Softening in reinforced concrete beams and frames

Zdeněk P. Bažant, Jiaying Pan, Gilles Pijaudier-Cabot

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


The softening postpeak load-deflection relation for cracking reinforced concrete beams and frames is analyzed by layered finite elements. Concrete is assumed to exhibit strain softening in both tension and compression, and the steel reinforcement is elastic-plastic. The bending theory assumptions are used and bond slip of reinforcement is neglected. It is shown that the model can satisfactorily approximate the existing test results for softening beams and frames. At the same time, the constitutive laws with strain softening, including those of continuum damage mechanics, are shown to lead to spurious sensitivity of results to the chosen finite element size, similar to that documented before for other strain-softening problems. In analogy to the finite element crack-band model, this problem can be overcome if the minimum admissible element size is specified as a cross section property; its suitable value appears to be equal to the beam depth.

Original languageEnglish (US)
Pages (from-to)2333-2347
Number of pages15
JournalJournal of Structural Engineering (United States)
Issue number12
StatePublished - Dec 1987

ASJC Scopus subject areas

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


Dive into the research topics of 'Softening in reinforced concrete beams and frames'. Together they form a unique fingerprint.

Cite this