Damping modeling is important for the accurate evaluation of the seismic response of structures. Our group previously reported a damping modeling method using element Rayleigh damping and evaluated the effectiveness using a simple lumped-mass model with multiple damping properties; however, the effectiveness of the method was not evaluated for three-dimensional (3D) finite element method (FEM) models with multiple damping properties. Moreover, further studies showed that the method needed to be improved to be applied to 3D FEM models. Therefore, the method has been improved to enable application to the seismic analysis of 3D FEM models, and the effectiveness of the method has been evaluated. The proposed method uses a weighted least-squares method to automatically determine the coefficients of element Rayleigh damping. The weighted least-squares method minimizes the differences between the modal damping ratios to be modeled and those given by element Rayleigh damping. Although all modal damping ratios in a simple lumped-mass model were used for damping modeling in our previous study, obtaining them for 3D FEM models is impractical because these models have more natural modes than simple lumped-mass models. Therefore, we used modal damping ratios below a cut-off frequency. The effectiveness of the proposed method was evaluated by comparing it with conventional methods in terms of the modeling errors related to the modal damping ratios and the maximum absolute acceleration. The proposed method tended to have lower errors than the conventional methods and is concluded to be more effective for the seismic analysis of 3D FEM models with multiple damping properties. The proposed method can automatically determine the coefficients of element Rayleigh damping and can more accurately model the damping properties of analysis models, indicating that the proposed method is a powerful tool for the seismic analysis of 3D FEM models with multiple damping properties.

Two simplified methods for evaluating seismic margin due to elasto-plastic response were proposed. Generally, elasto-plastic response is evaluated by nonlinear time-history response analysis using three-dimensional FEM model (3D FEM model). It, however, takes an immense amount of time with commonly used computers. In order to evaluate it in a shorter time, this study developed seismic margin evaluation methods using Equivalent Single Degree Of Freedom (ESDOF) model and elasto-plastic response spectrum. Additionally, the accuracy of the two methods was verified by static loading tests and vibration tests. Simple cantilever test specimens with several natural frequencies were used in the vibration tests, and input waves with several frequency characteristics were applied to each vibration test. Response displacement, response acceleration of the test specimens and input acceleration were measured in each vibration test. Maximum displacement given by ESDOF model of the test specimens was compared with the corresponding measured values of each vibration test in order to verify the accuracy of ESDOF model. Difference between the maximum displacement given by the ESDOF model and the vibration tests was around 5%, and computation time of the ESDOF model was one-tenth of 3D FEM model of the test specimens. In addition, elasto-plastic response spectrum of input waves in the vibration tests were compared with measured yield accelerations of the specimens in order to verify the accuracy of elasto-plastic response spectrum. Difference between the calculated elasto-plastic response spectrum and the measured yield acceleration of the test specimens was around 10%, and computation time of elasto-plastic response spectrum was one-tenth of the 3D FEM model. As a result, it is concluded that ESDOF model and elasto-plastic response spectrum are powerful tool to evaluate seismic margin.

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