A stress function for 3D frames

F. A. McRobie, C. J. K. Williams

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


This paper generalises Rankine diagrams for 3D trusses to be applicable to 3D frames. Rankine diagrams are a graphical representation of a state of self-stress in a 3D truss, with the area of reciprocal polygons representing the axial force in their corresponding original bars. Rankine diagrams are a polyhedral version of the continuous Maxwell-Rankine stress function. In this paper we present a new stress function. It is piecewise linear and discontinuous and it allows the analysis of 3D frames, giving all six stress resultants of axial and shear forces and bending and torsional moments in any member. A succinct statement of the stress function is given in terms of 4D Clifford Algebra.

Original languageEnglish
Pages (from-to)104-110
JournalInternational Journal of Solids and Structures
Publication statusPublished - 8 Apr 2017


  • Clifford Algebra
  • Frames
  • Graphic statics
  • Grillage analysis
  • Maxwell stress function
  • Rankine reciprocal diagrams

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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