Optimization-Based Analysis of Diagonal Tension Failure of Reinforced Concrete Dapped-End Beams

Abstract

This work was conducted first to devise an explicit equation for the ultimate strength of reinforced concrete dapped-end beams failing in diagonal tension caused by re-entrant corner cracks and second to gain insight into its mechanical behavior. To these ends, we introduce force equilibrium equations that explicitly account for the relevant internal force-resisting components: hanger reinforcement; dowel action of longitudinal reinforcement; concrete compression zone; aggregate interlock; and other reinforcement-related terms. These equations are solved within the framework of a constrained optimization problem. The solution process enables us to quantify the ultimate strength and the contributions of all force transfer actions. Strength prediction validity was confirmed through comparisons with experimentally obtained strength data from 50 specimens collected from the available literature. Our findings indicate the prediction accuracy as superior to that of a strut-and-tie model and design provisions of the Precast/Prestressed Concrete Institute. For practical purposes, a minimalist version of the equilibrium equation is derived to estimate the ultimate strength of diagonal tension failure based on rational simplifications of the force transfer mechanisms.