Evaluation of NSP to Estimate Seismic Deformation: SDF Systems

• Published in: Journal of structural engineering (New York, N.Y.) Vol. 126; no. 4; pp. 482 - 490
• Main Authors: Chopra, Anil K, Goel, Rakesh K
• Format: Journal Article
• Language: English
• Published: American Society of Civil Engineers 01.04.2000
• Subjects: TECHNICAL PAPERS
• ISSN: 0733-9445; 1943-541X
• DOI: 10.1061/(ASCE)0733-9445(2000)126:4(482)

Investigated in this paper is the approximation in the ATC-40 nonlinear static procedure (NSP) that the earthquake-induced deformation of an inelastic single-degree-of-freedom (SDF) system can be estimated by an iterative method requiring analysis of a sequence of equivalent linear systems. Several deficiencies in the ATC-40 Procedure A are demonstrated. This iterative procedure did not converge for some of the systems analyzed. It converged in many cases, but to a deformation much different than dynamic (nonlinear response history or inelastic design spectrum) analysis of the inelastic system. The ATC-40 Procedure B always gives a unique value of deformation, same as that determined by Procedure A if it converged. These approximate procedures underestimate significantly the deformation for a wide range of periods and ductility factors with errors approaching 50%, implying that the estimated deformation is about half the "exact" value. Surprisingly, the ATC-40 procedures are deficient relative to even the elastic design spectrum in the velocity-sensitive and displacement-sensitive regions of the spectrum. For systems with a period in these regions, the peak deformation of an inelastic system can be estimated from the elastic design spectrum using the well-known equal displacement rule. However, the approximate procedure requires analyses of several equivalent linear systems and still produces worse results.