is 3% higher than that obtained from the test results, the mid-

span deflection at failure which predicted by FE analysis is 7% less than the mid-span

deflection obtained from the experimental results.

Figure (4.1): Deflected shape for RC beam with conventional reinforcement. 15

35

.

The crack pattern at failure load is shown in Figure (4.3). When applied loads increase,

diagonal tensile cracks appear. Then continued to develop and propagate toward the

loading point until the failure. Zhang, Fu et al. (2016) mentioned that the mode of

failure of RC beam with conventional reinforcement is shear tension failure, which

agrees very well with that obtained from the finite element model at the failure load as

shown in Figure (4.3).

Figure (4.3): crack pattern at failure for RC beam with conventional reinforcement 17

Figure (4.2) : load-deflection curve RC beam with conventional reinforcement 16

0

50

100

150

200

250

300

350

400

0 1 2 3 4 5 6 7 8

Load

(kN

)

Deflection (mm)

FE results

EXP results

36

4.3 RC beam with flat plate steel embedded truss

Results of RC beams models with flat plate steel embedded truss indicated that, the load

at failure is 465 kN and the corresponding deflection is 4.6 mm. The deflected shape at



RC beam with flat plate embedded truss is shown in Figure (4.5). The failure load

predicted by FE model is 4% less than that obtained from the test results, the mid-span

deflection at failure which predicted by FE analysis is 6% less than the mid-span

deflection obtained from the experimental results.

Figure (4.4): Deflected shape for RC beam with flat plate steel embedded truss 18

0 1 2 3 4 5 6 7

0

100

200

300

400

500

600

Deflection (mm)

Load

(kN

)

FE results

EXP results

Figure (4.5): load-deflection curve for RC beam with flat plate embedded truss 19

37

The crack pattern at failure load is shown in Figure (4.6). The beam failed in the shear-

flexural mode. It is obvious that the first cracks appear near the mid span and continued

to develop toward to the mid height of the beam. These cracks were followed by

diagonal shear cracks near the support. Diagonal shear cracks continued to develop and

propagate toward the loading point until the failure. Zhang, Fu et al. (2016) mentioned

that the mode of failure of RC beam with flat plate steel embedded truss is shear-

flexural failure, which agrees very well with that obtained from the finite element model

at the failure load as shown in figure (4.6).

4.4 RC beam with steel angle embedded truss

Results of RC beams models with steel angle embedded truss revealed that, the load at

failure is 510 kN and the corresponding deflection is 5.2 mm. The deflected shape at


Figure (4.6): crack pattern at failure for RC beam with flat plate steel embedded truss 20

Figure (4.7): Deflected shape for RC beam with steel angle embedded truss 21

38


RC beam with steel angle truss is shown in Figure (4.8). The failure load predicted by

FE analysis is 2% higher than the failure load obtained from the experimental results,

the mid-span deflection at failure which predicted by FE analysis is 8% less than the

mid-span deflection obtained from the experimental results.

As shown in Figure (3.14) in chapter (3) for RC beam with steel angle embedded truss,

two strain gauges are installed on the rod of steel truss, the comparison between strain

curves (strain gauge1 and strain gauge 2) are shown in Figures (4.9) and (4.10). These

figures indicated that the strain curves obtained from the finite element analysis agrees

well with the experimental data for the RC beam reinforced with embedded steel truss.

0 500 1000 1500 2000 2500 3000

0

100

200

300

400

500

600

700

Microstrain

Load

s (k

N)

FE results

Exp results

Figure (4.9): Strain curve (strain gauge 1) of steel truss rod. 23

Figure (4.8): load-deflection curve for RC beam with steel angle embedded truss 22

0

100

200

300

400

500

600

700

0 2 4 6 8 10 12 14

Load

(kN

)

Deflection (mm)

FE Resluts

EXP Results

39

The crack pattern at failure load is shown in Figure (4.11). When applied loads increase,

flexural cracks appear near the mid span and continue to develop toward to the mid

height of the beam. Then, diagonal shear cracks appear and continue to develop and

propagate toward the loading point until the failure. Zhang, Fu et al. (2016) mentioned

that the mode of failure of RC beam with steel angle embedded truss is shear-flexural

failure, which agrees very well with that obtained from the finite element model at the

failure load as shown in figure (4.11).

