Abstract
This paper is concerned with the earthquake analysis of suspension bridges, in which the effects of large deflections are taken into account. The first part of the study deals with an iteration scheme for the nonlinear static analysis of suspension bridges by means of tangent stiffness matrices. The concept of tangent stiffness matrix is then introduced in the frequency equation governing the free vibration of the system. At any equilibrium stage, the vibrations are assumed to take place tangent to the curve representing the force-deflection characteristics of the structure. The bridge is idealized as a three dimensional lumped mass system and subjected to three orthogonal components of earthquake ground motion producing horizontal, vertical and torsional oscillations. By this means a realistic appraisal is achieved for torsional response as well as for the other types of vibration. The modal response spectrum technique is applied to evaluate the seismic loading for the combination of these vibrations. Various numerical examples are introduced in order to demonstrate the method of analysis. The procedure described enables the designer to evaluate the nonlinear dynamic response of suspension bridges in a systematic manner.
Highlights
The suspension bridge is a highly nonlinear three dimensional structure
This paper is concerned with the earthquake analysis of suspension bridges, in which the effects of large deflections are taken into account
The natural frequencies and mode shapes of the structure are obtained from a solution of the eigenvalue problem in which the frequency determinant is expressed in terms of the tangent stiffness matrix of the system
Summary
The suspension bridge is a highly nonlinear three dimensional structure. As a consequence, in dynamic studies the governing nonlinear equations of motion are frequently simplified by introducing assumptions which linearize these equations [1]. The natural frequencies and mode shapes of the structure are obtained from a solution of the eigenvalue problem in which the frequency determinant is expressed in terms of the tangent stiffness matrix of the system Once these fundamental dynamic properties are determined, the response spectrum concept can be used in conjunction with classical modal analysis to evaluate the seismic forces acting on suspension bridges during earthquakes. Details of these two basic steps are given
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