Evaluation of the shakedown limit load multiplier for stochastic seismic actions

A new approach for the evaluation of the shakedown limit load multiplier for structures subjected to a combination of quasi-statically variable loads and seismic actions is presented. The common case of frame structures constituted by elastic perfectly plastic material is considered. The acting load history during the lifetime of the structure will be defined as a suitable combination of never ending quasi-statical loads, variable within an appropriate given domain, and stochastic seismic actions occurring for limited time interval. The proposed approach utilizes the Monte Carlo method in order to generate a suitable large number of seismic acceleration histories and the corresponding shakedown limit load multipliers are determined. A generalized Ceradini approach to the dynamic shakedown is utilized. The shakedown load multipliers obtained for the generated seismic acceleration histories allow to define the related limit load multiplier cumulative distribution function, to characterize the shakedown sensitivity of the structure and, finally, to identify the relevant optimal limit load multiplier as the one with a probability not lower than a suitably assigned value. An application devoted to plane steel frames concludes the paper.

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