Some Engineering Applications of the Probabilistic Strength of Materials

Three types of aleatory variables can be considered here as determinants of the probabilistic strength of a structure, namely, material properties, boundary conditions, and external agents. The probability of fracture or yielding of some material subjected to external forces verifies F˜(V₁ + V₂, σ) = F˜(V₁, σ) F˜(V₂, σ), where F = 1 – F˜ is the cumulative probability of fracture or yielding and σ is a constant stress on the material. In this manner there can be treated general frameworks or truss structures, soil problems, pressure vessels in general, tunnels in the rock, fatigue, and finally seisms caused by sudden earth-crust fractures.