Size effect on punching shear strength of RC slabs with and without shear reinforcement

Zdeněk P. Bažant, Abdullah Dönmez

Research output: Contribution to journalConference articlepeer-review


Comparison of various design codes reveals major differences among the design provisions for punching shear, especially with respect to the size effect. This indicates the need for deeper analysis of the existing test data supplemented by realistic finite element (FE) analysis. This study presents a refined statistical analysis of the ACI-445 database comprising 440 punching shear tests, and an FE analysis based on concrete microplane model M7 calibrated by test data. Computer filtering of the database is used to create data subsets in which the averages of secondary variables, such as the steel ratio and shape parameters in subsequent size intervals, are almost constant. The resulting trend of the mean punching shear strength vc clearly reveals that the slope of the diagram of log vc versus log d is milder, but not much milder, than -1/2, and that the trend does not disagree with the theoretically well justified energetic size effect law (endorsed for shear failures by ACI Committee 446). A new design equation with a size effect factor, emulating previous equations in many respects, is proposed. The equation is verified and calibrated by nonlinear least-square multivariate regression of the database, with weights compensating for the crowding and scarcity of data in various parts of the range. The size effect and other trends are also verified by finite element fitting of selected data series with a broader range. The size effect factor validated here can be applied to improve any design equation missing the size effect, including a plastic limit analysis equation, provided it fits the small-scale test data well (for which the size effect factor is defined as 1).

Original languageEnglish
Pages (from-to)23-34
Number of pages12
JournalAmerican Concrete Institute, ACI Special Publication
Issue numberSP 315
Publication statusPublished - 2016
EventACI-fib International Symposium on Punching Shear of Structural Concrete Slabs 2016 - Philadelphia, United States
Duration: 25 Oct 201625 Oct 2016

Bibliographical note

Publisher Copyright:
© 2016 American Concrete Institute. All rights reserved.


  • Design codes
  • Failure
  • Finite element analysis
  • Optimum data fitting
  • Punching shear
  • Quasibrittle fracture
  • Reinforced concrete
  • Size effect
  • Statistical analysis


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