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Response Spectrum Analysis (RSA) and modal combination techniques are widely used to estimate the peak response of structures subjected to earthquake vibrations. This paper presents the numerical modeling and seismic analysis of structures. The response spectra based on Eurocode 8 is implemented for a five storey moment-resisting 3D structure to estimate peak response to earthquake-induced vibration. Eigenvector analysis is carried out to determine undamped free vibration mode shapes and frequencies. The lumped mass matrix, stiffness matrix of the full 3D structure is derived and natural periods, modal shapes, modal participation factors, and effective modal mass ratios are calculated. The structural response in different modes is combined to estimate the total dynamic response. The Square Root of Sum of Squares (SRSS), Complete Quadratic Combination (CQC), and Absolute Sum (AbsSum) rules are discussed and compared. The results of the SRSS and CQC rule for the examined building are almost identical as all cross-correlation coefficients are approximately equal to zero, and the responses of the individual modes are completely uncorrelated. CQC rule is appropriate when the natural frequencies are close to each other. AbsSum method shows an upper bound estimate of the total response since it assumes that all modal peaks occur at the same time. The simulation for numerical modeling and response spectrum analysis (RSA) is implemented in MATLAB® software.

Three-Dimensional Numerical Model for Seismic Analysis of Structures