Response spectra of two-story frames with racks on the elastic floor

Abstract

Two-story frames with six-story racks placed on the first floor is studied for the elastic shear force spectra of the frame and the rack. Three types of models are analyzed: racks as independent structures, simplified structures on which racks are live loads (SS), and the real structures (RS). The SS models are used in current design practice, and RS is used to check the adequacy of the SS models. Base shear force spectra of racks as independent structures and the ground floor and first floor shear force spectra of SS are determined for an ensemble of 102 earthquake records used in this paper. The relationship between the periods of three types of models are established. For the study of main structures, two kinds of story shear force ratio spectra of the RS to the SS with different periods as the abscissa are presented to check the adequacy of the current practice treating racks as live loads. Equations are proposed for the shear force ratio spectra and are compared with the numerical statistical data. For the racks on the floor, the ratios of the bottom shear force of racks in RS to those in SS, determined in proportion to mass of the rack, are computed. The bottom shear forces of racks in the RS are also compared with those of racks as independent structures. Equations for two kinds of rack's shear force ratio are presented for modifying the base shear force of racks in practice. Simplified design methods are provided both for the frame and for the racks on the floor.