Analytical Solutions for Earthquake Responses of Single-span,One-story Structure to Wave Passage Excitation
In order to explore the mechanism of earthquake wave passage effect for small-span structure,the influence of frequency content in earthquake wave on wave passage effect is studied in this paper.The analytical solutions of structural responses to earthquake wave passage excitation for a single-span,one-story structure are given in this paper.The dynamic equilibrium equation for the structure subjected to earthquake wave passage excitation is given,and the relative motion method is adopted to solve the equation.The analytical solutions in series form of absolute displacement of the roof and column shear forces are derived respectively.The peak column shear forces for earthquake waves with sufficient and insufficient frequency contents are studied respectively.It is found that the analytical solutions of column shear forces to wave passage excitation are not only related to the time delay,but also related to the square of the ratio of structural fundamental frequency to excitation frequency.For the earthquake waves with sufficient low-frequency content,the peak column shear forces under wave passage excitation are larger than those under uniform excitation.On the contrary,the peak column shear forces under wave passage excitation are smaller than those under uniform excitation for the earthquake waves with insufficient low-frequency content.The results show that the earthquake wave passage effect for small-span structure depends not only on the time delay,but also on the low-frequency content.There are wave passage effects for small-span structures subjected to the earthquake waves with sufficient low-frequency content,and the more sufficient low-frequency content in earthquake wave,the more obvious wave passage effect.The wave passage effects will not occur for those earthquake waves in which the low-frequency contents are not sufficient.
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