Reliability of Structural Systems

Abstract

In the preceding chapters the concept of reliability has mainly been concerned with single structural elements such as a beam or a column. In the fundamental case the loading is described by a single random variable S and the strength by a single random variable R (see chapter 4). The probability of failure P_f is then defined as

$${P_f} = P\left( {S \ge R} \right)$$

(7.1)

assuming that the failure condition is R − S ⩽ 0. P_f can be calculated from

$${P_f} = \int_{{w_f}} {{f_{R,S}}\left( {r,\,s} \right)\,drds} $$

(7.2)

where f_R,S is the joint probability density function and ω_f the failure region {(r, s)/r−s ⩽ 0}. When f_R,S is known, the probability of failure P_f can be calculated relatively easily from (7.2) by a suitable numerical technique or by simulation.