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Cracking moment - NISTIR 5634 Prediction of Cracking in...

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NISTIR 5634 Prediction of Cracking in Reinforced Concrete Structures Nicholas J. Carino Structures Division and James R. Clifton Building Materials Division April 1995 Building and Fire Research Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 U.S. Department of Commerce Ronald H. Brown, Secretary Technology Administration Mary L. Good, Under Secreta~ for Technology National Institute of Standards and Technology Arati Prabhakar, Director
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ABSTRACT The useful life of a buried concrete, containment structure for low level nuclear wii.ste may be controlled by the loss of its load-bearing capacity or an increase in permeability. The latter factor is controlled by the general degradation of the concrete and by the presence of discrete cracks resuking from extermdl y applied loads or from restraint to normal volume changes. To be able to predict the effects of cracks on permeability, it is necessary to understand the causes and mechanisms of discrete crack formation in reinforced concrete structures. The objective of this report is to provide an overview of the design and behavior of reinforced concrete members and to discuss the factors affecting the formation of cracks in hardened concrete. The underlying philosophy of modern reinforced concrete design is presented, and it is shown that it allows for the formation of cracks of controlled widths under service loads. Models for predicting the width of flexural cracks are reviewed. Factors affecting drying shrinkage cracks and approximate methods for considering them are discussed. An example is provided to illustrate how to determine whether drying shrinkage cracks will develop under specific conditions. This is followed by a discussion of techniques to predict the number and widths of drying shrinkage cracks. Finally, there is a discussion of the interaction between flexural and drying shrinkage cracking. The report is directed to the general audience who is unfamiliar with the structural aspects of reinforced concrete. Keywords: building technology; concrete; cracking; creep; reinforced concrete; restrained shrinkage ... 111
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TABLE OF CONTENTS ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 l.lObjective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. PRINCIPLES OFREINFORCED CONCRETEBEHAVIOR . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Reinforced Concrete DesignMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Flexural Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Uncrackedsection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.2 Cracked. elastic section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3.3 Ultimate strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. CONTROL OF W’IDTH AND SPACING OF FLEXURAL CRACKS . . . . . . . . . . . . . . . 3.1 ACIApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2CEB/FIPApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.30ther Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. RESTRAINED SHRINKAGECRACKING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Factors AffectingDrying Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Elapsed time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Duration ofthecurin~~eriod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Ambient relativehumidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Volume-to-surface ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Creep Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Comection factors . . . . . . . . . . . . . . . . . . . . . . . . . .. $ ...... . . . . . . . . .
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