A Modal Pushover Analysis Procedure to Estimate Seismic Demands for Buldings

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A Modal Pushover Analysis Procedure to Estimate Seismic Demands for Buldings

info:
by:
Anil K. Chopra, University of California - Berkeley
Rakesh K. Goel, California Polytechnic State University - San Luis Obispo

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*n = mφn, where m is the mass matrix and φn its nth-mode, and the structure is pushed to the roof displacement determined from the peak deformation Dn of the nth-mode elastic SDF 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 rno of the inelastic MDF system to individual modal terms, peff,n(t) = −snüg (t) , in the modal expansion of the effective earthquake forces, peff,n (t) = −mιüg (t) . The base shear-roof displacement (Vbn −um ) curve is developed from a pushover analysis for force distributions*n. This pushover curve is idealized as bilinear and converted to the force-deformation relation for the nth-“mode” inelastic SDF system. The peak deformation of this SDF system is used to determine the roof displacement, at which the seismic response, rno , is determined by pushover analysis. Second, the total demand, ro , is determined by combining the rno (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 results presented for El Centro ground motion scaled by factors varying from 0.25 to 3.0, show that MPA estimates the response of buildings responding well into the inelastic range to a similar degree of accuracy when compared to standard RSA for estimating peak response of elastic systems. Thus the MPA procedure is accurate enough for practical application in building evaluation and design.
Comparing the earthquake-induced demands for the selected 9-story building determined by pushover analysis using three force distributions in FEMA-273, MPA, and nonlinear RHA, it is demonstrated that the FEMA force distributions greatly underestimate the story drift demands, and the MPA procedure is more accurate than all the FEMA force distributions methods in estimating seismic demands. However, all pushover analysis procedures considered do not seem to compute to acceptable accuracy local response quantities, such as hinge plastic rotations. Thus the present trend of comparing computed hinge plastic rotations against rotation limits established in FEMA-273 to judge structural performance does not seem prudent. Instead, structural performance evaluation should be based on story drifts known to be closely related to damage and can be estimated to a higher degree of accuracy by pushover analyses.



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A Modal Pushover Analysis Procedure to Estimate Seismic Demands for Buildings: Theory and Preliminary Evaluation

Anil K. Chopra
University of California
Berkeley
Rakesh K. Goel
California Polytechnic State University
San Luis Obispo
A report on research conducted under grant no. CMS-9812531
from the National Science Foundation:
U.S.-Japan Cooperative Research in Urban Earthquake Disaster Mitigation


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 *
sn =mφn , where m is the
mass matrix and φ n its nth-mode, and the structure is pushed to the roof displacement
determined from the peak deformation Dn of the nth-mode elastic SDF system. Combining
these peak modal responses by modal combination rule leads to the MPA procedure

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A Modal Pushover Analysis

A report on research conducted under Grant No. CMS-9812531 from the National Science Foundation: U.S. Japan Cooperative Research in Urban Earthquake Disaster Mitigation.

Abstract:
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.

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