Study On Plastic Energy Spectrum Of Elastoplastic Single Degree Of Freedom System By Force Analogy Method

Plastic energy (PE) is one of the dissipative modes of the earthquake input energy for inelastic structures which is generally considered to be the main damage of structures due to the unrecoverable performance of the plastic deformation. When research of PE is investigated in deep, the plastic energy spectrum (PES) is a basic problem. Force analogy method (FAM) is a variable-displacement computing method. Compared with traditional nonlinear method, it overcomes the limitations of huge computation, long computing time and bad stability, and is reliability in nonlinear dynamic analysis. The appliciation of FAM into energy analysis could take the analysis of energy dissipation into the structural members. So, the combination of FAM and PES has engineering significance which can achieve more accurate results. Based on above reasons, the study contents in this article as follows:1) The static condensation is used to reduce rotational degrees of freedom. The motion equation is improved which just retain the displacement degrees of freedom. Based on FAM, the expression of plastic energy is found. According to the assumption of equivalent single degree of freedom system (ESDOF) and mode analysis method, two kinds of formulas of plastic energy of multi-degree freedom system (MDOF) and equivalent single degree of freedom (ESDOF) system are established. Some structures are uese to compare plastic energy of ESDOF and the plastic energy of MDOF to vertify the effectiveness and application conditions of the two kinds of formulas.2) The possible influencing factors of plastic energy spectrum are presented in two ways of engineering properties of ground motion and structure dynamic characteristics. Taken bilinear force-displacement curves into consideration, the formula of plastic energy of SDOF system based on FAM is improved. According to the plastic energy spectrum curve of SDOF system subjected to earthquake ground motions, the effects of the acceleration amplitude, ratio of the peak values of acceleration and velocity, strong motion duration of input ground motion and the damping ratio, yield strength coefficient, stiffness reduction factor of the structure are analyzed and discussed.3) With the effect of the influencing factors, the plastic energy spectrum of per unit mass is simplified into three parts. The peak value of standard spectrum can be calculated by ratio of the peak values of acceleration, velocity and strong motion duration of input ground motion. The adjusting coefficient for the peak values of plastic energy spectrum can be determined by the acceleration amplitude, the damping ratio, yield strength coefficient, and stiffness reduction factor. And also, the damping ratio and yield strength coefficien are used to compute the attenuation coefficient of descent part.The proposesd plastic energy spectrum is compared with the real plastic energy spectrum.