Stochastic Model of Self‐Weight Load

Abstract

The unit volume weight of the material in a structural body is modeled as a random field, and the boundary of the body is modeled to be random. Both sources of randomness contribute in an interacting way to the variance of any considered self‐weight load effect. A specific type of random vector‐field modeling of the uncertain boundary is particularly useful. It enables an application of Gauss' integral theorem to reduce the problem of the uncertain boundary to a problem of the enhanced uncertainty of the random volume weight field considered solely within the expected structural body.