Probabilistic Methods in the Theory of Structures

Abstract

For an adequate description of structural behavior, probabilistic methods must be resorted to. Properly speaking, an element of probability is embodied even in the deterministic approach, which claims to “simplify” the structure by eliminating all aspects of uncertainty. Under the deterministic approach, external loading and the properties of the structure are represented as though they were fully determined, and available (often highly sophisticated) tools yield, with sufficient accuracy, the strains and stresses in systems with complex configurations. At the same time, these stresses are compared with allowable ones obtained by dividing their ultimate levels by a “safety factor,” so as to yield a level below that of failure, a practice that recognizes the uncertain, and random, features of the stress distribution in the material. This is how a probabilistic consideration is admitted “via the back door”; indeed, the safety factor has often been referred to as the “ignorance factor”…