Study On Response Spectra, Ground Motion And Structural Vulnerability

This paper makes up of three partsThe first part mainly involves the calculation of response spectrum. In the first section we talk about the basic ideas of the promotion which is the foundation of the promotion of the next several sections;in the second section we make an extension to the exact step by step integration method which calculates the response spectrum, and the numerical example shows that this promotion is successful; in the third section, we put this promotion to the higher order, and also gives the derivation formula; in the fourth section, we use the Romberg integration formula to make a promotion to the exact step by step integration method, finally, examples demonstrate the reasonableness of this promotion; in the fifth section, we compare the exact step by step integration method with convolution method which also calculates response spectrum, and profoundly point out the shortcomings of the convolution method when it was used to calculate the response spectrum, and point out that the convolution method has serious shortcomings in efficiency and precision when it was used to calculate the response spectrum. Finally, we do a summary to this part.The second part involves the comparison of the relative strength of ground motion. First, we make a description to the physical meaning of Fourier transform. It is necessary to reduce the number of ground motion indicators since there are too many indicators which describe ground motion intensity, and we also need to know which indicators are important and which indicators are less important, and thus we introduced to the principal component analysis to seismic analysis, we give a method to measure the relative strength of ground motion. Finally, we do a little summary to this part. As excessive, we also do a little thinking to the relationship between the intensity of ground motion and structure vulnerability.The third part, which follows the previous section, we also introduce the principal component analysis to the structural vulnerability, and we give a method to measure the relative vulnerability of the structural when the same structure receives different ground motions. At present, the standard response spectrum in Code for seismic design of buildings only takes into the peak and the spectrum of the ground motion, does not take into account the duration of the ground motion, therefore, the main research followed in this part studies the ground motion duration effects on the structural vulnerability, and we draw the conclusion that the duration effects on the structural vulnerability is small when the peak of ground motion is small and the duration effects on the structural vulnerability is big when the peak of ground motion is big. We draw the conclusion that the peak of ground motion is the main factor for the structural vulnerability. Finally, the author studies the difference of damage between single-stage load exerted on structure and step by step load on structure.In the last chapter, we do a summary to the previous work.