Dynamic analysis of rigid bodies on inclined plane surfaces: application to prediction of merchandise response in steel storage racks under earthquake excitation

Abstract eng:
In this study, an analytical model describing the dynamic behavior of slidingdominated rectangular rigid bodies placed on rigid inclined plane surfaces under bi-axial earthquake excitation is presented. In addition, the option of limiting the inward motion of the bodies with rigid walls perpendicular to the ground surfaces is taken into account, since it appears in many practical applications. The model incorporates planar rigid body dynamics, Coulomb and hysteretic friction laws, and Newtonian impact concepts. Three modes of response are considered: a rest mode, a slide mode and a free-flight mode. Conditions for transition from one mode to another are determined so as to result in consistent response behaviors. A consistent impact model is also derived for collisions of bodies with rough or frictionless boundaries assuming instantaneous impact and velocity-based coefficients of restitution to account for energy losses (Newton’s Hypothesis). The frictional behavior is described by a Coulomb rigid plastic spring in parallel with a modified Bouc-Wen spring. The proposed modification rectifies inherent inconsistencies of this rule when different static and kinetic coefficients of friction are considered. Variations of the frictional properties with the contact force and the relative velocity are also taken into consideration. The proposed model is implemented in a computer code and is used to investigate the response of palletized merchandise in steel storage racks under earthquake excitation. Experimental data from pull tests and shake table tests are used to calibrate the model and a comparison between predicted and measured response is provided. The numerical predictions appear to be in good agreement with the measured response.

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