Civil Engineering Association

Applicability of Nonlinear Multiple-Degree-of-Freedom Modeling for Design

Prevailing practice for performance-based seismic design is based largely on products that have been developed under the direction of National Earthquake Hazards Reduction Program (NEHRP) agencies and other key contributors. Many of
these documents recognize and allow several different performance-based analytical methods, but much of their focus is on nonlinear static analysis procedures.
The Federal Emergency Management Agency (FEMA) report, FEMA 440 Improvement of Nonlinear Static Seismic Analysis Procedures (FEMA, 2005), was
commissioned by FEMA to evaluate and develop improvements to nonlinear static
analysis procedures. In FEMA 440, differences between nonlinear static and
nonlinear response history analysis results were attributed to a number of factors
including: (1) inaccuracies in the “equal displacement approximation” in the short
period range; (2) dynamic P-Delta effects and instability; (3) static load vector assumptions; (4) strength and stiffness degradation; (5) multiple-degree-of-freedom effects; and (6) soil-structure interaction effects. Recommendations contained within FEMA 440 resulted in immediate improvement in nonlinear static analysis procedures and were incorporated in the development of the American Society of Civil Engineers (ASCE) standard ASCE/SEI 41-06, Seismic
Rehabilitation of Existing Buildings (ASCE, 2007). The FEMA 440 report, however, also identified certain technical issues needing additional study. These included: (1)
expansion of component and global modeling to include nonlinear degradation of strength and stiffness; (2) improvement of simplified nonlinear modeling to include multiple-degree-of-freedom effects; and (3) improvement of modeling to include soil-foundation-structure interaction effects.
FEMA has since supported further developmental work on the first of these issues, nonlinear degradation of strength and stiffness. The results of this work are
contained in the FEMA P-440A report, Effects of Strength and Stiffness Degradation on Seismic Response (FEMA, 2009a).
Regarding the second of these issues, FEMA 440 concluded that current nonlinear static analysis procedures, which are based on single-degree-of-freedom (SDOF) models, are limited in their ability to capture the complex behavior of structures that experience multiple-degree-of-freedom (MDOF) response, and that improved nonlinear analysis techniques to more reliably address MDOF effects were needed.

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