Self-similar interstory drift spectrum and response distribution of flexural-shear beam with nonuniform lateral stiffness

This paper proposes the concept of self-similar interstory drift spectrum based on the dimensional analysis of flexural-shear beam with nonuniform lateral stiffness, and scrutinizes the effects of lateral stiffness reduction on the seismic responses and response distribution. Firstly, the finite element formulation for the combined beam is established, which is convenient for parametric analysis. Subsequently, the intrinsic length scale and time scale are proposed to conduct correctly the dimensional analysis for seismic responses of flexural-shear beam, indicating that the normalized maximum interstory drift ratio and normalized maximum floor acceleration present a complete similarity in the normalized building height and the beauty of order. Hence, the concept of self-similar interstory drift spectrum is suggested to avoid the use of empirical relationship between fundamental period and building height. Moreover, the effects of lateral stiffness reduction on the normalized responses and response distribution of flexural-shear beam are examined under the idealized pulses and near-fault ground motions. With the exception of significant stiffness reduction, the effect of lateral stiffness reduction is generally small. In particular, the vertical distribution of interstory drift mainly depends on the structural type, whereas the floor acceleration generally increases along the building height. Finally, the established regression model can sufficiently fit the mean self-similar interstory drift spectrum and mean self-similar floor acceleration spectrum, and the normalized seismic responses can be well predicted by the fitted curves.