Modal and elastic time-history analysis of frames with tapered sections by non-prismatic elements

Rui Bai, Si Wei Liu, Siu Lai Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


Low-cost robotic welding and wide availability of high strength steel plates of grades over 500MPa make the use of tapered members an economical alternative to conventional prismatic members for modern steel structures, as experienced by the authors in some practical projects in Hong Kong and Macau. This paper proposes a new and efficient numerical method for modal and elastic time-history analysis of the frames with tapered sections. A series of non-prismatic elements is derived on the basis of analytical expressions, and the exact consistent mass and tangent stiffness matrices are formulated. Five common types of tapered sections for practical applications, namely the circular solid, circular hollow, rectangular solid, rectangular hollow and doubly symmetric-I sections, are studied. Contrary to the conventional method using the approximate assumptions for the section properties along the member length, this research analytically expresses the flexural rigidity and cross-sectional area for the stiffness and mass matrices of an element. Further, the techniques for obtaining the dynamic performances, such as natural vibrations and time-history responses, of non-prismatic members are investigated. Finally, three examples are conducted for validating and verifying the accuracy of the proposed formulations. The present work can be used in the dynamic response analysis of frame structures with tapered sections in seismic zones.

Original languageEnglish
Article number1850106
JournalInternational Journal of Structural Stability and Dynamics
Issue number9
Publication statusPublished - 1 Sept 2018


  • Dynamics
  • frame
  • mass matrix
  • natural frequency
  • non-prismatic element
  • time-history analysis

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics


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