Slepian simulation of distributions of plastic displacements of earthquake excited shear frames with a large number of stories

The object of study is a stationary Gaussian white noise excited plane multistory shear frame with a large number of rigid traverses. All the traverse-connecting columns have finite symmetrical yield limits except the columns in one or more of the bottom floors. The columns behave linearly elastic within the yield limits and ideally plastic outside these without accumulating eigenstresses. Within the elastic domain the frame is modeled as a linearly damped oscillator. The white noise excitation acts on the mass of the first floor making the movement of the elastic bottom floors simulate a ground motion that interacts with the structure above the bottom floors. As in a recent work by the authors the paper is about application of so-called Slepian model simulation, but in this paper supplemented by a simplification principle that allows a manageable calculation for the considered type of elasto-plastic oscillator also when it has a large number of elasto-plastic columns.