An improved capacity spectrum method for ATC-40

In order to account for the non-linear behavior of structures via non-linear static procedure, the capacity spectrum method has been adopted by ATC-40 for evaluation and retrofit of reinforced concrete buildings. For elastic-perfectly-plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo-acceleration response spectrum (PSa) is used to create the demand diagram. It is found that the ATC-40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15 sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S-a) instead of the PSa to establish the demand diagram. The step-by-step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake-induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC-40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (mu) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when mu > 4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright (C) 2003 John Wiley Sons, Ltd.