Limit Load Analysis of Plane Frames Under Stochastic Uncertainty

Using the first collapse theorem the necessary and sufficient constraints of a structure consist of the yield condition and the equilibrium condition. In the recent field of research stochastic uncertainties have been taken into account. This leads to a stochastic optimization problem which cannot be solved using the traditional methods. Instead of that appropriate (deterministic) substitute problems must be formulated. In the following, the limit load analysis of plane frames is treated where the load is supposed to be stochastic. Here, both forces and moments have to be taken into consideration. The recourse problem will be formulated in general and in the standard form of stochastic linear programming (SLP). After the formulation of the stochastic optimization problem, the expected value problem and the recourse problem with discretisation are introduced as representatives of substitute problems. Subsequently, some numerical results of the application of the presented methods to a two-storey frame are shown.