Prediction of Deflection of Shear-Critical RC Beams Using Compatibility-Aided Truss Model

Sang-Woo Kim

doi:10.3390/app112311478

Abstract

This study proposes a method for predicting the deflection of shear-critical reinforced concrete (RC) beams. Shear deterioration of shear-critical RC beams occurs before flexural yielding. After shear deterioration occurs in the shear-critical RC beams, the deflection caused by shear is greater than the flexural deflection obtained from the elastic bending theory. To reasonably predict the deflection of shear-critical RC beams, it is necessary to evaluate deflections due to shear as well as flexure. In this study, the deflections produced by flexure and shear were calculated and superposed to evaluate the deflection of shear-critical RC beams. The method recommended by ACI 318-19 was employed to calculate the flexural deflection, and a compatibility-aided truss model able to calculate the shear stress and shear deformation at each load stage was used to consider the shear deflection. A comparison of the experimental and analytical results showed that the proposed analytical method can effectively predict the deflection of shear-critical RC beams.

Highlights

A lot of existing structures worldwide remain vulnerable to shear stress due to the lack of shear analysis and design technologies
Branson [1] proposed a deflection analysis method that reflects the decrease in the stiffness of reinforced concrete (RC) beams due to flexural cracks using the effective moment of inertia
A method to predict the deflection of shear-critical RC beams was developed

Summary

Introduction

A lot of existing structures worldwide remain vulnerable to shear stress due to the lack of shear analysis and design technologies. Most shear analysis theories, including the 45-degree truss model, cannot predict shear deformation because they only consider the stress equilibrium condition. After the shear-critical RC beam reaches the peak load, as shown, the deflection increases, but the load decreases. This post-peak behavior is the result of a sudden collapse in the shear-resistance mechanism of the shear-critical RC beam. In this step, shear deformation is dominant rather than flexural one. The flexural deflection, ∆ f , in Equation (1) can be calculated from the curvature of the section; it shows a different behavior from the elastic theory due to cracking, which is a characteristics of concrete structures.

Shear Analytical Model for Calculating Shear Deflection

Governing Equations

V shear critical sectioan a b'

VerificaCtioOnVof Proposed Method

Findings

Conclusions