Concrete contribution to the shear resistance of FRP reinforced concrete beams

The experimental program was conducted at the University o f Sherbrooke to investigate the effect o f using FRP bars as longitudinal reinforcement on the shear strength and behaviour o f

m SHERBROOKE

Faculte de genie Departement de genie civil

CONCRETE CONTRIBUTION TO THE SHEAR RESISTANCE OF

FRP-REINFORCED CONCRETE BEAMS

A Dissertation Submitted in Partial Fulfilment o f the Requirements for the Degree o f

Doctor o f Philosophy

Specialty: Civil Engineering

Ahmed Kamal El-Sayed Ahmed

Published Heritage Branch

395 W ellington Street Ottawa ON K1A 0N4 Canada

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A bstract

ABSTRACT

Corrosion o f steel reinforcement in concrete structures causes deterioration o f concrete, resulting in costly maintenance and repair Many steel-reinforced concrete structures exposed to deicing salts and marine environments require extensive and expensive maintenance Recently, the use o f fibre-reinforced polymers (FRP) as an alternative reinforcing material in reinforced concrete structures has emerged as an innovative solution to the corrosion problem However, due to the difference in mechanical properties between steel and FRP reinforcements, the shear strength o f concrete members reinforced with FRP longitudinal reinforcement may differ from that o f members reinforced with steel

An experimental program including two phases is described The experimental program was conducted at the University o f Sherbrooke to investigate the effect o f using FRP bars as longitudinal reinforcement on the shear strength and behaviour o f concrete beams without web reinforcement The first phase included 15 large-scale concrete slender beams reinforced with glass FRP, carbon FRP, or conventional steel bars Nine beams were constructed using normal-strength concrete, whereas six beams were constructed using high-strength concrete The test variables were the reinforcement ratio and the modulus o f elasticity o f the reinforcing bars as well as the concrete compressive strength The second experimental phase included 12 large-scale concrete deep beams reinforced with glass FRP, carbon FRP, or conventional steel bars The test beams o f this phase were constructed using normal-strength concrete and the test parameters were the reinforcement ratio and the modulus o f elasticity o f the reinforcing bars as well as the shear span-to-depth ratio The influence o f the considered variables on the shear strength and behaviour o f the tested beams in the two phases is presented

An analytical investigation to examine the validity o f the available design provisions o f concrete contribution to shear strength for members longitudinally reinforced with FRP bars is reported For this purpose, the shear strengths o f the tested beams are analyzed using the shear design provisions o f the different available codes, manuals, and design guidelines The results o f the analysis are compared with the experimental values Based on the findings o f this investigation, a proposed shear design

equation is presented The proposed equation is verified against experimental shear strengths o f 107 specimens tested to date, including the specimens in this investigation In addition, the proposed equation is compared to the major design provisions using the available test data to further evaluate its reliability.

During the course o f the research work, the following related papers have been published or submitted for publication:

Journal Papers

1 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006a), “Shear Strength o f FRP-Reinforced Concrete Deep Beams without Web Reinforcement,” Submitted to ACI Structural Journal

2 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006d), “Shear Capacity of High-Strength Concrete Beams Reinforced with FRP Bars,” ACI Structural Journal, Vol 103, No 3, pp 383-389

3 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006e), “Shear Strength o f FRP-Reinforced Concrete Beams without Transverse Reinforcement,” ACI Structural Journal, Vol 103, No 2, pp 235-243

Conference Papers

4 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005a), “Shear Strength o f Concrete Beams Reinforced with FRP Bars: Design Method,” Proceedings o f the 7th International Symposium on Fiber Reinforced Polymer Reinforcement for Concrete Structures (FRPRCS-7), ACI-SP-230, Kansas City, MO., USA, Nov 5-9, pp 955-974

5 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005b), “Analytical Modeling o f FRP-Reinforced Concrete Beams Failed in Shear,” Proceeding on CD, 1st CSCE Specialty Conference on Infrastructure Technologies, Management and Policy, Toronto, Ontario, Canada, June 2-4, FR-127, lOp

6 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2005c), “Shear Design o f Concrete Beams Reinforced with FRP Bars,” Proceeding on CD, 4th Middle East Symposium on Structural Composites for Infrastructure Applications (MESC-4), Alexandria, Egypt, May 20-23, 12p

A bstra ct

7 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2004a), “Concrete Contribution to the Shear Resistance o f High-Strength Concrete Beams Reinforced with FRP Bars,” Proceeding on CD, International Conference: Future Vision and Challenges for Urban Development, Cairo, Egypt, December 20-22, 12p

8 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2004c), “Evaluation o f Concrete Shear Strength for Beams Reinforced with FRP Bars” Proceeding on CD, 5th Structural Specialty Conference o f the CSCE, Saskatoon, Saskatchewan, Canada, June 2-5, ST-224, lOp

Also the candidate has participated in the following publications during hisdoctorate study at the Universite de Sherbrooke:

Journal Papers

9 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006b), “Mechanical and Structural Characterization o f New Carbon FRP Stirrups for Concrete Members,” Accepted for publication in the Journal o f Composites for Construction, ASCE

10 El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B., (2005d), “Shear Strength o f One-way Concrete Slabs Reinforced with FRP Composite Bars,” Journal o f Composites for Construction, ASCE, Vol 9, No 2, pp 147-157

Conference Papers

11 Ahmed, E A., El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006),

“Shear Behaviour o f Concrete Bridge Girders Reinforced with Carbon FRP Stirrups,” Submitted to the 7th International Conference on Short and Medium Span Bridges, Montreal, Canada, Aug 23-25, 10 p

12 El-Sayed, A K., El-Salakawy, E F., and Benmokrane, B., (2006c), “Structural Behaviour o f Carbon FRP Stirrups Used as Shear Reinforcement for Concrete Beams.,” Proceedings on CD, 1st International Structural Specialty Conference o f the Canadian Society for Civil Engineering, CSCE, Calgary, Alberta, Canada, May 23-

26, 10 p

13 El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B (2004b), “New Carbon FRP Stirrups as Shear Reinforcement for Concrete Beams,” Advanced Composites Materials in Bridges and Structures (IV-ACMBS), Proceedings on CD, Calgary, Alberta, Canada, July 20-23, 8 p.

