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Figure 1 shows a concrete test specimen with transverse cracking 

Fig. 1. Cracking Test Specimen.
            

Fundamentals of Crack Control in Reinforced Concrete
Robert J. Frosch, PhD, PE, Purdue University

Crack control is an important issue for primarily two reasons: aesthetics and durability. Wide cracks detract from a structure visually as well as may unduly alarm the public that there are structural problems. In addition, wide cracks may cause durability related problems. Cracks provide a rapid route for oxygen, water, and, depending on exposure, chlorides to reach the reinforcement, which may lead to corrosion and structural deterioration. Both analytical and experimental research continue to provide improved tools to assist in the control of cracking (Figure 1).

Current design approaches for the control of cracking focus on limiting the spacing of the reinforcement. To understand this relationship, it is important to review the fundamentals of cracking behavior which is discussed in detail in Frosch (1999). As shown in Figure 1, the crack width wc at the level of the reinforcement can be calculated as wc=εsSc where εs is the reinforcement strain (fs /Es) and Sc is the crack spacing.

Figure 2 shows a diagram of a concrete beam showing rebar position and tensile stress distribution 

Fig. 2. Cracking Model.
            

To calculate the crack width at the beam surface, it is necessary to account for the strain gradient (Figure 2). Plane sections are assumed to remain plane, and the crack width at the level of the reinforcement is multiplied by an amplification factor

resulting in the surface crack width.

Cracks develop in concrete because the tensile strength of the concrete has been exceeded. Once cracking initiates, the tension in the section is fully transferred to the reinforcement at the crack. Between cracks, tension is resisted jointly by the concrete and the reinforcement. Obviously, the tensile stress in the concrete at the crack is zero, and the tensile stresses in the concrete distribute approximately as shown in Figure 2. If there is sufficient spacing between cracks and adequate bond of the reinforcement, an increase in the reinforcement stress results in an increase in the concrete tensile stress. This increase continues until the tensile strength of the concrete is reached. The maximum concrete tensile stress occurs halfway between existing cracks resulting in formation of a crack approximately halfway between the cracks. This process continues until the crack spacing is sufficiently small that there is not enough distance to produce high enough tension between cracks; therefore, a stabilized crack pattern results.

It has been found that the crack spacing depends primarily on the maximum concrete cover. Specifically, the minimum theoretical crack spacing is equal to the distance from the center of the reinforcement to the point on the cover furthest from the reinforcement d* (Figure 3). This spacing is the smallest that can develop as smaller spacings cannot develop sufficient tensile stresses to exceed the tensile strength of the concrete. The maximum crack spacing is equal to twice this distance as a crack may not develop halfway between the adjacent cracks. In other words, if the crack forms, the minimum spacing results.

Figure 3 is a diagram of a concrete beam which shows the minimum theoretical crack spacing is equal to the distance from the center of the reinforcement to the point on the cover furthest from the reinforcement 

Fig. 3. Controlling cover dimensions.
            

Putting these expressions together results in the equation for the maximum crack width. This equation can be rearranged to solve for the maximum permissible bar spacing. As evident from these expressions, the spacing of the reinforcement is controlled primarily by the reinforcement stress and concrete cover.

Maximum crack widths are typically controlled to a target value of approximately 0.016 in. This value is based primarily on aesthetics as research has shown that corrosion is not clearly, if at all, correlated with surface crack widths (Darwin et al. 1985, Oesterle 1997). It is for this reason that the ACI 318 building code, which is based on a crack width of 0.016 in., does not differentiate between interior and exterior exposure. The equations presented in the AASHTO design specifications were derived from the expression above using a crack width of 0.017 in. While it was not felt necessary to have a more restrictive exposure condition, AASHTO decided to provide this as an option for states resulting in the Class 2 exposure condition.

The control of crack widths presented here focuses on flexural behavior and cracking on the tension face of the member. It is possible that crack widths in deep members can be greater on the side face rather than on the tension face. For this reason skin reinforcement is required which is discussed in more detail in Frosch (2002). Furthermore, crack control based on this flexural model is applicable only for the design of flexural members such as beams and slabs. For bridge decks, cracking is primarily caused by a different mechanism. Bridge decks typically develop full depth, transverse cracks which are caused by restrained shrinkage (Figure 4). Therefore, controlling bar spacings as outlined here is not appropriate or sufficient for the control of bridge deck cracking. This topic is discussed in an earlier HPC Bridge Views bridge deck article (Frosch 2007), and more resent research provides additional guidance on the control of bridge deck cracking (Frosch et al. 2010).

Figure 4 is a photograph showing a bridge deck with typically developed full depth, transverse cracks which are caused by restrained shrinkage 

Fig. 4. Transverse Bridge Deck Cracking.
            

References

  1. Darwin, D., Manning, D.G., and Hognestad, E. “Debate: Crack Width, Cover, and Corrosion,” Concrete International, V. 7, No. 5, May 1985, pp. 20-35.
  2. Frosch, R.J. (1999). “Another Look at Cracking and Crack Control in Reinforced Concrete,” ACI Structural Journal, Vol. 96, No. 3, May-June 1999, pp. 437-442.
  3. Frosch, R.J. (2002). “Modeling and Control of Side Face Beam Cracking,” ACI Structural Journal, Vol. 99, No. 3, May-June 2002, pp. 376-385.
  4. Frosch, R.J. (2007). “Controlling Bridge Deck Cracking in Indiana,” HPC Bridge Views, Issue No. 46, September/October 2007.
  5. Frosch, R.J., Gutierrez, S., Hoffmann, J., (2010). “Control and Repair of Bridge Deck Cracking,” Joint Transportation Research Program, FHWA/IN/JTRP-2010/4, 318 pp. doi: 10.5703/1288284314267.
  6. Oesterle, R.G., “The Role of Concrete Cover in Crack Control Criteria and Corrosion Protection,” RD Serial No. 2054, Portland Cement Association, Skokie, IL, 1997.