Combined upper–lower bound analysis for shear strength of transversely reinforced concrete beams under axial tension

Abstract

Axial tension force exerted because of a temperature change or shrinkage can cause the collapse of reinforced concrete (RC) structural members. Earlier work on this subject has revealed that axial tension imposed on a lightly reinforced section led to the partial collapse of the Wilkins Air Force Depot in 1955. Design code provisions and analytical models such as modified compression field theory yield reasonable estimates of shear strength of RC beams subjected to axial tension. Nevertheless, their semi-empirical nature is not always appropriate for shear assessment of existing RC structural members. The extra conservativeness and empirically determined parameters can incorrectly estimate the actual strengths of existing structures. A generalized mechanical model with rigorous formulation must be developed. This paper presents an analytical model that is useful to predict the shear strength of RC beams with transverse reinforcement under axial tension. Without regressive functions or empirical parameters, the combined upper and lower bound analysis enables shear strength derivation based on the force equilibrium and compatible patterns of failure. The accuracy of these analyses has been validated through comparison of its predictions with five available experimental campaigns and international shear design expressions as well as the modified compression field theory. Comparisons reveal the limitations of design code provisions and the general validity of the developed analysis.