Technical Reports

14 Benmokrane, B., El-Sayed, A K., and El-Salakawy, E F., (2005e), “Conception de Poutres de Pont en Beton on Precontraint Renforcees avec des Etriers en Materiaux Composites,” Technical Report-Phase 2, Submitted to the Ministry o f Transportation

o f Quebec, Quebec, Canada, March, 18p

15 Benmokrane, B., El-Sayed, A K., El-Salakawy, E F., and Massicotte, B., (2004d),

“Conception de Poutres de Pont en Beton on Precontraint Renforcees avec des Etriers

en Materiaux Composites,” Technical Report-Phase 1, Submitted to the Ministry o f Transportation o f Quebec, Quebec, Canada, January, 21 p

RESUME

La corrosion de l’acier d’armature des structures de beton provoque la deterioration du beton, ce qui entraine des couts de reparation et d ’entretien importants De nombreuses structures de beton arme d ’acier exposees aux sels de degla9age o u a u n environnement marin necessitent des travaux de refection generalises et couteux Recemment, l ’emploi

de polymeres renforces de fibres (PRF) comme materiau de renfort altem atif pour les structures de beton est apparu comme etant une solution innovatrice aux problemes de corrosion Cependant, du fait des differences de proprietes mecaniques entre les armatures d ’acier et de PRF, la resistance au cisaillement des membrures de beton arme d’armature de traction en PRF peut differer de celle observee avec l’acier d ’armature

Un programme experimental incluant deux phases est decrit Le programme experimental a ete mene a l ’Universite de Sherbrooke afin d ’evaluer l’effet de

l ’utilisation des barres de PRF comme armature longitudinale de traction sur la resistance

au cisaillement (ou a 1’ effort tranchant) et le comportement des poutres de beton sans armature d ’ame (sans armature transversale) La premiere etape a porte sur 15 poutres elancees de beton a grande echelle renforcees avec des barres d ’armature en PRF de verre, en PRF de carbone et de Lacier d ’armature conventionnel N eu f poutres ont ete fabriquees en utilisant du beton normal tandis que les six autres l’ont ete avec du beton a haute resistance Les variables d’essai etaient le taux d’armature et le module d ’elasticite des barres d ’armature de meme que la resistance a la compression du beton La seconde phase experim ental portait sur 12 poutres profondes de beton a grande echelle renforcees avec des barres d ’armature en PRF de verre, en PRF de carbone et de l’acier

d ’armature conventionnel Les poutres d ’essai etudiees lors de cette phase etaient fabriquees a partir de beton normal et les parametres d ’essai etaient le taux d ’armature et

le module d ’elasticite des barres d’armature de meme que le rapport portee de la zone de

cisaillem ent sur hauteur de la poutre L ’influence des variables considerees sur la

resistance au cisaillement et le comportement des poutres d ’essai des deux phases est presentee

Une etude analytique portant sur la validite des equations de calcul disponibles sur la contribution du beton a la resistance au cisaillement pour les membrures en beton

renforces longitudinalement avec des barres de PRF est aussi rapportee Dans cet objectif, les resistances au cisaillement des poutres testees ont ete analysees a l’aide des equations

de calcul concemant le cisaillement a partir des divers codes, manuels et guides de calcul disponibles Les resultats de cette analyse sont compares aux valeurs experimentales Une equation de calcul pour le cisaillement est proposee et verifiee a partir des valeurs experimentales de resistance au cisaillement des 107 poutres etudiees a date, incluant les poutres de la presente etude

A c know I edgem ents

A C K N O W LED G EM EN TS

I would like to express my profound gratitude to my advisors Professor Brahim Benmokrane and Professor Ehab El-Salakawy for their support, encouragement, guidance, and valuable advice throughout the research program

I would like to thank the structural laboratory technical staff in the Department o f Civil Engineering at the Universite de Sherbrooke, in particular Mr Francois Ntacorigira and

Mr Simon Sindayiagaya for their help in my experimental work

This research program has been carried out through the NSERC Chair o f Professor Benmokrane on FRP composite reinforcement for concrete structures at the Universite de Sherbrooke Thus, the financial support received from the Natural Sciences and Engineering Research Council o f Canada (NSERC), Pultrall Inc (Thetford Mines, Quebec), the Ministry o f Transportation o f Quebec, the Network o f Centres o f Excellence ISIS-Canada, and the Universite de Sherbrooke is greatly acknowledged

I would like to express my deep appreciation and thanks to my parents, my brother, and

my sisters for their endless love, support, and encouragement Finally, my words stand helpless and cannot express my appreciation to my wife and my twin sons for their patience and support; to them this thesis is dedicated

