The Earthquake Engineering Online Archive

A modal pushover analysis procedure to estimate seismic demands for buildings: theory and preliminary evaluation

Chopra, Anil K.; Goel, Rakesh K.

PEER-2001/03, Pacific Earthquake Engineering Research Center, University of California, Berkeley, 2001-01, 87 pages (400/P33/2001-03)

The principal objective of this investigation is to develop a pushover analysis procedure based on structural dynamics theory, which retains the conceptual simplicity and computational attractiveness of current procedures with invariant force distribution, but provides superior accuracy in estimating seismic demands on buildings. The standard response spectrum analysis (RSA) for elastic buildings is reformulated as a modal pushover analysis (MPA). The peak response of the elastic structure due to its nth vibration mode can be exactly determined by pushover analysis of the structure subjected to lateral forces distributed over the height of the building according to s* subscript n = (m)(phi subscript n), where m is the mass matrix and phi subscript n its nth-mode, and the structure is pushed to the roof displacement determined from the peak deformation D subscript n of the nth-mode elastic single degree-of-freedom system. Combining these peak modal responses by modal combination rule leads to the MPA procedure. The MPA procedure is extended to estimate the seismic demands for inelastic systems: first, a pushover analysis determines the peak response r subscript (n)(o) of the inelastic multidegree-of-freedom system to individual modal terms, in the modal expansion of the effective earthquake forces. The base shear-roof displacement curve is developed from a pushover analysis for force distribution s* subscript n. This pushover curve is idealized as bilinear and converted to the force-deformation relation for the nth-"mode" inelastic single degree-of-freedom system. The peak deformation of this single degree-of-freedom system is used to determine the roof displacement, at which the seismic response, r subscript (n)(o), is determined by pushover analysis. Second, the total demand, r subscript o, is determined by combining the r subscript (n)(o) (n = 1,2,...) according to an appropriate modal combination rule. Comparing the peak inelastic response of a 9-story SAC building determined by the approximate MPA procedure with rigorous nonlinear response history analysis (RHA) demonstrates that the approximate procedure provides good estimates of floor displacements and story drifts, and identifies locations of most plastic hinges; plastic hinge rotations are less accurate. The earthquake-induced demands for the selected 9-story building determined by pushover analysis are compared using three force distributions in FEMA-273, MPA, and nonlinear RHA.

Available online: http://peer.berkeley.edu/publications/peer_reports/reports_2001/0103.pdf