Bounds on the Reliability of Structural Systems

TLDR

Civil engineering structures are complex systems with mutually dependent modes and loads, making reliability assessment difficult, and often failure events are more nearly perfectly dependent than independent. The study demonstrates that bounds on system reliability can be determined with relative ease. The bounds are derived for general modal resistance and load distributions, including time‑dependent cases. These bounds can approximate reliability, especially under near‑perfect dependence, and show how the number of modes, design life, and probabilistic dependence influence overall system reliability.

Abstract

Most civil engineering structural problems are characterized not by a single random resistance subjected to a single random load, but by a complicated structural system exhibiting a number of mutually dependent modes acted on by a sequence of mutually dependent random loads. The task of determining the reliability of such a system under these conditions would be extremely difficult even if the necessary joint distribution functions were known. It is possible, however, to determine, with relative ease, bounds on the system reliability. One or the other of these bounds may also serve as an approximation to the desired reliability if the conditions leading to its derivation bold. In particular, it is likely that in many civil engineering situations the conditions are more nearly those of perfect dependence among modal failure events than perfect independence as is often assumed. In this case, a system reliability approximation is most readily obtained. The bounds are derived for general conditions of modal resistance and load distribution including time-dependent cases. The results prove valuable in a qualitative sense by showing the effect of such factors as number of modes, length of design life, and probabilistic dependence among modal resistances and among successive loads on the reliability of the system as a whole.