2.2 Shear in Reinforced Concrete Beams without Transverse Reinforcement 8

Table o f Contents

2.3 Shear in Reinforced Concrete Beams with Transverse Reinforcement 172.3.1 Internal forces in a beam with transverse reinforcement 17

2.5.4 Canadian Highway Bridge Design Code (CHBDC), CSA-S6-00 59

BEHAVIOUR OF CONCRETE BEAMS REINFORCED

3.2.1.2 Glass fibres 63

3.4 Shear Behaviour o f Flexural Members Reinforced with FRP Bars as

3.5.2 Shear behaviour o f concrete beams reinforced with FRP stirrups 913.6 Shear Design Provisions for FRP-Reinforced Concrete Members 106

3.6.1.2 Design recommendations by Building Research Institute 111

3.6.2.1 Canadian Highway Bridge Design Code (CHBDC),

Table o f Contents

5.2.2.2.1 Effect o f reinforcement ratio and modulus o f elasticity o f

5.2.2.2.2 Effect o f concrete compressive strength 164

5.4.2.2.1 Effect o f reinforcement ratio and modulus o f elasticity o f

5.6 Comparison between the Shear Behaviour o f Slender and Deep Reinforced

Table o f Contents

Figure 2.1

Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8 Figure 2.9

Figure 2.10

Figure 2.11 Figure 2.12 Figure 2.13

Figure 2.14

Figure 2.15

Figure 2.16 Figure 2.17 Figure 2.18

LIST OF FIGURES

Shear transfer mechanism in a cracked reinforced concrete beam

Typical diagonal tension failure in slender beams (a/d > 2.5) 13

Typical shear failures in short beams (a/d - 1.0 to 2.5) 14

Modes o f failures o f deep beams (a/d < 1 0 ) (adapted from

Internal forces in a cracked beam with stirrups (adapted from

Stress distribution and trajectories o f principal stresses in a

Equilibrium considerations for 45° truss (adapted from Collins 25 and Mitchell 1997)

Equilibrium considerations for variable-angle truss (adapted from

Examples o f B and D regions (adapted from Ali and White 2001) 30 Arch action in a beam (adapted from MacGregor 1997) 31Examples o f D regions modeled with compressive struts and

Strut and tie model for a deep beam (adapted from Collins and

Equilibrium conditions o f modified compression field theory

Figure 3.10 Figure 3.11 Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Stress-strain relationship for cracked concrete (adapted from

Force transmission across cracks (adapted from Collins and

Spacing o f inclined cracks (adapted from Collins and Mitchell

Reinforced concrete membrane elements subjected to in-plane

Typical tensile stress-strain relationships for FRP and steel rebars 67 Relationship between reinforcement ratio and experimental shear

Relationship between normalized reinforcement ratio and normalized shear strength (Alkhrdaji et al 2001) 73Comparison o f results for slabs reinforced with carbon FRP bars

Comparison o f results for slabs reinforced with No 16 glass FRP

Comparison o f results for slabs reinforced with No 22 glass FRP

Relationship between tensile strength and bend radius (Maruyama

General view o f the hooked bar specimens (Ehsani et al 1993) 83Load versus slip for three No 6 hooked bars (Ehsani et al 1993) 83Failure loads o f the hooked bars (Ehsani et al 1993) 84

Effect o f bend radius, rh, on strength capacity o f the bend,fbend,

Stirrups specimens and arrangement o f strain gauges (El-Sayed et

Figure 3.16 Test setup for bend testing (El-Sayed et al 2004) 90Figure 3.17 Fibre-rupture failure mode at the bend (El-Sayed et al 2004) 92Figure 3.18 Effect o f bend radius on bend capacity (El-Sayed et al 2004) 92

Figure 3.20 Stirrup strain distribution proposed by Zhao et al (1995) 96Figure 3.21 Effect o f stirrup spacing on effective capacity o f FRP stirrups

Figure 3.22 Effect o f flexural reinforcement on shear resisting components

Figure 3.23 Applied shear versus crack width for beams reinforced with

Figure 4.1 Glass and carbon FRP sand-coated reinforcing bars 123Figure 4.2 Typical FRP tension specimens and mode o f failure 123Figure 4.3 Typical stress-strain relationships o f the reinforcing bars 125

Figure 4.6 LVDTs used for measuring deflection and crack widths 131Figure 4.7 Schematic drawing o f the test setup o f Phase I-test beams 132Figure 4.8 A photograph o f the test setup o f Phase I-test beams 133

Figure 4.10 Instrumentation layout of: (a) all beams o f Phase II except beams

Figure 4.11 Schematic drawing o f the test setup o f Phase II-test beams 141Figure 4.12 A photograph o f the test setup o f Phase II-test beams 142

Figure 5.4 Load-deflection relationships for beams o f Series 3 and 4 150

Figure 5.7 Diagonal tension failure mode: (a) associated with no concrete

L ist o f Figures

splitting; and (b) associated with concrete splitting 154

Figure 5.10 Typical load-crack widths relationship (Series 3) 157Figure 5.11 Load- versus crack widths for beams o f Series 3 and 4 157

Figure 5.15 Load-strain relationships for beams o f Series 3 and 4 160Figure 5.16 Normalized shear strength versus reinforcement ratio for NSC

Figure 5.17 Experimental shear strength versus reinforcement ratio for HSC

Figure 5.18 (a) Experimental shear strength versus concrete compressive

strength; and (b) Normalized shear strength versus concrete

Figure 5.22

Figure 5.23

Figure 5.24 Load versus crack widths for beams having a/d = 1.69 192Figure 5.25 Load versus crack widths for beams having p = 1.24% 192Figure 5.26 Load-strains relationships for beams having a/d = 1.69 193Figure 5.27 Load-strains relationships for beams having p = 1.24% 193

