Probabilistic analysis of nonlinear response to sustained load processes

Reliability study of structural members subjected to a stochastic load process has been extended to include material nonlinearity. Tractable expressions for the first moment statistics of the number of load exceedances and damage duration were derived previously, primarily for a Poisson square wave process and for material with a bilinear force-deformation relationship. A probability distribution for the number of load exceedances is derived herein. It is found that the derived distribution, when approximated by a Taylor series, is in good agreement with that obtained from the simulated sustained load processes if the coefficient of variation of load exceedances is under 50%. In addition, the relationship between linear load effect and non-linear structural response is examined for different elastic limits both in load exceedances and in damage duration. It appears that for high threshold levels, nonlinear response may not be as critical as linear response.