Enhanced Displacement Coefficient Method for Degrading Multi-Degree-of-Freedom Systems

Abstract

The displacement coefficient method proposed in FEMA 440 was evaluated using response statistics from a comprehensive set of nonlinear simulations of multi degree of freedom systems under both far-fault and near-fault ground motions. The study finds that it is practically difficult to achieve high relative strength factors (R values equal to or greater than 6.0) for very stiff systems thereby dictating the need to define R-dependent demand coefficients. The approximate expressions proposed in FEMA 440 for the C₂ coefficient is shown to underestimate the displacement demand of stiffness-degrading short period systems. Additional nonlinear simulations were performed to investigate the combined effect of strength degradation and P-Delta effects on the displacement demands of MDOF systems. A new expression for the modification factor that reflect combined P-Delta and degrading effects for the estimation of displacement demands is proposed.

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References

Akkar

S. D.

, and Miranda

, 2005. Statistical evaluation of approximate methods for estimating max deformation demands on existing structures, J. Struct. Eng. 131, 160–172.

Akkar

S. D.

, and Metin

, 2007. Assessment of improved nonlinear static procedures in FEMA 440, J. Struct. Eng., 133, 1237–1246.

Applied Technology Council (ATC), 1996. Seismic Evaluation and Retrofit of Concrete Buildings, Vol 1, ATC-40, Redwood City, CA.

Applied Technology Council (ATC), 2005. Improvement of Nonlinear Static Seismic Analysis Procedures, FEMA-440, Redwood City, CA.

Federal Emergency Management Agency (FEMA), 2000. Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA 356, Washington, D. C.

Freeman

S. A.

, Nicoletti

J. P.

, and Tyrell

J. V.

, 1975. Evaluations of existing buildings for seismic risk—A case study of Puget Sound Naval Shipyard, Proceedings 1st U. S. National Conference on Earthquake Engineering, Berkeley, CA.

Gulkan

, and Sozen

, 1974. Inelastic response of reinforced concrete structures to earthquake motions, ACI J. 71, 604–610.

Gupta

, and Krawinkler

, 2000. Estimation of seismic drift demands for frame structures, Earthquake Eng. Struct. Dyn. 29, 1287–1305.

International Code Council (ICC), 2000. International Building Code, Falls Church, VA.

10.

Kowalsky

M. J.

, 1994. Displacement based design methodology for seismic design applied to RC bridge columns, Master's thesis, University of California, San Diego.

11.

Luco

, 2002. Probabilistic seismic demand analysis, SMRF connection fractures, and near-source effects, Ph.D. thesis, Stanford University, California.

12.

Mander

J. B.

, Priestley

M. J. N.

, and Park

, 1988. Theoretical stress-strain model for confined concrete, J. Struct. Div. 114, 1804–1826.

13.

Miranda

, and Ruiz-Garcia

, 2002. Evaluation of approx methods to estimate maximum inelastic displacement demand, Earthquake Eng. Struct. Dyn. 31, 539–560.

14.

OpenSEES, 2007. Open System for Earthquake Engineering Simulation. Available online; http://opensees.berkeley.edu.

15.

PEER NGA Strong Motion Database (2009). http://peer.berkeley.edu/nga/ (Accessed 8/10/2009).

16.

Ruiz-Garcia

, and Miranda

, 2003. Inelastic displacement ratios for evaluation of existing structures, Earthquake Eng. Struct. Dyn., 32, 1237–1258.