Figure 5.28

Figure 5.29

Figure 5.30

Figure 5.31 Figure 5.32

Strut and tie model for beams o f Phase II failed in shear

Effect o f shear span-to-depth ratio on cracking and ultimate shear strength

Experimental-to-predicted shear strength o f slender beams versus axial stiffness o f reinforcing bars: (a) ACI 440.1R-03; and

Experimental-to-predicted shear strength o f slender beams versus effective depth: (a) ACI 440.1R-03; and (b) proposed equation

Experimental-to-predicted shear strength o f deep beams versus axial stiffness o f reinforcing bars: (a) ACI 440.1R-03; and (b) proposed equation

L ist o f Tables

Table 2.1 Table 2.2

Table 2.3

Table 3.1 Table 3.2 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 5.1

Table 5.2 Table 5.3

Table 6.1

LIST OF TABLES

Values o f /? and 8 for sections with transverse reinforcement

Values o f /? and 9 for sections with less than minimum

Details o f test results o f bend specimens (Shehata et al 1999) 87Test results o f carbon FRP stirrups (El-Sayed et al 2004) 91

Comparison o f theoretical and experimental failure loads for

Comparison o f predicted and experimental shear capacities for

Comparison o f predicted and experimental shear capacities for

Experimental and predicted service load deflections and crack widths for the beams reinforced with FRP bars 175Experimental and predicted service load deflections and crack widths for the beams reinforced with steel bars

176Comparison o f theoretical and experimental failure loads for

Comparison o f predicted and experimental ultimate shear

Verification o f the proposed equation and comparison with

Table 6.2

Verification o f the proposed equation and comparison with

N otation

NOTATION

Af = nominal cross-sectional area o f FRP bars

A ft = total nominal cross-sectional area o f FRP stirrup within distance s

A r nominal cross-sectional area o f reinforcement

As nominal cross-sectional area o f steel bars,

A v = total nominal cross-sectional area o f stirrup within distance 5

c = cracked transformed section neutral axis depth

D = resultant o f diagonal compression stress

d = effective depth o f tensile reinforcement

E c = modulus o f elasticity o f concrete

E f = modulus o f elasticity o f FRP bars

Efl = modulus o f elasticity o f longitudinal FRP bars

Efv = modulus o f elasticity o f FRP stirrup

E r = modulus o f elasticity o f reinforcement

E s = modulus o f elasticity o f steel

Esi = modulus o f elasticity o f longitudinal steel

Fnt = nominal tensile strength of tie

F nn = nominal compressive strength o f nodal zone

f 2 = principal compressive stress

f 2 max = effective compressive strength o f diagonally cracked concrete

fb en d = tensile strength o f FRP stirrup at the bend

f c = compressive strength o f concrete

f cd = design compressive strength o f concrete

f cr - concrete cracking strength

fj v = FRP stirrup stress at failure

fjv d - design tensile strength o f FRP stirrup ffu = ultimate tensile strength o f FRP longitudinal reinforcing bars

f/u v = ultimate longitudinal tensile strength o f FRP stirrup

f y - yield strength o f reinforcing steel bars

I - moment o f inertia o f cross section ICr = moment o f inertia o f cracked section

Ie = effective moment o f inertia o f cross section

Ig = moment o f inertia o f gross section

j d = shear depth, defined as the distance between the compressive force and

the tensile force acting on the cross-section

K = factor representing the beneficial effect o f the prestress force on

concrete diagonal tensile strength

M f = factored moment at section o f interest

N d = design axial compressive force

N otation

N u = required force in tension tie

N v = tensile force in longitudinal reinforcement due to shear

Q = statical moment o f cross-sectional area above or below a level about

neutral axis

rb = bend radius o f FRP stirrup

s = spacing between FRP stirrups

sz = crack-spacing parameter for members without shear reinforcement

Smi, smv, sme = crack spacing in longitudinal, transverse, and inclined directions

Vcr = inclined cracking shear strength

Vcrexp = experimental inclined cracking shear strength

Vcz = shear component resisted by the compression zone

Vd = shear component resisted by the dowel action

Vf = factored shear force at section o f interest

Vs = shear-resisting force provided by stirrups

= shear-resisting force provided by FRP stirrups

Vuexp = experimental ultimate shear strength Eupred = predicted ultimate shear strength

W p red = predicted crack width

a = angle o f principal stresses with the longitudinal axis o f the beam

Pi = depth reduction factor o f the equivalent rectangular stress block

&exp experimental deflection

3 p re d = predicted deflection

&max = maximum deflection

S i = principal tensile strain

S cr = concrete strain at cracking

Scu = maximum usable compressive strain in concrete

Sjb = ultimate strain in FRP bent bars

S fvd = design strain in FRP stirrup

Sfuv = ultimate strain in straight portion o f FRP bent bars

Ss = strain in steel reinforcing bars

£ y = yield strain o f reinforcing steel bars or transverse strain

= strength-reduction factor

</>c = resistance factor for concrete

A = modification factor for concrete density

P act actual reinforcement ratio

P b reinforcement ratio at balanced strain condition

P fl = FRP longitudinal reinforcement ratio

P fv = FRP transverse reinforcement ratio

p s l longitudinal steel reinforcement ratio

N otation

0 = inclination angle o f diagonal compression stresses with the

longitudinal axis o f the beam ojv = stress in concrete due to axial load

Tfuv = transverse shear strength

CHAPTER 1 INTRODUCTION

1.1 General

Corrosion o f steel reinforcement constitutes one o f the major problems that shorten the lifetime serviceability o f concrete structures Many steel-reinforced concrete structures exposed to deicing salts and marine environments require extensive and expensive maintenance Several techniques, including epoxy coating o f reinforcing bars, cathodic protection, increased concrete cover thickness, and polymer concrete overlays have been used to inhibit or eliminate corrosion None o f these techniques, however, has proven to

