Unified Shear Strength Model for Reinforced Concrete Beams-Part II: Verification and Simplified Method

In a companion paper, shear strength models for reinforced concrete (RC) slender beams and deep beams were developed, addressing the transition of shear failure mechanism according to the shear span-to-depth ratio (a/d). In the present study, by integrating these two shear strength models, a unified shear strength model was developed that was applicable to both slender beams and deep beams with and without shear reinforcement. The proposed model was verified by comparisons with existing experimental results. The comparisons showed that, for a wide range of values of design parameters, the proposed model predicts the shear strength of concrete beams better than current design methods. For convenience in design practice, a simplified design equation was developed.

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

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

INTRODUCTION

Many experimental and theoretical studies have been performed to investigate the shear failure mechanism of reinforced concrete (RC) beams. Based on the results, various shear strength models were developed (refer to Appendix*). Because the shear failure mechanism of concrete beams is affected by various design parameters, however, it is not easy to accurately evaluate the shear strength of beams. According to Kani,1 Zararis and Papadakis,2 Aguilar et al.,3 and Leonhardt and Walther,4 the shear failure mechanism significantly varies, particularly as a function of the shear span-to-depth ratio (a/d). If the a/d is greater than 2.5, an inclined tensile crack penetrates the entire depth of the compression zone and causes a diagonal tension failure. On the other hand, if the a/d is less than 2.5, compression crushing occurs in the upper region of the compression zone, which is called a shear-compression failure. Due to the difference in the failure mechanism, the shear strength of slender beams with a/d greater than 2.5 and that of deep beams with a/d less than 2.5 have been studied separately.1-4

According to the results of experimental and theoretical studies, although the failure mechanisms are different, the shear failures of both slender beams and deep beams are closely related to the failure mechanism of the compression zone. In a companion paper,5 using the failure mechanism of the compression zone, the authors developed shear strength models for slender and deep beams. To investigate the shear failure mechanism of the compression zone of concrete beams that is subject to combined shear and normal stresses, Rankine's material failure criteria of concrete were used. The shear capacities, as controlled by tension and compression, were defined as functions of tensile and compressive material strengths of concrete and compressive normal stress. Figure 1 shows the failure mechanisms of a slender beam and a deep beam. Because the shear capacity controlled by tension is usually less than that controlled by compression,5 the compression zone is susceptible to inclined tensile cracking (shear failure controlled by tension) (Fig. 1). In slender beams, because the shear span is long enough, the inclined tensile cracking can penetrate the entire compression zone. Therefore, slender beams fail by diagonal tension cracking in the compression zone. The length of a diagonal tension crack, which is required to penetrate the compression zone, can be calculated as c/tan?c, where c equals the depth of the compression zone, and ?c equals the angle of an inclined tension crack in the compression zone that is defined as the principal tensile stress axis. On the other hand, as shown in Fig. 1, in deep beams, because the shear span is short, an inclined tensile crack cannot penetrate the entire depth of the compression zone. The upper part of the compression zone is subjected to compression crushing. Consequently, the compression zone of a deep beam is subject to the combined shear failure mechanism of tension cracking and compression crushing. As a/d decreases, the depth of the compression zone subject to compression crushing increases. As a result, the shear strength of a deep beam increases (Fig. 1). In the present study, a unified shear strength model will be developed by integrating the shear strength models that were developed for slender beams and deep beams in the companion paper.5 The unified model will be verified by comparisons with various experimental results.

RESEARCH SIGNIFICANCE

A unified shear strength model for RC beams was developed, which is applicable to both slender beams and deep beams with and without shear reinforcement. The proposed strength model was verified by comparisons with experimental results. Comparisons showed that the proposed shear strength model can accurately predict the shear strength of slender and deep beams as a function of various design parameters.

UNIFIED SHEAR DESIGN METHOD

In the companion paper,5 the shear strength of a beam was defined as the sum of the shear contributions of concrete and shear reinforcement