Structural and System Reliability

Chapter 4 presents the basic formulation of the structural reliability problem. It starts with the so-called R-S problem with R denoting a capacity (resistance, supply, strength, etc.) value and S denoting a measure of the corresponding demand (load, stress, etc.), both modeled as random variables. Solutions in integral form are presented for the failure probability by conditioning on R or S, or using formulations in terms of the safety margin or safety factor that lead to the introduction of the concept of reliability index. Exact solutions are presented for specific distributions of R or S. This allows examination of the so-called tail-sensitivity problem, i.e., the sensitivity of the failure probability to the selected probability distributions. It is shown that small failure probabilities are sensitive to the shape of the selected distributions in the tail. The formulation of the structural reliability problem is then generalized and presented in terms of a limit-state function of basic random variables. Using this formulation, the probability of failure is expressed as a multifold integral over the outcome space of the basic random variables. Descriptions of several example applications of the generalized structural reliability formulation conclude the chapter.