Figure (4.11): crack pattern at failure for RC beam with steel angle embedded truss 25

0 500 1000 1500 2000 2500 3000

0

100

200

300

400

500

600

Microstrain

Load

s (k

N)

FE results

Exp results

Figure (4.10): Strain curve (strain gauge 2) of steel truss rod.24

40

4.5 Parametric Study

As seen in the previous section, the developed FE models for the RC beam with

conventional reinforcement, RC beam with flat plate embedded truss and RC beam with

steel angle truss embedded truss are able to predict the failure loads and the failure

modes very closely to what were observed in the experiments. According to

experimental and finite element analysis results, the steel angle truss is the optimum

layout with respect to the plate steel truss when embedded in concrete, therefore, a

parametric study was performed to evaluate the effect of different parameters on RC

beam with steel angle embedded truss as explained in the following sections.

4.6 Effect of Shear Span-To-Depth Ratios (a/d)

To evaluate the effect of (a/d) ratio on the behavior of reinforced concrete beam with

embedded steel truss, fourteen beams model with different (a/d) ranged from 1 to 2.5

were analyzed using the verified FE model. The different (a/d) ratios were attained by

changing the distance between the loading points as shown in Figure (4.12).

4.6.1Failure loads and Load-Deflection Response

Table (4.1) shows the ultimate failure load for RC beams with conventional

reinforcement and RC beams with embedded steel truss. A comparison between two

beams typologies shows that, all RC beams with embedded steel truss showed a

significant increase in failure loads. For all RC with conventional reinforcement with

Figure (4.12): Shear span to depth ratio (a/d) 26

41

different (a/d) ratios, a fixed reinforced steel content of 2.12 was used, while the steel

content of 3.25 was used in all RC beams with embedded steel trusses.

Table (4.1): Ultimate failure loads for RC beams with conventional reinforcement and RC beams with embedded steel truss 4

(a/d) RC beams with

conventional reinforcement (kN)

RC beams with embedded steel

truss (kN) Percentage increased (%)

1 480 780 62.5%

1.25 420 650 54.7%

1.5 365 550 50.6%

1.75 300 475 58.3%

2 270 400 48.1%

2.25 235 365 55.3%

2.5 217 340 56.6%

It is clear form table (4.1) that, the ultimate failure load decreases with the increase in

the (a/d) ratios. The increase in ultimate failure load is much noticeable for lower (a/d)

ratios. The increase in the failure load for RC beams with conventional reinforcement

and RC beams with embedded steel truss is respectively about 129% and 121% when

the (a/d) ratios decreased from 2.5 to 1. It can be concluded that, the rate of increasing

in the ultimate load is almost constant with the increase in the (a/d) ratios for RC beams

with conventional reinforcement and RC beams with embedded steel truss.

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7

Load

s (k

N)

Deflection (mm)

(a/d)=1

(a/d)=1.25

(a/d)=1.5

(a/d)=1.75

(a/d)=2

(a/d)=2.25

(a/d)=2.5

Figure (4.13): load-deflection relationship for RC beams with embedded steel truss at different (a/d) 27

42

Figure (4.13) shows the deflection of RC beams with embedded steel truss at different

(a/d) ratios. It can be seen that increasing of the (a/d) ratios increases the beam

maximum mid-span deflection. RC beams with embedded steel truss at (a/d) ratio = 1,

shows maximum load at failure and maximum central deflection value.

4.6.1.1 Von Mises Stress of embedded steel truss at failure load

Von Mises Stress was used to describe the distribution of stress, and color in each mesh

showed the stress value. The stress increase is obtained when color turns from blue to

red, and the von Mises Stress values can be obtained. The Von Mises Stress of

embedded steel truss was shown in Figure (4.14). The maximum Von Mises Stress, 348

MPa appears in the bottom of the central region of the embedded steel truss, around the

supports and around the applying loads. The stress increased from 217 MPa to 295 MPa

at the diagonal steel angles.

4.6.1.2 Comparison between numerical and analytical models

To verify the numerical results, the ultimate shear strength of RC beams with

conventional reinforcement and RC beams with embedded steel trusses was calculated

using equations (4.1) to (4.5) which were derived by Zhang, Fu et al. (2016).

