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Abstract
This study develops a modified multi-support response spectrum (MSRS) method, in order to efficiently and accurately calculate the response of multi-support structures under incoherent ground motions. The modified MSRS method adopts three ancillary processes, constructing structural displacement vectors or constructing infinite stiffness members or increasing the degrees of freedom at structural supports. Then, the modified MSRS method is verified in a comparison with the existing MSRS method through a model of a five-span reinforced concrete continuous rigid frame bridge. Finally, the collective structural response spectrum, the structural power spectrum, and the simplified structural power spectrum are deduced from the equation of the motion taking ground motion displacements as the input, and validated through the same bridge model.
Highlights
In recent decades, multi-support structures, such as long-span bridges, in cities or on coasts have been constructed with the development of infrastructures around the world [1]
The bending moment and the biggest displacement at this point calculated by the Complete Quadratic Combination (CQC) method are zero under coherent ground motion, while the corresponding values calculated by the multi-support response spectrum (MSRS) method are 322 kN∙m and 4.075 mm, respectively
This study further verifies that the MSRS method without the contribution of the structural support degrees of freedom in the seismic response of the multi-support structure can result in a large deviation of the structural response, when near to the structural supports
Summary
Multi-support structures, such as long-span bridges, in cities or on coasts have been constructed with the development of infrastructures around the world [1]. This tendency is promoting the development of analytical techniques for the structural elastic working behavior in both calculating efficiency and simulating accuracy [15] Infrastructures, such as multi-support structures and long-span structures, are huge in scale and complex in configuration. In the real situation, a structure presents two different features: (a) the structure undergoes a relatively low-intensity ground motion in the linear phrase of structural vibration; (b) all the parts of the structure could achieve their working states, only when the ground motion reaches to a certain intensity This implies that the MSRS method might overestimate or underestimate the anti-seismic ability of the structure, even in its linear analysis. In view of the problems mentioned above, a modified MSRS method in this study is proposed to calculate the seismic response of long-span or multi-support structures under incoherent ground excitations more concisely and accurately, which can provide the useful reference to the rational seismic design of the bridge with multi-supports. This study tries to obtain the collective structural response spectrum and structural power spectrum from the equation of the motion taking ground motion displacements as the input; it proposes the simplified structural power spectrum
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