Interval Fractile Levels for Stationary Stochastic Response of Linear Structures With Uncertainties

In the framework of stochastic analysis, the extreme response value of a structural system is completely described by its CDF. However, the CDF does not represent a direct design provision. A more meaningful parameter is the response level which has a specified probability, p, of not being exceeded during a specified time interval. This quantity, which is basically the inverse of the CDF, is referred to as a fractile of order p of the structural response. This study presents an analytical procedure for evaluating the lower bound and upper bound of the fractile of order p of the response of linear structures, with uncertain stiffness properties modeled as interval variables subjected to stationary stochastic excitations. The accuracy of the proposed approach is demonstrated by numerical results concerning a wind-excited truss structure with uncertain Young’s moduli.