be cost-effective or a long-term solution An alternative reinforcing material, fibre reinforced polymers (FRP), is being considered as a solution to the corrosion problem FRPs are corrosion-free materials and have recently been used as reinforcement to avoid the deterioration o f concrete structures caused by corrosion o f steel reinforcement

The use o f FRP as reinforcement for concrete structures has increased rapidly over the last decade FRP reinforcement is made from high tensile strength fibres such as carbon, glass, and aramid embedded in polymeric matrices and produced in the form o f bars, strands, ropes, and grids, in a wide variety o f shapes and characteristics FRP reinforcement is used as prestressing, non-prestressing, and shear reinforcement for concrete structures Extensive research programs have been conducted to investigate the flexural behaviour o f concrete members reinforced with FRP reinforcement On the other hand, the shear behaviour o f concrete members reinforced longitudinally with FRP reinforcement has not yet been explored Because FRP and steel bars have different properties, including the modulus o f elasticity, transverse strength, and the surface and bonding characteristics, the shear strength o f concrete members longitudinally reinforced with FRP bars may differ from those o f steel-reinforced ones In fact, in recent flexure

Michaluk et al (1998), shear failures were reported for specimens reinforced longitudinally with FRP bars

Cracked reinforced concrete members resist the applied shear stresses by means

o f a number o f mechanisms: 1) the shear resistance o f uncracked concrete; 2) aggregate

Chapter 1: Introduction

interlock; 3) the dowel action o f the longitudinal reinforcement; 4) the residual tensile stresses across the inclined crack; 5) arching action; and 6) the shear carried by the shear reinforcement The aggregate interlock results from the resistance to relative slip between the two rough interlocking surfaces o f the crack, much like frictional resistance As long

as the crack is not too wide, this action can be significant The dowel force in the longitudinal reinforcement is the force resisting relative transverse displacements between two segments o f the member separated by a crack The basic explanation o f residual tensile stresses is that when concrete first cracks, a “clean break” does not occur Small pieces o f concrete bridge the crack and continue to transmit tensile force up to crack widths in the range o f 0.05-0.15 mm (ASCE-ACI 1998) The arching action occurs

in deep members or in members where the shear span-to-depth ratio (a/d) is less than 2.5

This is not a shear transfer mechanism in the sense that it does not transmit a tangential force to a nearby parallel plane, but permits the transfer o f a vertical concentrated force to

a reaction, thereby reducing the contribution o f the other types o f shear transfer Traditional reinforced concrete design codes generally lump the first five mechanisms

into one term and refer to it as, Vc, the contribution o f concrete to shear resistance o f a member The sixth mechanism is referred as, Vs, the contribution o f the shear

reinforcement to shear resistance

Due to the relatively low modulus o f elasticity o f the FRP composite material, concrete members reinforced with FRP bars will develop wider and deeper cracks than those reinforced with steel Deeper cracks decrease the contribution to shear strength from the uncracked concrete due to the lower depth o f concrete in compression Wider cracks, in turn, decrease the contributions from aggregate interlock and residual tensile stresses Additionally, due to the relatively small transverse strength o f FRP bars and relatively wider cracks, the contribution o f dowel action may be negligible Finally, the overall shear capacity o f concrete members reinforced with FRP bars as flexural

Based on the results from the literature and the discussion above, the shear

strength Vc and behaviour o f FRP-reinforced concrete beams differ from those o f steel-

reinforced ones Therefore, concrete members longitudinally reinforced with FRP bars cannot be designed using the shear design provisions related to concrete members

longitudinally reinforced with steel bars Currently, limited research has been performed

to quantify the difference in the shear strength Vc between FRP- and steel-reinforced members Therefore, the shear strength Vc and behaviour of FRP-reinforced concrete

beams is o f particular interest

1.2 Objectives and Originality

The use o f FRP as reinforcement for concrete structures is rapidly increasing

Nevertheless, the shear strength Vc and behavior o f concrete flexural members reinforced

with FRP bars as main tensile reinforcement have not yet been fully explored Several codes and design guidelines addressing FRP bars as primary reinforcement for structural concrete have been recently published Most o f the shear design provisions incorporated

in these codes and design guides are based on the design formulas o f members reinforced with conventional steel considering some modifications to account for the substantial differences between FRP and steel reinforcement Taking into account the empirical nature o f most o f the current shear design methods, investigations are required to examine the validity o f these methods The main objectives o f this investigation are:

1 To investigate the influence o f FRP longitudinal reinforcement on the concrete shear

strength Vc o f flexural members.