V� = ∑ ��∑ ��

��

�−

∑ ��

��

� =��±√��

��

� = �∑ ��

��

�� − (��)�

� = ��

� ∑ ��

�−

(∑ ��∑ ��∑ ��)∑ ��

��

��

��

��

(4.1)

(4.2)

(4.3)

(4.4)

Figure (4.14): Von Mises Stress of embedded steel truss at failure load 28

43

� =�∑ ��∑ ��∑ ��

��

��

�

��

Where ∑Tsi is the total ultimate tensile forces of longitudinal reinforcement and angle

steel; ∑Tvi is the total ultimate tensile forces of vertical stirrups and vertical component

of steel angle; hsi are the distances from the top fibers of the beam to the centroidal

position of longitudinal reinforcements and angle steel; dvi are the distances from the

loading point to the centroidal position of vertical stirrups and vertical component of

angle steel; a is the shear span of the beam; b is the width of the beam; Vu is the ultimate

shear-flexural strength of the reinforcement concrete beam; υ is the softened coefficient

of compressive strength of concrete; and x is the equivalent compressive depth of the

beam in the shear compression zone.

Comparison between the calculated and numerical ultimate load carrying capacity of

RC beams are presented in Table (4.2). It is clear that, the numerical results agree well

as compared with the analytical results.

Table (4.2): Comparison between the calculated and numerical ultimate load carrying capacity of RC beams 5

a/d

FEM results Calculated results

Control Beams, (kN)

Beams with embedded truss

reinf. (kN)

Control Beams, (kN)

Beams with embedded truss

reinf. (kN)

1 480 780 475.856 745.504

1.25 420 650 406.451 612.906

1.5 365 550 354.116 522.201

1.75 300 475 285.426 448.535

2 270 400 251.076 391.775

2.25 235 365 223.902 347.024

2.5 217 340 201.906 311.018

(4.5)

44

4.6.2 Crack pattern and failure modes

The following sections explained the crack pattern and the modes of failure for RC

beams with conventional reinforcement and RC beams with embedded steel angle truss

at deferent (a/d) ratios ranged from 1 to 2.5.

4.6.2.1 RC beams with conventional reinforcement

For the beams with conventional reinforcement and having (a/d) ratios between 1 and

2 the crack pattern is similar as shown in Figure 4.15 to 4.19. The beams failed in shear

failure mode. For these beams diagonal shear cracks appears near to supports when the

applied load increases. As the load increased, the diagonal cracks developed further up

to the critical failure of the beams. For beams with (a/d) = 2, few

hairline flexural cracks were observed.

Figure (4.15): crack pattern at failure for RC beam with conventional reinforcement at (a/d) = 1 29

Figure (4.16): crack pattern at failure for RC beam with conventional reinforcement at (a/d) = 1.25 30

45



Figure (4.19): crack pattern at failure for RC beam with conventional reinforcement at (a/d) = 2 33

46

For the beams with (a/d) ratios 2.25 and 2.5, the beams failed in shear - flexural and

flexural modes respectively as shown in Figure 4.20 and 4.21. For thes beams vertical

cracks appear in the mid span region between the two point loads when the applied load

increases. As the load increased, the flexural cracks developed further up to the critical

failure of the beams. Flexural failure of these two beams may be occurred due to the

distance between the two loading points, this distance is less than one third clear span,

according to ASTM (2010) this test can be considered as flexural test.

.

4.6.2.2 RC beams with embedded steel truss

For the RC beams with embedded steel truss and having (a/d) ratios between 1.25 and

2.25, flexural cracks were formed in the bottom of the central region of the beam and

continued to develop and elongate toward the mid height of the beams. Then diagonal

shear cracks began to form in the critical shear span regions followed by the appearance



47

of the main diagonal cracks. Flexural cracks kept their length and width until failure.

This beams failed in shear-flexural mode as shown in Figure 4.22 to 4.26

Figure (4.22): crack pattern at failure for RC beam with embedded steel truss at (a/d) = 1.25 36

Figure(4.23): crack pattern at failure for RC beam with embedded steel truss at (a/d) = 1.5 37

Figure (4.24): crack pattern at failure for RC beam with embedded steel truss at (a/d) = 1.7538

48

For the beam with (a/d) ratio = 1, the RC beam failed in shear mode as shown in Figure

4.27. It is clear that from the Figure, when applied loads increase few hairline vertical

cracks appears. As the load increased diagonal shear cracks appears near to supports

and developed further up to the critical failure of the beam.

Figure (4.25): crack pattern at failure for RC beam with embedded steel truss at (a/d) = 239


Figure (4.27): crack pattern at failure for RC beam with embedded steel truss at (a/d) = 1 41

49

For the beam with (a/d) ratio = 2.5, the RC beam failed in flexural mode as shown in

Figure 4.28. It is clear that from the Figure when applied loads increase flexural cracks

appears. As the load increased the flexural cracks developed further up to the critical

failure of the beam. Hairline diagonal cracks were observed before failure.

