Proposal for standard test of modulus of rupture of concrete with its size dependence

Zdenek P Bazant*, Drahomír Novák

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Recently accumulated test data on the modulus of rupture, as well as analytical studies and numerical simulations, clearly indicate that the flexural strength of concrete, called the modulus of rupture, significantly decreases as the beam size increases. This paper proposes a method to incorporate this size effect into the existing test standards, and focuses particularly on ASTM Standards C 78-94 and C 293-94. The proposed method is based on a recently established size effect formula that describes both the deterministic-energetic size effect caused by stress redistribution within the cross section due to finite size of the boundary layer of cracking at the tensile face of beam, and the classical Weibull-type statistical size effect due to the randomness of the local strength of material. Two alternatives of the test procedure are formulated. In the first alternative, beams of only one size are tested (as is recommended in the current standard), and the size effect on the mean modulus of rupture is approximately predicted on the basis of the average of existing information for all concretes. In the second alternative, beams of two sufficiently different sizes are tested. The latter is more tedious but gives a much better prediction of size effect for the concrete at hand; it allows for the estimation of size effect on not only the mean but also the coefficient of variation of the modulus of rupture (particularly, its decrease with increasing size). Numerical examples demonstrate the feasibility of the proposed approach.

Original languageEnglish (US)
Pages (from-to)79-87
Number of pages9
JournalACI Materials Journal
Issue number1
StatePublished - Jan 1 2001


  • Concrete
  • Fracture
  • Modulus of rupture
  • Stress

ASJC Scopus subject areas

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


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