Approximate Floor Acceleration Demands in Multistory Buildings. I: Formulation

An approximate method to estimate floor acceleration demands in multistory buildings responding elastically or practically elastic when subjected to earthquake ground motion is presented. The method can be used to estimate floor acceleration demands at any floor level for a given ground motion record. The dynamic characteristics of the building are approximated by using a simplified model based on equivalent continuum structure that consists of a combination of a flexural beam and a shear beam. Closed-form solutions for mode shapes, period ratios, and modal participation factors are presented. The effect of reduction of lateral stiffness along the height is investigated. It is shown that the effect of reduction in lateral stiffness on the dynamic characteristics of the structure is small in buildings that deflect laterally like flexural beams. For other buildings, approximate correction factors to the closed-form solutions of the uniform case are presented to take into account the effects of reduction of lateral stiffness. Approximate dynamic properties of the building are then used to estimate acceleration demands in the building using modal analysis.