4.7 Effect of shear reinforcement

RC beams with embedded steel truss had stirrups consisted of 8 mm diameter bars

spaced at 150 mm as shown in Figure (3.6) in chapter (3). To evaluate the effect of

shear reinforcement (stirrups) on the behavior of RC beam with embedded steel truss,

seven reinforced concrete beams using embedded steel truss without stirrups model

with different (a/d) ratios ranged from 1 to 2.5 were analyzed using the verified FE

model.

4.7.1 Failure loads and Load-Deflection Response

Table (4.3) shows the comparison of ultimate loads carrying capacity of RC beams

using embedded steel truss with and without shear reinforcement (stirrups). As seen

from the table, web reinforcements (stirrups) have a small effect on the ultimate loads

carrying capacity of RC beams using embedded steel truss.


50

Table (4.3): Comparison of ultimate loads carrying capacity of HSTC beams with and without shear reinforcement (stirrups) 6

a/d RC beams using

embedded steel truss with stirrups, (kN)

RC beams using embedded steel truss without stirrups, (kN)

% of Reduction

1 780 720 7.7

1.25 650 585 10.0

1.5 550 498 9.5

1.75 475 425 10.5

2 400 380 5.0

2.25 365 342 6.3

2.5 340 310 7.3

From the Table (4.3) it is clear that, for (a/d) ratios between 1 and 2 the failure load

decrease significantly when (a/d) ratio decrease. For (a/d) ratios between 2 and 2.5 the

reduction rate in failure load is minimal. Figure (4.29) shows a variation of the failure

loads with different (a/d) ratios predicted by the FE models. It is cleared from the plot

that the failure loads decreases with the increase in the (a/d) ratios. The increase in

failure loads is much perceptible for lower (a/d) ratios.

Figure (4.29): load-deflection relationship for RC beams using embedded steel angle

truss without stirrups 43

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7

Load

s (k

N)

Deflection (mm)

a/d=1

a/d=1.25

a/d =1.5

a/d=1.75

a/d=2

a/d=2.25

a/d=2.5

51


Figure 4.30 to 4.36 shows the crake pattern for RC beams using embedded steel truss

without shear reinforcement. It can be concluded that, RC beams using embedded steel

truss without shear reinforcement had almost the same behavior and failure pattern of

the RC beams with embedded steel truss and with shear reinforcement at different (a/d)

ratios.

Figure (4.30): crack pattern at failure for the beam using embedded steel truss without stirrups at (a/d) =1 44

Figure (4.31): crack pattern at failure for the beam using embedded steel truss without stirrups at (a/d) =1.25 45

52


Figure (4.34): crack pattern at failure for the beam using embedded steel truss without stirrups at (a/d) =2 48 49

Figure (4.33): crack pattern at failure for the beam using embedded steel truss without stirrups at (a/d) =1.7547

53

4.8 Effect of longitudinal reinforcement

To evaluate the effect of longitudinal reinforcement on the behavior of reinforced

concrete beam with embedded steel truss, longitudinal reinforcement ratio was reduced

in the verified FE model. Three steel bars with 16 mm diameter were used instead of

three steel bars with 22 mm diameter in the bottom of the verified simulated beam to

get the same longitudinal reinforcement ratio of the control beam.


A comparison of failure load with the decrease in the longitudinal reinforcement ratio

for RC beam using embedded steel angle truss presented graphically in Figure (4.37).

As seen from the figure, RC beam using embedded steel truss with the decrease in the

longitudinal reinforcement ratio did not show a significant increase in failure load

compared to the RC beam with conventional reinforcement.

Figure (4.35): crack pattern at failure for the beam using embedded steel truss without stirrups at (a/d)=2.25 50


54

It can be seen from the Figure (4.37), the failure load obtained by FEA is 380 kN, and

the mid span deflection at failure is 5.5 mm. Compared to the RC beam with embedded

steel truss, reduction of the longitudinal reinforcement ratio, showed a significant

decrease in failure load. As seen in Figure (4.38) the failure load obtained from FEA is

decreased for 510 kN to 380 kN.

0 1 2 3 4 5 6 7

0

50

100

150

200

250

300

350

400

Defection (mm)

Load

(kN

)

RC beam using embedded steeltruss with reduction in thelong. reinf. ratioRC beam wiith conventionalreinf.

