AbstractThe theoretical background and capabilities of a program for stochastic analysis of plane frames of reinforced concrete, under seismic excitation with emphasis on the analysis of stiffness degradation due to severe plastic deformations, are presented. As a constitutive moment-curvature relation an extended version of the model of Roufaiel-Meyer, taking into account the transition from uncracked to cracked sections, has been applied. Further, a different mechanism for the strength deterioration is utilized.Different positive and negative yield moments for unsymmetrical cross-sections may be specified, as well as moments and axial forces due to gravity loads or due to residual stresses from plastic deformations during previous earthquake excitations. The effect of axial forces on the moment-curvature relationship is taken approximately into account through a modified initial yield moment. The $P\; -\; \sigma$ effect of the axial force is considered by the introduction of a global geometrical stiffness matrix. The finite length of plastic length of plastic end zones is taken into account, controlling the plasticity at the end sections and at three internal cross-sections of the member. Incremental bending stiffness between these control sections is determined by linear interpolation. The stochastic earthquake excitation may be specified either as a standardized acceleration time-series, applied at the earth-surface and scaled with stochastically varying maximum acceleration and duration, or as an intensity modulated Gaussian white noise process filtered through a Kanai-Tajimi filter. Based on Monte-Carlo simulation the program calculates the mean values and the standard deviations of storey displacements and bending moments in critical sections, as well as the mean values, standard deviations and correlation coefficients of various maximum softening damage indicators, defined from time-averaged first and second eigen-periods.In order to reduce the calculation time during extensive simulations, a system reduction scheme has been implemented, based on a truncated expansion of external nodal point degrees-of-freedom in the linear eigenmodes of the initial undamaged structure. Further, only beam-elements, with non-linear behaviour are treated as nonlinear elements. These elements are identified adaptively during the simulation process. In order to demonstrate the ability of the program to predict the actual seismic response of reinforced concrete structures, computed results have been successfully compared to the experimentally recorded results of a 10-storey 4-bay reinforced concrete model.