Postprint version. Published in Journal of Structural Engineering, Volume 126, Issue 4, April 1, 2000, pages 482-490. © American Society of Civil Engineers. The definitive version can be found online at http://dx.doi.org/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.
Civil and Environmental Engineering