Figure (4.37): load-deflection relationship for RC beam using embedded steel truss with reduction in the long. reinf. Ratio and RC beam with conventional reinf.52

0 1 2 3 4 5 6 7

0

100

200

300

400

500

600

Deflection (mm)

Load

(kN

)

RC beam with embeddedsteel truss without reductionlong. Reinf. ratioRC beam with embeddedsteel truss with reductionlong. Reinf. ratio

Figure (4.38): load-deflection relationship for RC beams using embedded steel truss with and without reduction in the long. reinf. ratio 53

55


Compared to RC beam with conventional reinforcement, embedded steel truss

improves the mode of failure at the same longitudinal reinforcement ratio. As seen in

Figure (4.39) RC beam using embedded steel truss with the reduced in the longitudinal

reinforcement ratio failed in shear flexural mode, whereas RC beam with conventional

reinforcement failed in shear tension mode at the same longitudinal reinforcement ratio.

4.9 Effect of shape of the embedded steel truss

To evaluate the effect of shape of the embedded truss, diagonal steel angles were used

in critical shear span of the verified simulated beam as shown in Figure (4.40).

Figure (4.40): embedded steel truss with diagonal steel angles in critical shear span only 55

Figure (4.39): crack pattern at failure for RC beams using embedded steel angle truss with reduction in the longitudinal reinforcement ratio 54

56


Compared to RC beam with conventional reinforcement, using embedded steel truss

with diagonal angle steel in critical shear span only, showed a significant increase in

failure load as seen in Figure (4.41). It is clear that, using embedded steel truss with

diagonal angle steel in critical shear span only increased failure load from 350 kN to

465 kN, that mean the failure load increased by 30%.

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

deflection (mm)

Load

(kN

)

RC beam with embeddedsteel truss (diagonal steelangles in shear span only)RC beam with conventionalreinforcement

Figure (4.41): load-deflection relationship for RC beam using embedded steel truss with diagonal steel angles in critical shear span only and RC beam with conventional reinf. 56

0 2 4 6 8 10 12 14

0

100

200

300

400

500

600

700

Deflection (mm)

Load

(kN

)

RC beam with embeddedsteel truss

RC beam with embeddedstee truss (diagonal steelin shear span only)

Figure (4.42): load-deflection relationship for RC beam using embedded steel truss and RC beam using embedded steel truss with diagonal steel angles in critical shear span only

57

Compared to RC beam with embedded steel truss in full span length, using embedded

steel truss with diagonal angle steel in critical shear span only did not show a significant

decrease in failure load as seen in Figure (4.42). It is clear from the figure that, using

embedded steel truss with diagonal angle steel in critical shear span only decreased

failure load from 510 kN to 465 kN, that mean the failure load decreased by 9% only.


Compared to the RC beam with conventional reinforcement, using embedded steel truss

with diagonal angle steel in critical shear span only, showed an improvement in beam

ductility and mode of failure.

As seen in Figure (4.43) using embedded steel truss with diagonal steel angles in critical

shear span only failed in shear flexural mode, while the RC beam with conventional

reinforcement failed in shear tension mode at the same longitudinal reinforcement ratio.

For RC beams with embedded steel angle truss, if diagonal steel angles were used in

the critical shear span only or in full span, we can get the same mode of failure. In both

cases, the beams failed in shear flexural mode. 4.10 Summary

In this chapter, the developed finite element models were verified by comparing the

results obtained from the FE analysis with results obtained from the adopted

experimental test. The FEM results agree will with the experiments regarding failure

mode and load capacity.

Figure (4.43): pattern of crack at failure for RC beam using embedded steel truss with diagonal steel angles in critical shear span only5 8

58

The validation models were used to investigate the influence of the shear span-to-depth

ratios, shear reinforcement, different shape of embedded truss and longitudinal

reinforcement. To verify the numerical results, a reference analytical model is

employed to calculate the ultimate shear strength of RC control beams and RC beams

with embedded steel trusses at different (a/d) ratios. The numerical results showed well

agree with the analytical results.

The analysis indicated that, using embedded steel truss enhanced the shear capacity and

improved the ductility of the RC beams. The analysis also indicated that the shear

capacity of reinforced concrete beams using embedded steel trusses is inversely

dependent on the shear span-to-depth ratio. It is also showed that the shear

reinforcement (stirrups) has almost small effect on shear capacity of reinforcement

concrete beams with embedded steel trusses.

The numerical results further demonstrated that longitudinal reinforcement have

significant effect on the shear capacity of reinforced concrete beams using embedded

steel trusses. It is also showed that reinforcement concrete beam using embedded steel

truss with diagonal angles steel in critical shear span only have almost the same failure

load and shear behavior of reinforcement concrete beam using embedded steel truss

with diagonal angles steel in full span.

