Continuous approximation of large regular frameworks and the problem of a substitute frame

Zdenek P. Bažant, Martin Christensen

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


Large regular frames under initial axial forces may be approximated by a continuum which is identical with Eringen's micropolar continuum. The finite difference method is then applied to the continuum problem. For a grid step equal to the distance between joints this solution is exact and coincides with the displacement method, while for a larger step, which allows considerable reduction in the number of unknowns, an approximate solution is obtained. Furthermore, it is found that a substitute (or equivalent) frame, which has been sought by structural analysts, in general does not exist. But the solution presented serves, in fact, the same purpose. Finally, numerical examples are given to verify the method.

Original languageEnglish (US)
Pages (from-to)257-278
Number of pages22
JournalAmerican Concrete Institute, ACI Special Publication
StatePublished - Jan 1 1972
EventSymposium on Response of Multistory Concrete Structures to Lateral Forces at the 1972 68th ACI Annual Convention - Dallas, United States
Duration: Mar 5 1972Mar 9 1972


  • Approximation
  • Axial loads
  • Buckling
  • Failure
  • Finite difference theory
  • Frames
  • High rise buildings
  • Joints (junctions)
  • Lateral pressure
  • Moments
  • Multistory buildings
  • Reinforced concrete
  • Stiffness
  • Structural analysis
  • Wind pressure

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Materials Science(all)


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