Novel theory for shear stress computation in cracked reinforced concrete flexural beams

Abstract

This study is conducted because of the lack of an existing theory to accurately predict the diagonal tension cracking in shallow reinforced concrete beams. A rational approach is followed to numerically derive the shear stress profile across the depth of the beam in cracked beams based on the smeared crack approach. Furthermore, the determined shear stress distribution coupled with the normal axial stress distribution are used to predict the principal stress variation across the depth and along the shear span using standard Mohr’s circle. Following a biaxial stress cracking criterion, the likely diagonal tension cracks along their orientation profile are predicted.

Furthermore, this study is conducted to provide a mechanics-based understanding of the shear stress distribution in cracked reinforced concrete. This approach utilizes the transversal shear differential equation to evaluate the shear stress at any given depth by the variation of the axial stress distribution within an infinitesimal beam segment at that depth. In addition, this study presents a more accurate representation of the change in the strain profile parameters with respect to the sectional applied moment. Furthermore, the dowel action effect is derived to illustrate its significance on the shear stress distribution at various stages of loading.