Probabilistic Evaluation of the Adaptation Time for Structures under Seismic Loads

Abstract

In this paper, a probabilistic approach for the evaluation of the adaptation time for elastic perfectly plastic frames is proposed. The considered load history acting on the structure is defined as a suitable combination of quasi-statical loads and seismic actions. The proposed approach utilizes the Monte Carlo method in order to generate a suitable large number of seismic acceleration histories and for each one the related load combination is defined. Furthermore, for each load combination the related adaptation time is determined, if any, as the optimal one for which the structure is able to shakedown under the unamplified applied actions. A known generalized Ceradini's theorem is utilized. The adaptation time values obtained with reference to all the generated seismic acceleration histories for which the shakedown occurs allows us to define the related cumulative conditioned probability function and, therefore, to identify the optimal adaptation time as the one with a probability not lower than a suitably assigned value.