Fracture and Size Effect Suppression by Mesh Reinforcement of Concrete and Justification of Empirical Shrinkage and Temperature Reinforcement in Design Codes
Publication: Journal of Engineering Mechanics
Volume 146, Issue 10
Abstract
A minimum mesh reinforcement, called the shrinkage and temperature reinforcement, has been required by ACI design code for to attain ductility with no formation of large localized cracks. The required steel ratio, which is 0.18%, has been empirical. In this paper, it is shown that it can be explained theoretically and justified approximately by finite-element analysis of the size effect and crack growth based on quasibrittle fracture mechanics, in which the microplane model M7 and crack band model are used. The premise, which simplifies the analysis, is that the cracking would localize into wider cracks if and only if there is a size effect. The size effect can be completely avoided only if, for the same cross-section area, the tensile strength of yielding reinforcement is greater that the tensile strength of concrete. The effect of increasing the reinforcement ratio is also explored. The calculations indicate that fracture mechanics can, and should, be used to check ductility and size effect implications in the two-sided reinforced members, boundary beams, and more complicated designs such as in shear walls.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
The coding of M7, directly usable as a material subroutine in, e.g., VUMAT of ABAQUS, can be freely downloaded from Bažant’s website: www.civil.northwestern.edu/people/bazant.
Acknowledgments
Partial funding under NSF Grant No. CMMI-2029641 to Northwestern University is gratefully appreciated.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 10 • October 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jan 8, 2020
Accepted: May 26, 2020
Published online: Aug 11, 2020
Published in print: Oct 1, 2020
Discussion open until: Jan 11, 2021
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