Curved-quartic-function elements with end-springs in series for direct analysis of steel frames

Si Wei Liu, Jake Lok Yan Chan, Rui Bai, Siu Lai Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


A robust element is essential for successful design of steel frames with Direct analysis (DA) method. To this end, an innovative and efficient curved-quartic-function (CQF) beam-column element using the fourth-order polynomial shape function with end-springs in series is proposed for practical applications of DA. The member initial imperfection is explicitly integrated into the element formulation, and, therefore, the P-δ effect can be directly captured in the analysis. The series of zero-length springs are placed at the element ends to model the effects of semi-rigid joints and material yielding. One-element-per-member model is adopted for design bringing considerable savings in computer expense. The incremental secant stiffness method allowing for large deflections is used to describe the kinematic motion. Finally, several problems are studied in this paper for examining and validating the accuracy of the present formulations. The proposed element is believed to make DA simpler to use than existing elements, which is essential for its successful and widespread adoption by engineers.

Original languageEnglish
Pages (from-to)623-633
Number of pages11
JournalSteel and Composite Structures
Issue number5
Publication statusPublished - 1 Jan 2018


  • Design
  • Imperfection
  • Plastic hinge
  • Second-order
  • Semi-rigid
  • Steel

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Metals and Alloys


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