Structural and System Reliability

Chapter 11 addresses time- and/or space-variant structural reliability problems. It begins with a description of problem types as encroaching or outcrossing, subject to the type of dependence on the time or space variable. A brief review of essentials from the random process theory is presented, including second-moment characterization of the process in terms of mean and auto-covariance functions and the power spectral density. Special attention is given to Gaussian and Poisson processes as building blocks for stochastic load modeling. Bounds to the failure probability are developed in terms of mean crossing rates or using a series system representation through parameter discretization. A Poisson-based approximation for rare failure events is also presented. Next, the Poisson process is used to build idealized stochastic load models that describe macro-level load changes or intermittent occurrences with random magnitudes and durations. The chapter concludes with the development of the load-coincidence method for combination of stochastic loads. The probability distribution of the maximum combined load effect is derived and used to estimate the failure probability.