EXACT AND APPROXIMATE SOLUTIONS, AND VARIATIONAL PRINCIPLES FOR STOCHASTIC SHEAR BEAMS UNDER DETERMINISTIC LOADING

Probabilistic response of shear beams with stochastic flexibility, and subjected to deterministic static loads is studied in this paper. The differential equations governing the probabilistic responses, as well as the variational principles for the probabilistic responses are formulated apparently for the first time. New exact solutions are also derived for specific cases. Stochastic versions of Galerkin and Rayleigh-Ritz method are then applied to obtain approximate solutions when exact solution is unfeasible to derive. Both the exact and the approximate solutions possess a unique characteristic : they are applicable to any value of the coefficient of variation. Previous investigations were unable to capture this remarkable characteristic.