Non-Iterative Equivalent Linearization Based on Secant Period for Estimating Maximum Deformations of Existing Structures

The capacity spectrum method of ATC-40 uses the secant period as the equivalent period of equivalent linear systems. Therefore, it results in a direct graphical comparison. The maximum inelastic displacement and acceleration demands of structures can be simultaneously obtained from the intersection of the demand and capacity diagrams. However, for evaluation of existing structures, the demands need to be determined through iterations since the equivalent period and damping of the equivalent linear systems currently available are both a function of the (displacement) ductility ratio, which is unknown and is the target of evaluation. In addition, the equivalent damping used in the capacity spectrum method is independent of periods of vibration. It may lead to poor estimations of maximum responses especially for short-period systems. This article proposes two equivalent linear systems based on the secant period to estimate the maximum displacement and acceleration responses of existing structures. Both the recommended equivalent period and damping are defined by the strength ratio (elastic lateral strength/yield lateral strength), rather than the ductility ratio. Because the strength ratio of existing structures is a known parameter, the maximum displacement and acceleration responses of these structures can be determined without iterations. Besides, effects of periods of vibration on the equivalent linear systems are also included in this study. The equivalent damping is derived from statistical analyses for bilinear single-degree-of-freedom (SDOF) systems with different periods of vibration, strength ratios and post-yield stiffness based on 72 earthquake ground motions recorded on firm sites. Procedures and examples for applications of the proposed equivalent linear systems on nonlinear static analysis procedures are also provided.