Zdenek P. Bazant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

331 Scopus citations


Analysis of structural instability due to strain-softening (i. e. , declining branch of the stress-strain diagram) is presented. In a continuum, strain-softening is impossible; it can exist only in a heterogeneous material. Failure occurs by unstable localization of strain or beam curvature, in which the stored strain energy of the structure is transferred into a small strain-softening region whose size is several times the aggregate size, or the spacing of reinforcement, or the depth of the beam. The existence of a lower limit on the size of this region permits ductility, along with its dependence on the size and stored energy, to be predicted by a stability analysis. Calculations of limit loads and moment redistributions in strain-softening beams and frames must include instability checks of possible curvature localization. The same applies to finite element analyses of reinforced concrete structures with account of tensile cracking, and predictions of limit loads of these structures which are questionable because they depend on the size of the finite elements.

Original languageEnglish (US)
Pages (from-to)331-344
Number of pages14
JournalASCE J Eng Mech Div
Issue number2
StatePublished - Jan 1 1976

ASJC Scopus subject areas

  • Environmental Science(all)
  • Engineering(all)
  • Earth and Planetary Sciences(all)


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