Interaction of axial force and bending moment by using Bouc-Wen hysteresis and stochastic linearization

Among the probabilistic methods of analysis of multi-degree-of-freedom nonlinear structural systems, stochastic equivalent linearization is a common alternative to Monte Carlo simulation. Using the Bouc-Wen model in particular, may yield the equivalent system in analytical closed form, which is fundamental to efficient computation. Within this context, the Bouc-Wen model is here extended in a simple fashion to introduce the interaction of the resisting axial force and bending moment, as is typical of short columns. The member is idealized as a massless linearly elastic beam element provided with terminal rotational springs whose behavior follows the extended Bouc-Wen model. Consistent with a parabolic interaction diagram, the probabilistic moments of the response are formulated by the common stationary Gaussian nonzero-mean linearization method with random earthquake motion, deterministic gravity load and asymmetric hysteresis. The interaction model is validated by comparing the response of two portal frames, whose different sensitivity to interaction is captured. In addition, Monte Carlo simulation is carried out using a piecewise linear interaction model. The effect of parabolic interaction on the displacement and hysteretic rotation from linearization does not match quantitatively the piecewise-linear interaction in the simulation. Nevertheless, qualitative agreement is satisfactory. Full agreement appears between other response quantities. The proposed interaction model proves to be suitable at least for comparative probabilistic seismic analyses of framed structures with possible yielding of columns.