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A mathematical basis for the convergence of the capacity spectrum method

The capacity spectrum method is adopted by the ATC‐40 document for evaluating the inelastic deformation demands of reinforced concrete structures. Several studies have shown that the iterative procedure needed in the method may not give convergent outcomes in some cases. This paper focuses on the convergence of the capacity spectrum method in the constant velocity region of the response spectrum. The results obtained from the examples discussed in this study show that the convergent characteristics of this method depend on the elastic period, the hysteretic damping model, the yield displacement and the ductility ratio of the system analyzed. The capacity spectrum method can converge only for the case that the absolute value of the first derivative of the government equation derived from the demand and capacity diagrams of structures is smaller than 1.0. Copyright © 2004 John Wiley & Sons, Ltd.