A Unified Form for Response of 3D Generally Damped Linear Systems Under Multiple Seismic Loads Through Modal Analysis

Abstract eng:
Accurate estimation of the seismic response of structures is an important issue in aseismic design. Under earthquake excitations, the deformation and internal force distributions of structures are quite complex. This is particularly true for irregular structures under multiple directional seismic loads. In most current engineering practice, only those response quantities which are linear combinations of the nodal displacements are considered to be critical for design. However, this may not always be the case, especially for those systems enhanced with high damping devices. For example, the relative nodal velocities are important for the design of the dampers and the nodal absolute accelerations determine the strength demand of the nonstructural components. This paper presents a time-history-based formulation of the responses for generally damped linear systems excited by multiple directional seismic loads through modal analysis. Solutions to the structural nodal displacements, the nodal velocity and absolute acceleration responses are derived. It is shown that the modal response quantities required in the nodal velocity and absolute acceleration are identical to those that are required in the structural displacement responses. Moreover, most response quantities of interest for seismic evaluation and design can be obtained through the linear transformation of the structural displacement, velocity or absolution acceleration as long as the structure remains in the elastic range (e.g. inter-story drift, story shear, nodal relative velocity, floor acceleration, etc.). A unified form capable of representing these response quantities is therefore established.

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