2 To examine the validity o f the current analytical and design approaches for shear to members longitudinally reinforced with FRP reinforcement

3 To develop a shear design equation for evaluating the concrete shear strength Vc for

concrete members longitudinally reinforced with FRP bars

The various specific objectives can be summarized as follows:

a) Evaluating the shear strength Vc o f FRP-reinforced concrete slender beams (a/d >

2.5) without shear reinforcement considering the effect o f the reinforcement ratio and the modulus o f elasticity o f the reinforcing bars as well as the concrete

strength (normal- and high-strength concrete).

b) Evaluating the shear strength Vc o f FRP-reinforced concrete deep beams (a/d <

2.5) without shear reinforcement considering the effect o f the reinforcement ratio and the modulus o f elasticity o f the reinforcing bars as well as the shear span-to- depth ratio

Chapter 1: Introduction

1.3 Methodology

To achieve the objectives o f this research, experimental and analytical programs were designed The experimental program consisted o f two main phases The two phases comprised reinforced concrete beams laying in two different categories concerning

slenderness ratio (shear span-to-depth ratio, a/d): slender beams and deep beams It is

well established that the shear transfer mechanism in a cracked reinforced concrete beam

is dependent on this ratio In reinforced concrete slender beams where the ratio a/d is

greater than 2.5, most o f the shear stresses in the shear span are resisted by the so-called

“beam action” On the other hand, in reinforced concrete deep beams where the ratio a/d

is lower than 2.5, most o f the shear stresses in the shear span are resisted by the so-called

“arch action” The beams o f the two phases were designed to have no shear reinforcement to easily quantify the concrete contribution to the shear strength Considering evidence from steel-reinforced concrete members, most o f the design formulas concerned with evaluating the concrete shear strength o f such members have been derived empirically from a body o f test data o f beams without shear reinforcement Furthermore, there are many structural components in which the entire shear strength is provided by the concrete Examples o f such structures include slabs, walls, and foundations Consequently, a good knowledge o f the shear strength o f reinforced concrete members without shear reinforcement is also necessary in these cases

The first phase, Phase I, was designed to investigate the shear strength and behaviour o f reinforced concrete slender beams This phase was divided into two groups considering the concrete strength: normal- and high-strength concrete The normal- strength concrete group included nine large-scale concrete beams reinforced with three different types o f flexural reinforcement: carbon FRP, glass FRP, and conventional steel bars The high-strength concrete group included six large-scale concrete beams reinforced with the same three different types o f flexural reinforcement This phase was

reinforcing bars and the flexural reinforcement ratio on the shear strength, Vc, o f concrete

slender beams without shear reinforcement Additionally, the effect o f the concrete

strength on Vc o f such beams was also investigated The second phase, Phase II, included

twelve large-scale reinforced concrete deep beams to evaluate their shear strength and

behaviour The beams were constructed using normal-strength concrete and were reinforced with the same three different types o f flexural reinforcement as the beams o f Phase I The test parameters were the modulus o f elasticity and the reinforcement ratio o f the flexural reinforcement as well as the shear span-to-depth ratio.

The analytical investigation included analysis o f the test results using the different available shear design provisions pertinent to members longitudinally reinforced with FRP reinforcement The results o f each analysis were compared to the experimental values Based on the results o f this comparison and the experimental findings, a proposed modification to the ACI 440.1R-03 (2003) shear design method is presented The reliability o f the proposed equation is verified against experimental shear strengths o f 107 specimens tested to date, including the specimens in this investigation To further verify the proposed equation, the predictions o f the proposed equation are compared to the predictions o f the major design provisions using the available test data

1.4 Structure o f the Thesis

The thesis is divided into seven chapters The following is a brief description o f the contents of the thesis:

Chapter 1: This chapter defines the problem and summaries the objectives and originality

o f the research program The methodology followed to achieve these objectives is also described

Chapter 2: This chapter reviews the shear behaviour o f reinforced concrete beams

without or with shear reinforcement The chapter also presents background and review on the available analytical methods and theories for prediction o f the shear strength and behaviour o f concrete beams reinforced with steel The shear design provisions currently

in effect in North America are also presented

Chapter 3: This chapter provides general information on the FRP composite materials

and their characteristics The chapter presents the available literature review focusing on the effect o f the FRP flexural reinforcement on the shear capacity o f the concrete flexural

Chapter 1: Introduction

members and the use o f FRP as shear reinforcement for concrete structures The available shear design provisions for concrete members reinforced with FRP recently introduced in Japan, Europe, Canada, and USA are also presented

Chapter 4: This chapter describes the experimental program conducted at the University

o f Sherbrooke to test 27 concrete beams reinforced with FRP or steel bars In this chapter the details o f test specimens, configurations, test setups, and instrumentations are given The chapter also provides detailed characteristics o f the materials used in this research program

Chapter 5: The results obtained from the experimental investigation are presented in this

chapter The influence o f each test parameter on the behaviour and the shear strength o f the tested beams are also discussed In addition, the shear strengths o f the tested beams are analyzed using the different available shear design provisions and the results o f the analysis are compared with the corresponding experimental values A comparison between the shear strength and behaviour o f the slender beams tested in Phase I and the deep beams tested in Phase II is also discussed

Chapter 6\ A shear design equation based on the observed behaviour is proposed in this

chapter for both slender and deep concrete beams without shear reinforcement and reinforced in the longitudinal direction with FRP bars Verification o f the proposed equation against experimental results o f this study and test results o f other researchers is also presented This chapter also presents a comparison between the proposed equation and the major design provisions using the available test data

