Deflection-crack mouth opening displacement relationship for concrete beams with and without fibres

Sujing Zhao, David Lange, Wei Sun

Research output: Contribution to journalArticlepeer-review


The three-point bending (TPB) test of a notched beam is a method widely used to characterise the toughness of fibre reinforced concrete (FRC) in terms of fracture energy. However, since the measurement of deflection is significantly dependent on the test set-up, spurious deflections are sometimes obtained. Therefore, it is necessary to correlate deflection with crack mouth opening displacement (CMOD) so that the fracture energy can be evaluated from load-CMOD data. In this study, TPB tests were carried out on a series of beam specimens prepared with plain concrete, FRC and ultrahigh-performance concrete (UHPC). Load, deflection and CMOD were recorded. The results showed that a trilinear relationship could be established between deflection and CMOD. The FRC beams showed slightly higher deflection/CMOD ratios than the plain concrete beams, while a dependency of deflection/CMOD ratios on the fibre type or fibre content was not observed. Moreover, the trilinear relationship cannot apply to UHPC due to deflection-hardening and multiple-cracking behaviour.

Original languageEnglish (US)
Pages (from-to)532-540
Number of pages9
JournalMagazine of Concrete Research
Issue number10
StatePublished - May 1 2015

ASJC Scopus subject areas

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


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