Response Analysis of Stochastic Structures

Keywords: Stochastic Processes, Limit State Probability, Statically Indeterminate Linear Structures, Multi-story Structures, Frames, and Beams.

Abstract: The response variability of statically indeterminate linear structures due to spatial variation of material and/or geometrical properties is investigated. Utilizing a Green's function formulation, or the more general flexibility method, the mean square response of statically indeterminate beams and frames (multi-story/multi-bay) is determined without recourse to a finite element analysis. The response variability is expressed in terms of random variables even though the material and/or the geometrical properties (in this case, the flexibility) are considered to constitute stochastic fields. This makes it easier to estimate not only the response statistics but also the limit state probability, if the limit state conditions pertain to serviceability and hence are given in terms of linear structural response. The response variability can be estimated by various methods including the First-Order Second Moment method and Monte Carlo simulation techniques. The safety index for the beam midspan deflection and end moment are evaluated using standard methods. One of the example analyses deals with the effect of such spatial variability on the seismic structural response evaluated under quasi-static conditions. While the loading condition and structure considered in this example analysis are relatively simple, the result provides some insight into the extent of the response variability expected under these circumstances.