Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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



Michael Valley, Mark Aschheim, Craig Comartin, William Holmes, Helmut Krawinkler, Mark Sinclair


In 2008, NIST initiated Task Order 68241 entitled "Improved Nonlinear Static Seismic Analysis Procedures – Multiple-Degree-of-Freedom Modeling." The purpose of this project was to conduct further studies on multiple-degree-of-freedom effects as outlined in the Federal Emergency Management Agency (FEMA) report, FEMA 440, Improvement of Nonlinear Static Seismic Analysis Procedures (FEMA, 2005). The FEMA 440 Report 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. It further concluded that improved nonlinear analysis techniques to more reliably address MDOF effects were needed. In response, work on this project was structured to include a detailed review of recent research on nonlinear MDOF modeling and the conduct of focused analytical studies to fill gaps in available information. This work was intended to improve nonlinear MDOF modeling for structural design practice by providing guidance on: (1) the minimum level of MDOF model sophistication necessary to make performance-based engineering decisions; (2) selection of appropriate nonlinear analysis methods; and (3) possible alternative approaches to analytical modeling.
Grant/Contract Reports (NISTGCR) - 10-917-9
Report Number


NEHRP Consultants Joint Venture, ATC, Nonlinear Static Procedure, MDOF, Earthquake Engineering


Valley, M. , Aschheim, M. , Comartin, C. , Holmes, W. , Krawinkler, H. and Sinclair, M. (2010), Applicability of Nonlinear Multiple-Degree-of-Freedom Modeling for Design, Grant/Contract Reports (NISTGCR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed July 25, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created September 15, 2010, Updated February 19, 2017