Analytical Formulation and Response Analysis of a 3 Story Shear Frame subjected to Impulsive Loading

Abstract

The multi-story buildings are likely to be subjected to various types of dynamic loadings. In the present study, a three-story shear frame subjected to a rectangular pulse force at the top floor is studied and the equations for the floor displacements as functions of time have been obtained. Then the floor displacements under rectangular impulsive loading is plotted against time. One can easily observe that the displacement values at the top floor is maximum where the impulsive load is applied. On the other hand, the peak value of the response at the top floor is obtained at the end of the rectangular pulse force duration. The response of the system to pulse excitation does not reach a steady-state condition; the effects of the initial conditions must be considered. The response to such pulse excitations can be determined by several analytical methods. In the present study, the pulse was expressed as the superposition of two or more simpler functions for which response solutions are already available or easier to determine through modal analysis concept. The presented method of analysis can be applied to estimate the overpressure produced on structural elements due to impulsive loading. For blast analyses, the blast loads can be modelled as impulse loads assuming a uniform pressure applied to whole surface of the structure.