59

Chapter 5

Conclusion and

Recommendations

60

Chapter 5 Conclusions and Recommendations

5.1 Introduction

The thesis investigated a non-linear analysis of RC beams with embedded steel trusses

using FE software ABAQUS. The FE models are initially built for the three simply-

supported beams with embedded steel trusses subjected to two-point load. The results

of the three beams are verified against the experimental results in terms of the load-

deflection response, the failure load and the mode of failure. The models are used to

perform a parametric study of the effect of the following parameters on the behavior of

strengthened beams: shear-span to depth ratios, shear reinforcement at different shear-

span to depth ratios, truss shape, and longitudinal reinforcement. In the following

sections, the important conclusions drawn from this study and research

recommendations are presented.

5.2 Conclusion

1. The ABAQUS FE models are able to analyze reinforcement concrete beams with

embedded steel trusses and predict the failure load and the mode of failure closely

as observed in the experimental tests.

2. The difference between the FEA results and experimental results are within 5%

range of accuracy in terms of failure load prediction while the concrete strain at mid-

span from the FEA is 8% lower than the test results.

3. The failure loads of all reinforcement concrete beams using embedded steel trusses

are higher when compared to RC beams with conventional reinforcement.

4. Using of embedded steel trusses improved reinforcement concrete beam ductility

and mode of failure.

5. Reinforcement concrete beam using embedded steel truss with shear-span to depth

ratio value 1 failed in shear mode. However, using embedded steel truss improves

the ductility of the beam.

6. All reinforced concrete beams using embedded steel trusses with shear-span to depth

ratio between 1.25 and 2.5 failed in shear flexural mode.

7. For different (a/d) ratios, all RC beams using embedded steel angle trusses showed

reduction in deflection compare with control beams.

61

8. The average increase in the ultimate failure loads for all the reinforcement concrete

beams using embedded steel trusses is 55% when compared to RC beam with

conventional reinforcement.

9. In general, the behavior of tested beams influenced by (a/d) ratio. It was found that

the increase of (a/d) ratio from 1 to 2.5 decrease the ultimate failure load for RC

beam with conventional reinforcement and RC beam with embedded steel angle

trusses beams by about 129% and 121% respectively.

10. The reduction rate of ultimate failure load is very small when the shear-span to

depth ratio between 2 and 2.5.

11. All RC beam with conventional reinforcement with (a/d) ratios between 1.25 and

2.5 failed in shear, while RC beams using embedded steel angle trusses at the same

(a/d) ratios failed by shear flexural mode.

12. For RC beams using embedded steel angle trusses with different (a/d) ratios, web

reinforcement have some effect on shear strength, whereas have almost no effect

on failure mode of the beams.

13. Reduced longitudinal reinforcement ratio for reinforcement concrete beams using

embedded steel trusses, decrease significantly the failure load.

14. Failure mode of reinforcement concrete beams using embedded steel trusses do not

affect by reduction of longitudinal reinforcement ratio.

15. Reinforcement concrete beam using embedded steel truss with diagonal steel

angles in critical shear span only have almost the same failure load and shear

behavior of reinforcement concrete beam using embedded steel truss with diagonal

steel angles in full span.

5.3 Recommendations

Based on the findings and conclusions of the current study, the following

recommendations are made for future research:

1. The effect of different factors such as size of the beam, use of different shapes

of embedded trusses, and concrete compressive and tensile strength on the shear

behavior of RC beams should be studied.

2. The performance of high strength concrete beams with embedded steel trusses

should be studied.

62

3. Shear behavior of reinforced concrete slender and deep beams using embedded steel

trusses should be studied.

63

The Reference List

64

The Reference List

Abdul-Zaher, A. S., et al. (2016). "Shear Behavior Of Fiber Reinforced Concrete Beams." Journal of Engineering Sciences 44(2): 132 – 144.

ACI, (2004). "440.3 R-04." Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structure, ACI, Farmington Hills, Michigan.

Adhikary, B. B. and H. Mutsuyoshi (2006). "Prediction of shear strength of steel fiber RC beams using neural networks." Construction and Building Materials 20(9): 801-811.

Alhamad, S., et al. (2017). "Effect of shear span-to-depth ratio on the shear behavior of BFRP-RC deep beams." MATEC Web Conf. 120: 01012.

ASTM, C. (2010). Standard test method for flexural strength of concrete (using simple beam with third-point loading). American Society for Testing Materials.

