Unified Shear Strength Model for Reinforced Concrete Beams-Part I: Development

A theoretical model was developed to predict the shear strength of reinforced concrete (RC) beams with and without shear reinforcement. It was assumed that the shear strength of concrete beams can be determined from the failure of the compression zone of a beam cross section. The shear strength of the compression zone was evaluated, considering the interaction between the shear strength and normal stresses developed by the flexural moment. The failure mechanism of the compression zone changes from a tension failure to a compression failure as the shear span-to-depth ratio (a/d) decreases. The transition of the failure mechanism was properly addressed by considering the geometry of the beam and using material failure criteria of concrete. Therefore, the proposed strength model can describe the failure mechanisms of both slender beams and deep beams with and without shear reinforcement.

Keywords: beam(s); shear reinforcement; shear strength.

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

Many experimental studies have been performed to investigate the behavioral characteristics and the cause of the shear failure of reinforced concrete (RC) beams. According to the experimental results, the shear strength of simplysupported beams is significantly affected by the compressive strength of concrete, the ratio of tensile reinforcement, the shear span-to-depth ratio (a/d), and the size of a beam. In particular, the shear resistance mechanism starts to change at a/d (equal to 2.5). Based on this result, the shear resistance mechanism of slender beams with a/d > 2.5 is usually assumed to be different from that of deep beams with a/d

Based on experimental results, current design codes including ACI 318-99,1 and many researchers including Zsutty,2 proposed various empirical shear strength equations, which are defined by functions of the primary design parameters: the compressive strength of concrete, the ratio of tensile reinforcement, a/d, and the size of a beam. Although these equations are convenient for use because of their simple forms, most of the empirical strength equations do not accurately predict the test results with a wide range of design parameters.3

On the other hand, ACI 318-054 and Eurocode 2 (CEN5) use the strut-and-tie model to evaluate the shear strength of deep beams. This model is based on a firm theoretical background, and applicable to both slender beams and deep beams. According to Joint ASCE-ACI Committee 4456 and Al-Nahlawi and Wight,7 however, the current strut-and-tie model does not accurately predict the strength of the slender beams that fail by diagonal tensile cracking.

Bazant and Kim8 developed a theoretical strength model based on fracture mechanics. Nielsen9 developed a strength model based on the theory of plasticity. Marti,10 Walravan and Lehwalter,11 and Leonhardt12 developed various refined truss models. They reported that a/d is a primary design parameter that significantly affects the shear failure mechanism, and as a/d decreases, the shear strength considerably increases due to the arch action. Generally, these existing strength models apply different theories to determine the shear strength of deep beams and slender beams. Therefore, they do not properly explain the gradual transition of the failure mechanism, which varies according to a/d.

The results of existing experiments show that, except for local failures such as anchorage failure and bearing failure at supports and loading points, the shear failure of a beam is caused by the failure of the compression zone, although the failure mechanisms vary according to a/d (Fig. 1). For slender beams with a/d > 2.5, an inclined tensile crack penetrates the compression zone, and causes a diagonal tension failure.13-15 Also, for deep beams with a/d

In the present study, the shear failure of a concrete beam was assumed to be closely associated with the failure mechanism of the compression zone, regardless of a/d. Material failure criteria of concrete were used to investigate the failure mechanism of the compression zone, either a diagonal tension failure or a shear-compression failure.

RESEARCH SIGNIFICANCE

In the present study, it was found that the shear strength of a beam can be determined by the failure mechanism of the compression zone, which varies according to a/d. Based on the finding, the authors developed a unified shear strength model that could be applied to both slender beams and deep beams, with and without shear reinforcement. The proposed model can describe the failure mechanism of RC beams, which changes from a diagonal tension failure to a shearcompression failure as a/d decreases.

SHEAR FAILURE MECHANISM OF CROSS SECTION

In concrete beams, flexural cracks normally develop in the tension zone before a shear failure occurs. Bazant20 theoretically verified that the crack-bridging stresses at the surfaces of tensile cracks do not contribute significantly to shear resistance. According to Kotsovos and Pavlovic13 and Zararis and Papadakis,15 because the compression zone of intact concrete prevents any significant shear-slip along the tensile crack surface, aggregate interlock along the crack surface and dowel action of the longitudinal reinforcement do not significantly contribute to the shear strength of the beams.13,14 Jelic et al.21 reported that, based on experimental results for beams without shear reinforcement, the dowel action of the longitudinal reinforcing bars placed in a single layer can be neglected. In the present study, introducing the assumptions made in the previous studies, the shear resistance of a beam was assumed to be provided mainly by the compression zone of intact concrete. However, other assumptions such as the stress-redistribution (due to bond failure mechanism) used in the compressive force path concept13,22 were not used.