The use of stochastic stresses in the static approach of probabilistic limit analysis

In the framework of the structural reliability theory, the probabilistic limit analysis (PLA) represents a powerful tool for the evaluation of the safety of structures with stochastic strengths with respect to the ultimate limit state of plastic collapse. Aim of the PLA is to evaluate the conditional probability of collapse (CPC), that is, the probability of plastic collapse of the structural system for assigned value of the acting loads. In this paper the focus is on the static approach of the limit analysis theory, which is particularly attractive for engineers, because it gives upper bounds of the CPC, that is, safe bounds. The classical static approach, introduced more than 30 years ago, however, cannot in any case evaluate the exact CPC of the structural system, and moreover generally the bounds obtained are not very close, especially in the range of very small probabilities. In this paper an alternative static approach is proposed, which can obtain the exact CPC of the structural system considering a finite number of suitable chosen stochastic stress vectors through the use of the partial admissible domains; moreover, it gives good safe bounds of the CPC considering only a few stochastic stress vectors. Some simple numerical examples show the accuracy and effectiveness of the method.