Angelakos, D., Bentz, E. C., & Collins, M. P. (2001). Effect of concrete strength and minimum stirrups on shear strength of large members. Structural Journal, 98(3), 291-300.

Ballarini, R., et al. (2017). "Computational Study of Failure of Hybrid Steel Trussed Concrete Beams." Journal of Structural Engineering 143(8): 04017060.

Bazant, Z. and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle structures, Boca Raton, FL: CRC Press.

Bhide, S. B., & Collins, M. P. (1989). Influence of axial tension on the shear capacity of reinforced concrete members. Structural Journal, 86(5), 570-581.

Campione, G., et al. (2016). "Analytical evaluation of steel–concrete composite trussed beam shear capacity." Materials and Structures 49(8): 3159-3176.

Cladera, A. and Marí, A. R. (2005). "Experimental study on high-strength concrete beams failing in shear." Engineering Structures 27(10): 1519-1527.

Colajanni, P., et al. (2017). "Analytical prediction of the shear connection capacity in composite steel–concrete trussed beams." Materials and Structures 50(1): 48.

Colajanni, P., et al. (2014). "Stress transfer mechanism investigation in hybrid steel trussed–concrete beams by push-out tests." Journal of Constructional Steel Research 95: 56-70.

Colajanni, P., et al. (2018). "Stress transfer and failure mechanisms in steel-concrete trussed beams: Experimental investigation on slab-thick and full-thick beams." Construction and Building Materials 161: 267-281.

Drucker, D. C. and Prager, W (1952). "Soil mechanics and plastic analysis or limit design." Quarterly of applied mathematics 10(2): 157-165.

Fenwick, R. C., & Pauley, T. (1968). Mechanism of shear resistance of concrete beams. Journal of the Structural Division, 94(10), 2325-2350.

65

Ghannoum, W. M. (1998). Size effect on shear strength of reinforced concrete beams, McGill University Montreal, QC, Canada.

Hamid, N. A. A., et al. (2016). Effect of longitudinal reinforcement ratio on shear capacity of concrete beams with GFRP bars. InCIEC 2015, Springer: 587-599.

Hordijk, P. (1991). "Local approach to fatigue of concrete." Doctoral Thesis, Delft University.

Hou, C., et al. (2017). "Shear Behavior Of Reinforced Concrete And Prestressed Concrete Tapered Beams Without Stirrups." Journal of JSCE 5(1): 170-189.

Hu, B. and Y.-F. Wu (2018). "Effect of shear span-to-depth ratio on shear strength components of RC beams." Engineering Structures 168: 770-783.

Jung-Yoon Lee, I.-J. C. and Sang-Woo, K. (2011). "Shear Behavior of Reinforced Concrete Beams with High-Strength Stirrups." Structural Journal 108(5).

Kabaila, A., et al. (1964). "Equation for the stress-strain curve of concrete." ACI Journal, Farmington Hills, ACI 61(3): 1227-1239.

Kani, G. N. J. (1966, June). Basic facts concerning shear failure. In Journal Proceedings (Vol. 63, No. 6, pp. 675-692).

Kareemi, M. A., et al. (2016). "Experimental Tests on Composite Steel-Concrete Truss Beams." Applied Mechanics & Materials 847.

Khan, U., et al. (2017). "Modeling shear behavior of reinforced concrete beams strengthened with externally bonded CFRP sheets." Structural Engineering and Mechanics 61(1): 125-142.

Kmiecik, P. and Kamiński, M. (2011). "Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration." Archives of civil and mechanical engineering 11(3): 623-636.

Kong, P. Y. (1996). Shear strength of high performance concrete beams, Curtin University.

Lee, J. Y., & Kim, U. Y. (2008). Effect of longitudinal tensile reinforcement ratio and shear span-depth ratio on minimum shear reinforcement in beams. ACI Structural Journal, 105(2), 134.

Li, A., et al. (2002). "Shear strengthening effect by bonded composite fabrics on RC beams." Composites Part B: Engineering 33(3): 225-239.

Lim, D. H. and Oh, B. H. (1999). "Experimental and theoretical investigation on the shear of steel fibre reinforced concrete beams." Engineering Structures 21(10): 937-944.

Michael, D. K. (1984). "Behavior of Reinforced Concrete Beams with a Shear Span to Depth Ratio Between 1.0 and 2.5." ACI Journal Proceedings 81(3).