Chapter 7: A summary o f this investigation is given in this chapter The chapter also

presents the conclusions drawn based on the findings o f this investigation

Recommendations for future research are also given

CHAPTER 2 BACKGROUND AND REVIEW ON THE SHEAR BEHAVIOUR

OF CONCRETE BEAMS

2.1 General

The extensive research on the flexural behaviour o f reinforced and prestressed concrete members has clarified mechanisms to such an extent that well-understood conclusions are now incorporated in most o f the current design codes However, the dilemma o f the shear behaviour o f reinforced and prestressed concrete members has not been settled in spite o f the extensive research Shear behaviour in reinforced and prestressed concrete members has been the subject o f many controversies and debates since the turn o f the 20th century The shear mechanism is indeed a complex phenomenon involving many variables and cannot be rationalized into a simple model Several models are introduced by different codes defining the design procedure and the applicability conditions

Shear failures in reinforced and prestressed concrete members are sudden and catastrophic in nature and should be avoided in the design process That is why reinforced concrete members are first dimensioned in flexure and then checked out for shear The effect o f shear is to induce tensile stresses which may result in diagonal cracks Diagonal cracks occur when these stresses along with the longitudinal stresses due to bending exceed the tensile strength o f concrete Unless appropriate amounts o f web reinforcement have been provided, these diagonal cracks can result in a premature shear failure M ost o f the shear design provisions superimpose the shear strength o f a flexural reinforced concrete member into two components The two components

comprise the concrete contribution to shear strength, Vc and the shear reinforcement contribution, Vs The provisions give separate design equations for evaluating Vc and Vs The design shear strength is therefore the summation o f Vc and Vs, multiplied by a

suitable factor o f safety.

The literature on shear behaviour o f concrete beams is very extensive as it dates from the beginning o f the last century Thus, it is beyond the scope o f this study to encompass all the previous work relevant to this topic A comprehensive review is provided by the Joint ASCE-ACI Task Committee 426 on Shear and Diagonal Tension

Chapter 2: Background and Review on the Shear Behaviour o f Concrete Beams

(1973) and the Joint ASCE-ACI Committee 445 on Shear and Torsion (1998) This chapter reviews the shear behaviour o f reinforced concrete beams without or with shear reinforcement focusing on the mechanisms o f shear transfer, factors affecting shear strength, modes o f failure, and the role o f shear reinforcement in concrete beams The chapter also gives background and review on the available analytical methods and design approaches for shear in concrete beams reinforced with steel The shear design provisions currently in effect in North America are also presented A literature review on the shear behaviour o f concrete beams reinforced with FRP bars will be presented in the following chapter

2.2 Shear in Reinforced Concrete Beams without Transverse Reinforcement

The shear strength o f reinforced concrete beams without transverse reinforcement has generated a lot o f research since the beginning o f the last century However, a clear understanding o f shear behaviour o f those beams is still limited Therefore, most o f the design methods are based on empirical formulations by fitting these methods to the test results Many structural concrete members are constructed without transverse reinforcement such as slabs, footings, joists, and lightly stressed members

2.2.1 Mechanisms o f shear transfer

The 1973 ASCE-ACI Committee 426 report identified four mechanisms o f shear transfer: shear stresses in uncracked concrete; interface shear transfer, often called “aggregate interlock” or “crack friction”; the dowel action o f the longitudinal reinforcing bars; and arch action Since that report was issued, ASCE-ACI Committee 445 in 1998 identified a fifth mechanism o f shear transfer, residual tensile stresses transmitted directly across cracks Different researchers assign a different relative importance to each mechanism o f shear transfer in the total shear resistance, resulting in different models for members

without transverse reinforcement The five m echanism s are illustrated in Figure 2.1 and

will be discussed briefly in the following

2.2.1.1 Shear stresses in uncracked concrete

This shear transfer mechanism occurs in uncracked members or in the uncracked portions

V cz = shear in uncracked concrete

Va = shear from aggregate interlock

Vd = dowel action Vrt = residual tensile stresses

V t

Vac = arch action

Figure 2.1: Shear transfer mechanisms in a cracked reinforced concrete beam without

transverse reinforcement

o f cracked reinforced concrete members In an uncracked concrete member, the shear force is transferred by inclined principal tensile and compressive stresses In cracked members, this state o f stress is still valid in the uncracked compression zone Failure may occur either by inclined cracking or crushing o f the concrete depending on whether the principal tensile or compressive stresses reach the corresponding strength o f concrete The integration o f the shear stresses over the depth o f the compression zone gives a shear force component Some researchers quantified the contribution o f this shear mechanism

to the total shear force by about 20-40% (ASCE-ACI 1973)

2.2.1.2 Interface shear transfer

This shear transfer mechanism relies on the friction along the inclined crack interface, which develops due to the relative slip between the two surfaces o f the crack It is often called “aggregate interlock” for normal-density concrete as the aggregates protruding from the crack surface provide resistance against slip Because the cracks pass through instead o f around the aggregates in the lightweight and high-strength concrete and yet still have the ability to transfer shear, however, the term “friction” or “interface shear” is more appropriate The shear stresses transferred by this mechanism are affected by three different parameters The three parameters include stresses normal to the crack, crack

Chapter 2: Background and Review on the Shear Behaviour o f Concrete Beams

width, and crack slip Tests conducted to quantify the contribution o f this mechanism indicated that between 33% and 50% o f the total shear force on a beam may be carried by interface shear transfer (ASCE-ACI 1973)

2.2.1.3 Dowel action

When reinforcing bars cross a crack, shearing displacements along the crack will be resisted, in part, by a dowelling force in the bar The dowel force in combination with the radial forces developed by bond forces give rise to vertical tensile stresses in the concrete surrounding the bar and concrete splitting along the bars may occur For this reason, normally, dowel action is not very significant in members without stirrups, because the maximum shear in a dowel is limited by the tensile strength o f the concrete cover supporting the dowel Dowel action may be significant in members with large amounts o f longitudinal reinforcement, particularly when the longitudinal reinforcement is distributed in more than one layer (ASCE-ACI 1998) A number o f experimental investigations carried out on dowel action indicated that the dowel shear force is between 15% and 25% o f the total shear force (ASCE-ACI 1973)

