Title: Empirical Modeling of Cracking in Reinforced Concrete

Author(s): Evan C. Bentz

Publication: Structural Journal

Volume: 116

Issue: 3

Appears on pages(s): 233-242

Keywords: cracking; design equations; direct tension; modulus of rupture; size effect; split cylinder; web-shear cracking

DOI: 10.14359/51714476

Date: 5/1/2019

Abstract:
A source of confusion in design codes is that multiple equations are often provided for concrete tensile strength—for example, one for modulus of rupture and another for direct tension strength. This paper proposes that these differences in tensile strength result from a size effect that is based on the volume of concrete in tension. Volumes larger than approximately 30 L (1 ft3) do not show this size effect and crack at the stress recommended by ACI for diagonal web-shear cracking. For smaller volumes, the tensile stress at cracking can be up to three or more times larger than this value. When the volume of the specimen is accounted for by the presented empirical size effect equation, the different test methods show consistent results. Using a set of 511 tension tests on plain or reinforced specimens of different types and sizes, the proposed unified tension model is justified. Finally, a simple design equation for flexural cracking is presented.