Inelastic Displacement Spectrum Of Single Degree Of Freedom Systems Under StrongVertical Earthquakes

Based on the SDOF system to study the super high-rise building is a simple and practical method, and using this method to study the elastic structrue suffering the horizontal earthquake ground motion has entered its mature stage. In order to understand the structure’s horizontal mechanical property when the structrue comes into plastic stage, people usually use the SDOF system’s Rμ-μ-T spectrum to reduct the maximum restoring force which is getting from the SDOF elastic system. Rμ-μ-T spectrum is a response mean spectrum, which using a series of real earthquake groud motions selected under some certain conditions to act on a single-degree-of-freedom (SDOF) system to calculate the system’s displcements, then use these displcements to calculate the strength-reduction factor RM under assigned constant ductility coefficient, finally setting RM as the vertical axis and T as the horizontal axis to make the spectrum. There are a lot of studys on horizontal Rμ-μ-T spectrum, and the studys’whole variation tendency of Rμ-μ-T spectrums is basically the same at home and abroad. But for the vertical Rμ-μ-T spectrum, the study is less and the SDOF system’s response mechanism under vertical strong earthquake ground motions is not definite. So, this problem is needed to be solved.This paper aims at analyzing the SDOF elasto-plastic system’s response laws under vertical strong ground motions, after studying the SDOF elasto-plastic system’s responses for the different vertical strong earthquake motions under different site classfications and making the constant ductility coefficient Rμ-μ-T spectrum which has statistic meanings.So, first this paper selects208vertical strong earthquake ground motions upon B/C/D/E site classifications. Then referring to the horizontal hysterestic model of SDOF elasto-plastic system and vertical component hysteresis model, we abstract the vertical bilinear hysteresic model which can change its ratio (fyp) of axial compressive-tensile yield strength. Finally, using the Matlab to write programs, and under vertical strong ground motions to calculate the responses of SDOF elasto-plastic systems which has been vested five hysteresis models, and postprocessing the datas to make the vertical RM-μ-T spectrums. When calculating, we find that the Jingqing Zhu’s method of processing the inflection points is not accurate enough, so based on the Newmark-fl method we derive a new method which improves the datas’ accuracy of inflection points to order of magnitude of10"18. This method is used for processing the model’s unloading point, and the original point which produced because of the different stiffnesses in the first and third quadrant in the initial elastic stage of the hysteretic model.Through studying, we find that the Rvalue of the vertical Rμ-μ-T spectrum depends on the structure’s initial natural period of vibration To, displacement ductility coefficient μ and site classification, this is in accordance with the study of horizontal Rμ-μ-T spectrum at home and abroad. But the value Rμ, and amplitude of variation are obviously influnced by the vertical hysteretic model, especially the parameter fyp. In addition, in the same ductility coefficient, the value Rμ will change with the period T, and its trendency is not consistent with the variation trend of the horizontal Rμ-μ-T spectrum (large variation in amplitude in the short period, and showing a rising trend; small fall or none but variating near a constant value in the long period). This inconsistency is influnced by the ratio of axial compressive-tensile yield strength fyp,, constant ductility coefficient μ, site classification SC and the ground motions etc. The site classification will give a different influnce to different hysterestic models, especially when the value of constant ductility coefficient is large, this kind of variation is obviously. The hysterestic model’s ratio of axial compressive-tensile yield strength fyp’s influnce to the value of spectrum cannot be neglected, but through the observation from the vertical Rμ-μ-T spectrum, we find that when the value fyp is larger, its influnce’s trendency to spectrum’s value is the same with the larger value of μ and the hard ground.