Optimal seismic analysis of degrading planar frames using a weighted energy method to associate inelastic mode shapes: Part II application

Thomas L. Attard, Apostolos Fafitis

Research output: Contribution to journalArticle


The objective of this study is to predict the seismic demands in four steel planar test buildings, including the absolute displacements at each floor and the local member strains, by formulating suitable equivalent single-degree of freedom (E-SDOF) systems. The E-SDOF systems are generated using the buildings' capacity curves and three specified parameters (established in Part I) that are used to determine the pre- and post-yielded portions of the systems. The computed demands are compared to those using a nonlinear time-history analysis and also to those determined using an equal-energy approach that utilizes only the structures' fundamental mode shapes. It is found that by assembling several inelastic mode shapes to generate individual pre-and postyield mode shapes, the ensuing E-SDOF system analysis leads to reasonably accurate inelastic displacement demands over the heights of the test structures, especially at the target location. These demands are also significantly more accurate than the demands computed using an equal-energy approach. Local member strains are also computed by analyzing the formulated E-SDOF systems although it is concluded that local responses are not predicted with consistent accuracy over the buildings' heights. The entire procedure is automated using the program EQ-CAP (EQuivalent SDOF Formulation/CAPacity curves), which enables demands to be readily predicted without the need of a nonlinear time-history analysis.

Original languageEnglish (US)
Pages (from-to)1990-2000
Number of pages11
JournalEngineering Structures
Issue number8
StatePublished - Aug 1 2007



  • Capacity curves
  • E-SDOF formulation
  • Equal-energy approach
  • Local/global responses

ASJC Scopus subject areas

  • Civil and Structural Engineering

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