Near-optimal piecewise linear fits of static pushover capacity curves for equivalent SDOF analysis

Flavia De Luca*, Dimitrios Vamvatsikos, Iunio Iervolino

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

62 Citations (Scopus)
549 Downloads (Pure)


The piecewise linear ('multilinear') approximation of realistic force-deformation capacity curves is investigated for structural systems incorporating generalized plastic, hardening, and negative stiffness behaviors. This fitting process factually links capacity and demand and lies at the core of nonlinear static assessment procedures. Despite codification, the various fitting rules used can produce highly heterogeneous results for the same capacity curve, especially for the highly-curved backbones resulting from the gradual plasticization or the progressive failures of structural elements. To achieve an improved fit, the error introduced by the approximation is quantified by studying it at the single-degree-of-freedom level, thus avoiding any issues related to multi-degree-of-freedom versus single-degree-of-freedom realizations. Incremental dynamic analysis is employed to enable a direct comparison of the actual backbones versus their candidate piecewise linear approximations in terms of the spectral acceleration capacity for a continuum of limit-states. In all cases, current code-based procedures are found to be highly biased wherever widespread significant stiffness changes occur, generally leading to very conservative estimates of performance. The practical rules determined allow, instead, the definition of standardized low-bias bilinear, trilinear, or quadrilinear approximations, regardless of the details of the capacity curve shape. 

Original languageEnglish
Pages (from-to)523-543
Number of pages21
JournalEarthquake Engineering and Structural Dynamics
Issue number4
Early online date21 Jun 2012
Publication statusPublished - 10 Apr 2013

Bibliographical note

Accepted 24 May 2012


  • Equivalent SDOF
  • Incremental dynamic analysis
  • Piecewise linear fit
  • Static pushover


Dive into the research topics of 'Near-optimal piecewise linear fits of static pushover capacity curves for equivalent SDOF analysis'. Together they form a unique fingerprint.

Cite this