Mikata, Y., et al. (2001). "Effect Of Prestress On Shear Capacity Of Prestressed Concrete Beams." Doboku Gakkai Ronbunshu 2001(669): 149-159.

66

Monaco, A. (2016). Numerical prediction of the shear response of semi-prefabricated steel-concrete trussed beams.

Monti, G. and Petrone, F. (2015). "Shear resisting mechanisms and capacity equations for composite truss beams." Journal of Structural Engineering 141(12).

Neale, K., et al. (2005). "Modelling of debonding phenomena in FRP-strengthened concrete beams and slabs." International Institute for FRP in Construction.

Perera, S. V. T. J. and Hiroshi, M. (2013). "Shear Behavior of Reinforced High-Strength Concrete Beams." Structural Journal 110(1).

Pham, H. B., et al. (2006). "Modelling of CFRP–concrete bond using smeared and discrete cracks." Composite Structures 75(1): 145-150.

Rahal, K. N. and Rumaih, H. A. (2011). "Tests on reinforced concrete beams strengthened in shear using near surface mounted CFRP and steel bars." Engineering Structures 33(1): 53-62.

Rots, J. G. and Blaauwendraad, J. (1989). "Crack models for concrete, discrete or smeared? Fixed, multi-directional or rotating?" HERON, 34 (1), 1989.

Saeed, J. A. and Abubaker A. M. (2016). "Shear Strength and Behavior of High Strength Reinforced Concrete Beams without Stirrups." Sulaimani Journal for Engineering Sciences 3(3): 64-74.

Salh, L. (2014). Analysis and behaviour of structural concrete reinforced with sustainable materials, University of Liverpool.

Samir A. Ashour, G. S. H. and F. W. Faisal (1992). "Shear Behavior of High-Strength Fiber Reinforced Concrete Beams." Structural Journal 89(2).

Shaaban, I. G. (2004). "Shear Behavior of High Strength Fiber Reinforced Concrete Beams Subjected to Axial Compression Forces." Ain Shams Scientific Bulletin 39(4): 91-117.

Shah, A. and Ahmad, S. (2008). "Effect of Longitudinal Steel, Shear Span to Depth Ratio on the Shear Strength of High Strength Concrete Beams." Mehran University Research Journal of Engineering and Technology 27(2): 171.

Bǎzant, Z. P. (1982). State-of-the-art report on finite element analysis of reinforced concrete, American Society of civil engineers.

Subramanian, N. (2013). Design Of Reinforced Concrete Structures. UK, Oxford University Press.

Systèmes, D. (2014). "Abaqus Analysis User’s Guide." Solid (Continuum) Elements 6.

T. Shioya, M. I. Y. N. H. A. and Okada, T. (1990). "Shear Strength of Large Reinforced Concrete Beams." Special Publication 118.

Tarek K. Hassan, and Paul, Z. (2008). "Shear Behavior of Large Concrete Beams Reinforced with High-Strength Steel." Structural Journal 105(2).

67

Tavárez, F. A. (2001). Simulation of behavior of composite grid reinforced concrete beams using explicit finite element methods, University of Wisconsin--Madison.

Tesser, L. and Scotta, R. (2013). "Flexural and shear capacity of composite steel truss and concrete beams with inferior precast concrete base." Engineering Structures 49: 135-145.

Thanasis, C. T. (1998). "Shear Strengthening of Reinforced Concrete Beams Using Epoxy-Bonded FRP Composites." Structural Journal 95(2).

Tullini, N. and Minghini, F. (2013). "Nonlinear analysis of composite beams with concrete-encased steel truss." Journal of Constructional Steel Research 91: 1-13.

Wright, J. K. and MacGregor J. G. (2012). Reinforced concrete : mechanics and design. Boston, Pearson.

Yaseen, S. A. (2016). "An Experimental Study on the Shear Strength of High-performance Reinforced Concrete Deep Beams without Stirrups." Engineering and Technology Journal 34(11 Part (A) Engineering): 2123-2139.

Yosef Nezhad Arya, N. (2015). Second-order FE Analysis of Axial Loaded Concrete Members According to Eurocode 2.

Yu, L., et al. (2011). Effect of beam depth and longitudinal reinforcement ratio on shear strength of RC beams. Advanced Materials Research, Trans Tech Publ.

Zhang, N., et al. (2016). "Experimental Studies of Reinforced Concrete Beams Using Embedded Steel Trusses." ACI Structural Journal 113(4).

mechanical behavior of reinforced concrete beams with … · 2019. 2. 24. · mechanical behavior...

Documents