A New Codified Design Theory of Second-order Direct Analysis for Steel and Composite Structures – From Research to Practice

Siu Lai Chan, Yao Peng Liu, Si Wei Liu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)


The terms “Second-order Analysis” and “Direct Analysis” appear in many modern design codes but many engineers consider this as a method for checking only the second-order sway effect, nonlinear sway moment or a tool for academic research. This perception is incorrect in modern structural design and in fact this old approach is defined only as the second-order “indirect” analysis or P-Δ-only analysis. When used properly, the full second-order P-Δ-δ analysis method of design provides a reliable and proficient tool for practical design. Their underlying principle also carries a very different philosophy to the conventional design approach. This paper outlines the differences between the two design concepts, namely the first-order linear effective length method (ELM) and the second-order direct elastic or plastic analysis (SODEA and SODPA). The era for re-thinking our design and analysis philosophy seems to have arrived. In this paper, the experience and theory on using the new design concept and method are described with worked example given on their uses. Most previous works on second-order analysis do not provide reliable solutions to practical engineering problems, because they were not calibrated against benchmark solutions where the current design code is adequately accurate. As shown in the examples in this paper, the proposed design is able to reproduce some standard solutions of these benchmark examples so it can be used for practical design.
Original languageEnglish
Pages (from-to)105-111
Number of pages7
Publication statusPublished - 1 Feb 2017


  • Buckling
  • Nonlinear
  • Second-order direct analysis

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Architecture
  • Building and Construction
  • Safety, Risk, Reliability and Quality


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