Abstract Summary
The one of the authors proposed the causal hysteresis damping and the extended Rayleigh damping as damping models with low frequency dependence for damping ratio. The causal hysteretic model is based on the causality theory and past displacements are used in the calculation. The extended Rayleigh damping uses the causal hysteresis damping instead of the stiffness proportional part while both stiffness proportional part and mass proportional part are used in ordinal Rayleigh damping. However, only linear analysis has been studied well, and non-linear analysis has not been sufficiently studied for these damping properties. In this report, nonlinear time history response analyses are examined in addition to linear analyses for following models. The 20-story (60 m height) building is studied by a lumped mass model and its structure is either reinforced concrete (RC) or steel. For nonlinear analyses, the degrading-trilinear hysteretic curve is used for RC structure while the normal-trilinear hysteresis curve is used for steel structure. For linear analyses, Rayleigh damping, causal damping, and extended Ray damping are studied by comparing with modal damping. For nonlinear analyses, the same damping models as above of initial and tangent types are studied by comparing with nonlinear modal damping. The study is carried out by expanding the frequency range where damping ratio should be kept constant defined by 2 frequencies (F1 and F2). In the expansion analyses, F2 is changed from the horizontal second eigen frequency to the vertical first eigen frequency while F1 remains the horizontal first order frequency. This expansion is needed to consider from horizontal input only analysis to both horizontal and vertical simultaneous inputs analysis. Following results were obtained. 1) It can be confirmed that causal damping and extended Rayleigh damping are more accurate than Rayleigh damping in both linear and nonlinear analyses. 2) However, the greater the nonlinearity, the smaller the difference between these results and they were almost similar, finally. 3) For steel structures using the normal-trilinear hysteretic curve, both initial and tangent types have almost the same accuracy. However, for RC structures using the degrading-trilinear hysteretic curve, tangent type is better than initial type.
