Dynamics of Structures on Two‐Spring Foundation Allowed to Uplift

Abstract

Investigated in this paper is the dynamics of structures with their foundation mat supported only through gravity and thus permitted to uplift from the supporting system. In its fixed base condition the structure is idealized as a single‐degree‐of‐freedom system attached to a rigid foundation mat, which is supported at each edge by a spring‐damper element. Analytical expressions are presented for the free vibration response of the system and the effects of foundation uplift are examined. An effective numerical procedure, based on expressions of the Rayleigh‐Ritz concept, to evaluate the structural response to earthquakes is presented. Based on the response spectra presented it is shown that foundation mat uplift has the effect of reducing the base shear for shortperiod structures, with these reductions being especially significant for the more slender structures.