2.2.1.4 Arch action

The arching action occurs in deep members or in members where the shear span-to-depth

ratio, a/d, (i.e the distance from the support to the concentrated load over the effective

depth) is less than 2.5 For such members, a significant redistribution o f internal forces can be expected after cracking, and a large part o f the shear force is transferred directly to the supports This is not a shear transfer mechanism in the sense that it does not transmit

a tangential force to a nearby parallel plane, but permits the transfer o f a vertical concentrated force to a reaction, thereby reducing the contribution o f the other types o f shear transfer In general, arch action enhances the strength o f a section For arch action

to develop, a horizontal reaction component is required at the base o f the arch In beams this is usually provided by the tie action o f the longitudinal bars

2.2.1.5 Residual tensile stresses across cracks

The basic explanation o f residual tensile stresses is that when concrete first cracks, a

“clean break” does not occur Small pieces o f concrete bridge the crack and continue to

transmit a tensile force up to crack widths in the range o f 0.05-0.15 mm (ASCE-ACI 1998) Reineck (1991) has found that the shear stresses across inclined cracks can be related to the residual tensile stresses which provide a significant portion o f the shear resistance o f very shallow members (for depths less than about 100 mm) where the width

o f flexural and diagonal cracks are small

2.2.2 Modes o f inclined cracking and shear failure

A crack will form in concrete when the principal tensile stress at some location reaches the cracking strength o f the concrete The crack will form normal to the direction o f the principal tensile stress For members subjected to pure axial tension or pure bending, the principal tensile stresses are parallel to the longitudinal axis o f the member and hence cracks due to these actions will be perpendicular to the member axis If a cross section o f

a member is subjected to shear stresses, biaxial stress conditions occur and the principal tensile stress directions are inclined to the longitudinal axis o f the member Hence if a crack forms at a location where significant shear stresses exist, the crack will be inclined

to the member axis (Collins and Mitchell 1997)

There are two characteristic formations of inclined cracks that can occur Depending on the support conditions and load distribution, a combination o f high shear and low moment, or high shear and high moment can occur at a particular point The relative values o f the moments and shears have a significant impact on the magnitude and the direction o f the principal tensile stresses In the presence o f a high shear and low moment condition, a state o f maximum shear occurs at the neutral axis Consequently, inclined cracks will form from the neutral axis and will propagate from that location These cracks are known as web-shear cracks (see Figure 2.2a) and can occur in a beam with a narrow web such as an I-beam where the shearing stresses in the web are much larger in relation to the flexural stresses than they are in a rectangular beam On the other hand, in the presence o f a high shear and a high moment condition, inclined cracks develop as extensions of previously existing flexural cracks This second type o f inclined cracking is called flexure-shear cracking (see Figure 2.2b) and is more prevalent than web-shear cracking

Chapter 2: Background and Review on the Shear Behaviour o f Concrete Beams

(a) W eb-shear crack

flexure-shear crack

initiating flexural crack

(b) Flexure-shear crack

Figure 2.2: Types o f inclined cracks

Shear failure o f beams are characterized by the occurrence o f inclined cracks In some cases inclined cracks are immediately followed by member failure and in other cases, the inclined cracks stabilize and substantially more shear force may be applied before the member fails The primary variable that affects the mode o f failure o f reinforced concrete beams without web reinforcement and fail in shear is the shear span-

to-depth ratio, a/d Based on this ratio, the concrete beams can be divided into two main

In slender beams, the inclined crack disrupts the equilibrium to such an extent that the beam fails shortly after the onset o f inclined cracking This type o f failure is called diagonal tension failure A typical crack pattern on a beam fails in this mode is shown in Figure 2.3

Figure 2.3: Typical diagonal tension failure in slender beams (a/d > 2.5).

The term deep beam is used to describe beams with short and very short shear

spans (MacGregor 1997) Short shear spans, a/d from 1.0 to 2.5, develop inclined cracks

and, after a redistribution o f internal forces, are able to carry additional load, in part by arch action The inclined crack may trigger one o f two modes o f failure A secondary crack may propagate backward along the longitudinal reinforcement from the inclined crack, perhaps because o f dowel action in the longitudinal reinforcement This crack will cause a loss o f bond and contribute to a splitting o f the concrete resulting in an anchorage failure o f the longitudinal reinforcement This mode o f failure is referred to as shear- tension failure as shown in Figure 2.4a Alternatively, the concrete above the upper end

o f the inclined crack may fail by crushing resulting in a shear-compression failure as shown in Figure 2.4b

Very short shear spans, with a/d < 1.0, develop inclined cracks joining the load

and the support After inclined cracking occurs, a deep beam without web reinforcement transforms almost immediately into a tied-arch which can fail in a number o f ways (ASCE-ACI 1973) The numbers in Figure 2.5 correspond the following modes o f failure: (1) anchorage failure o f the tension reinforcement, usually combined with a dowel splitting effect; (2) crushing failure at the reactions; (3) flexural failure-either o f the steel reinforcement due to yielding, or o f the crown o f the arch when the concrete crushes; or (4) tension failure o f the arch-rib by cracking over the support; followed by (5) crushing along the crack