Safety Factors and Reliability: Deterministic Actual Stress & Random Yield Stress

Abstract

In the previous chapter we studied the case in which the actual stress was treated as a random variable, while the yield stress was considered as a deterministic quantity. In this report we investigate the reverse case, namely, when the actual stress is deterministic, while the yield stress is treated as a random variable. Various probability densities to model the actual behavior of the structural element in question are considered.

“The strength of a structure cannot be exactly calculated in advance. It is dependent a several quantities, which are accurately known, and therefore more or less uncertain.”

A.I. Johnson (1953)

“In deterministic design, the capacity reduction factor and load factor are determined subjectively based on judgement, intuition, and experience; in probabilistic design, they are estimated explicitly project by project considering the specific conditions, giving more control to the design engineers.”

A. Haldar and S. Mahadevan (2000)

“Since the late Professor A.M. Freudenthal presented a rational approach to the structural safety…an ever-increasing effort has been directed toward the application of the theory of probability and statistics in structural engineering.”

J.T.P. Yao (1985)

“Until all future designs use probabilistic approaches, the structural analysis community must use both deterministic and probabilistic approaches. The “rationale” of these two approaches is quite different, and therefore a temporary process that bridges the two should be implemented.”

G. Maymon (2002)