Structural Response Variability III

Abstract

The response variability of statically indeterminate linear structures due to spatial variation of material or geometry properties, or both, is investigated. Utilizing a Green's function formulation or the more general flexibility method, the mean square response of statically indeterminate beams and frames (multistory/multibay) is determined without recourse to a finite element analysis. The response variability is expressed in terms of random variables even though the material or the geometric property, or both, (in this case the fiexibility) 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 are given. The response variability can be estimated by various methods, including the first‐order second moment method and Monte Carlo simulation techniques. Finally, the safety index for the beam midspan deflection and end moment are evaluated using standard methods.