Abstract
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.
Highlights
Many structures are vulnerable to earthquake excitation.Reliable and practical numerical simulation of structures subjected to earthquake excitation is essential
The response spectrum was generated by solving the equation of motion for a group of single degree of freedom (SDOF) systems subjected to an accelerogram or conducting a Probabilistic Seismic Hazard Analysis (PSHA) to obtain a uniform-hazard spectrum [3], a scenario spectrum [4] or a conditional mean spectrum [5]
Considering that the Square Root of Sum of Squares (SRSS) and Complete Quadratic Combination (CQC) modal combination rules are based on random vibration theory, the total response should be interpreted as the mean of the peak values of the response of many earthquake excitation
Summary
Reliable and practical numerical simulation of structures subjected to earthquake excitation is essential. Response Spectrum Method (RSM) was implemented to approximate the peak response of a structure to earthquake excitation. The peak value of each mode contribution to the response or the modal static response was calculated by static analysis of the building subjected to lateral forces. The peak total response is estimated by combining its peak modal values by the SRSS, CQC, and AbsSum rule [6]. Considering that the SRSS and CQC modal combination rules are based on random vibration theory, the total response should be interpreted as the mean of the peak values of the response of many earthquake excitation. The smooth spectrum can be the mean or median of the individual response spectra, or it can be a more conservative spectrum, such as the mean-plus-one-standard-deviation spectrum
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