DYNAMIC ANALYSIS OF BUILDING BY IMPLICIT METhOD OF INTEGRATION

Abstract

This dissertation presents the elastic dynamic response of reinforced concrete building frames of storeys varying from 1 to 15 using implicit time integration scheme. The building frames are idealised as plane frames with masses lumped. at the joints. Five time integration algorithms namely Newmark, Wilson, Bossak, Hilber and Zienkiewicz et.al. have been used to solve the equations of motion. Stiffness matrix of the structure has been formed by considering both bending and shear deformations. Mass has been assumed to be lumped at nodes. The rotary inertia effect has also been considered in the mass matrix. Damping matrix is taken as a linear combination of mass and stiffness matrices. Dynamic response obtained by various algorithms'has been compared. Effect of variation of free parameters in the algorithms on the response have been studied. An attempt has been made to suggest the appropriate time step. It is observed that the different algorithms which have same algorithmic structure give comparable results. Bossak method is found to have high dissipation. Results of Zienkiewicz method are not affected by change in value of parameters when the parameters are choosen according to stability conditions. The time history response has been plotted for different structures. The time history response enables. us to study the building up of responses with application of Earthquake type of excitation and also the time of occurrence of maximum response.