Stochastic Equivalent Linearization for 3‐D Frames

Abstract

Recent state‐of‐the‐art reports emphasize the generality of stochastic equivalent linearization techniques in the nonlinear dynamic analysis of stochastically excited structures. When a three‐dimensional frame is considered, it cannot be studied by decomposing the structure into several plane frames due to the impossibility of summing the effects that characterize nonlinear analyses. The equations of motion must be written for the whole structure. This is made possible by the knowledge of the constitutive law for the single story of the frame. Such a constitutive law can be identified from experimental data for regular buildings; otherwise, its dependence on the geometrical and mechanical properties of each structural element must be specified. This paper shows how the equations of motion can be written starting from the hysteretic constitutive law in the single potential plastic hinge in terms of the two bending moments and of the associate inelastic rotations. The generalization, including axial and shear forces and twisting moment in every beam section, is straightforward, but the dimension of the solving system for the equations quickly becomes impressive. Limitation to the bending moments provides the general features of the response and permits the analyzer to determine possible global torsional effects.