Reliability‑based probabilistic numerical plastically limited analysis of reinforced concrete haunched beams

Abstract

Abstract This research proposes a novel method that considers the optimal reliability-based design of reinforced concrete haunched beams subjected to probabilistic concrete properties and complementary strain energy values. The theory is applied twice, once to evaluate a deterministic solution, where the plastic behaviour is constrained by the complementary strain energy of residual stresses induced within steel bars. Secondly, the same method is considered for a probabilistic solution where the concrete characteristics—compressive strength and modulus of elasticity—and complementary strain energy value vary randomly. The reliability index acts as a bound for the solution. It is important to mention that the model utilised in this publication is derived from recent research after being calibrated using Abaqus. This work represents an extension of that recent research that exclusively considered deterministic work. This research led deterministically to new estimates for the complementary strain energy, which will be interpreted as reflecting the behaviour of plastic thresholds and quantifying the associated loads. Afterwards, uncertainty is studied when probability interferes, showing various load values and damage in concrete and steel when the complementary strain energy and concrete properties are probabilistically evaluated, giving a less reliable solution as the load reduces. These effects are reflected in the varying plastic behaviour of the investigated haunched beams.