Weighted Integral Method. II: Response Variability and Reliability

Abstract

After obtaining in a companion paper an exact expression of the stochastic stiffness matrix in terms of random variables called weighted integrals, the response variability and the safety index of stochastic frame structures are calculated in this paper. The response variability is calculated using a first‐order Taylor's expansion and the safety index using the advanced first‐order second‐moment approach. It is concluded that the potential energy and virtual work approaches produce identical results for the mean value and the variance of nodal displacements and internal forces. On the contrary, the two approaches produce different values for the safety index of both nodal displacements and internal forces. These values for the safety index obtained using the two approaches compare very well. It is noted that the stochastic stiffness matrix obtained using the potential energy approach is an approximation of the corresponding one obtained using the virtual work approach. Finally, the effect of statistical dependence or independence among the stochastic fields of different elements is examined.