Effectivity Factor Method in Structural Reliability: Fid-Bau Portal

Effectivity Factor Method in Structural Reliability

Ditlevsen, O. / Arnbjerg-Nielsen, T.

Abstract From a practical reliability analysis point of view ideal rigid-plastic yield hinge structural models are very attractive. This is due to their clear way of functioning. In fact, the most fundamental geometrical and statical conditions of the real structures are satisfied at least to the first order by such models. However, such models may not be sufficiently realistic with respect to the physical conditions at the yield hinges. Also the beams may not be rigid enough for second order bending effects not to have substantial influence on the collapse load. It is illustrated in this paper by an example that there is a conceptually simple way to make accurate reliability analysis of proportionally loaded yield hinge structural models of the following type. Between the potential yield hinges the beams are elastic and in the potential yield hinges there is a strain softening mutual rotation-moment behavior upon the onset of yielding. The method is as follows. The random maximal yield moment capacities of the given model are everywhere reduced by a common random effectivity factor v which is a function of the vector X of basic random load and strength variables. The effectivity factor function v(X) is approximated by a zero order or first order Taylor expansion with expansion point equal to the most central limit state point corresponding to the considered rigid-ideal plastic collapse mode with unreduced yield moments. The coefficients of the Taylor expansion are computed by use of the realistic model of the structure for a necessary number of at least 1+dim(X) sets of values of the maximal yield moments chosen in the vicinity of the expansion point. Hereafter the structure is reliability analysed according to the rigid plastic model with random yield moments equal to the reduced maximal yield moments of the realistic model. This example illustration follows after a general formulation of the effectivity factor method with potential applications on any physically admissible limit state which can be suitably idealized into another physically admissible limit state.