Crack Advance Steel 2011 
The limits on yield strength are required to ensure adequate ductility of a section and are related to the prescribed limit on concrete compressive strain of 0.003. The limits on yield strength also serve to control of crack widths at service loads. Crack width is a function of steel strain and consequently steel stress (Nawy 1968). Therefore, the stress in the steel reinforcement will always need to be limited to some extent in order to prevent cracking from affecting serviceability of the structure. However, with recent improvements to the properties of concrete, the ACI 318 limit of 552 MPa (80 ksi) and AASHTO limit of 517 MPa (75 ksi) on the steel reinforcement yield strength are believed to be unnecessarily conservative for new designs. Additionally, an argument can be made that if a higher strength reinforcing steel is used but not fully taken into account in design, there may be an inherent overstrength in the member that has not been properly incorporated in design.
Crack Advance Steel 2011
When a reinforced concrete member is loaded gradually in pure tension, cracking of the concrete will take place in one or more places along the length of the member when the tensile stress in the concrete exceeds the tensile strength of the concrete. After cracking, the tensile stress in the concrete adjacent to the crack is relieved because of the slip that takes place between the concrete and reinforcement at this location. Away from the crack, tensile stress in the concrete between cracks is present because of the bond between the reinforcement and concrete. The distribution and magnitude of the bond stress along the reinforcement will determine the distribution of the concrete stress between cracks along the length of the member. As tension loading is increased, cracking will continue to take place until the stress in the concrete between cracks no longer exceeds the concrete tensile strength. This stage occurs due to excessive slip and the reduction of distance between cracks. Essentially, the distance between cracks becomes sufficiently small that the stress to cause concrete cracking can no longer be developed by the reinforcing steel present. When this condition is reached, the crack spacing reaches its minimum, but the crack widths will continue to increase as the tensile stress in the reinforcement increases (i.e., third stage cracking as described by Reis et al. 1964). Assuming this behavior to be valid and that second stage cracking is fully developed by ε s = 0.001 (Reis et al. 1964), it may be hypothesized that crack patterns in members having high strength reinforcing steel will not vary from those having conventional steel. Thus, only crack width, and not crack spacing, will be affected by utilizing the higher strength steel. The cracking behavior of reinforced concrete members in axial tension is similar to that of flexural members, except that the maximum crack width is larger than that predicted by the expressions for flexural members (Broms 1965a, b). The lack of strain gradient and restraint imposed by the compression zone of flexural members is probably the reason for the lower flexural crack width.
In members having high-strength reinforcing bars, early studies showed that an increase in crack width is due to an increase in steel stress and, to a lesser extent, due to an increase in the curvature of the member. Thomas (1936) pointed out that an increase in the curvature at a constant steel stress tends to distribute the cracking rather than widening individual cracks. An increase in the steel stress affects the difference in the elongation between the reinforcing steel and concrete and causes additional slip to occur. This slip is the main cause of the increase in crack size. Slip occurs in the vicinity of a crack and extends to a point where the differential strain is zero. At that point the bond stress and resistance to slip reach maximum values and decrease toward the mid-point between cracks. The overall values of bond force decrease with an increase in load. This decrease is attributed to (a) the effects of the increase in transverse contraction of the reinforcing bar (i.e., Poisson effect) and (b) the deterioration of the concrete at the concrete-steel interface (Odman 1962). Therefore, the crack width increases while the crack spacing remains constant. If the load is increased further, the slip between concrete and reinforcement continues to increase. Due to the comparatively low values of concrete extensibility, the increase in crack width can be considered essentially equal to the accumulation of the slip between adjacent cracks.
The adopted equations for calculation of crack width and crack spacing are based on the use of conventional steel. However, concrete members reinforced with high strength steel reinforcement [having a yield strength, f y , greater than 690 MPa (100 ksi)] have different behavior due to the expected higher service loads. An empirical parametric procedure has been introduced for determination of crack opening (crack width and crack spacing) in a reinforced concrete prism. Effective parameters have been investigated and finally the result has been compared to the available experimental data.
In the case of using conventional steel bars in flexural members, it has been shown that during the second stage of cracking, when steel strains are usually greater than 0.0005, the presence of existing primary cracks affects the formation of secondary cracks under increasing moment. Away from a primary crack, stresses are transferred by bond from the reinforcement to the concrete. If enough force is transferred from the steel at the crack to the concrete away from the crack, the strains that are developed may exceed the strain capacity or the tensile strength of the concrete at a section and another crack will form perpendicular to the reinforcement. Theoretically, the section at which secondary crack formation occurs is midway between existing cracks. This mechanism continues until the tensile forces developed through bond transfer are insufficient to produce additional cracks. To compare and demonstrate the crack behavior of members reinforced with conventional steel bars and members reinforced with high-strength steel bars, a relatively complex material modeling in a simple direct tension model is used.
Crack development in direct tension test. a Bond stress and resulting steel and concrete strain distribution before cracking. b No additional cracks have been developed after the first series of cracks at the tension load (T1).
Crack development and spacing are affected by bar size and the effective concrete area surrounding the reinforcement. As the reinforcing ratio falls, the behavior becomes dominated by a small number of large cracks (Table 1). Whereas at typical flexural reinforcing ratios (0.01 and 0.015), cracking is better distributed. As the reinforcing ratio becomes larger, cracking remains distributed but crack widths may be expected to be more uniform since cracking stresses vary very little. In all cases, for reinforcing ratio ρ = 0.01 and higher, all cracks form at bar stresses below 482 MPa (70 ksi). Consequently, in a concrete section having a reinforcing ratio ρ = 0.01 or higher, regardless of steel grade, the crack width and crack spacing are the same. Using higher strength bars allow higher stresses to develop in the steel, but additional cracks are only likely to form at lower reinforcing ratios.
The values obtained from this method represent the average crack width along the entire 5,080 mm (200 in.) specimen length. Figure 6 illustrates the average crack widths calculated for the range of reinforcing ratios and bar sizes considered. Figure 6 clearly shows the stress at which the cracks are expected to form (lower left data point in each curve) and the progression of crack opening as the bar stress increases. Also superimposed on this figure are expected service load stress levels 248, 414, and 496 MPa (36, 60, and 72 ksi), corresponding to 0.60f y for 414, 690 and 827 MPa (60, 100, and 120 ksi) reinforcing steel, respectively.
The parametric study of crack opening in a prism under direct tension is a simplified approach in calculating the crack widths in concrete beams. The obtained result from parametric study should be confirmed by comparing to some experimental data. Therefore, extensive crack width data were collected from flexural test specimens F1 to F6 tested as part of the NCHRP 12-77 study (Shahrooz et al. 2011). A summary of these specimens is shown in Table 2. To assess the effects of using higher strength steel, the measured crack widths corresponding to various stresses in the reinforcing steel are plotted in Fig. 7.
Considering the measured crack widths in this experimental study, it appears that the existing equations are inherently conservative. This conservativeness allows present specifications to be extended to the anticipated higher service level stresses associated with the use of high strength reinforcing steel.
During the accelerated corrosion process, cracks due to corrosion were mapped and recorded. Delaminations and spalled areas of concrete cover in the test spans were also identified. Although the damaged specimens showed similar visual corrosion including extensive cover cracking, delaminations, and rust staining, each of the four experimental beams exhibited different amounts of stirrup damage estimated by monitoring current flow into the stirrups. The specimens ranged from no damage to severe damage and were designated as specimen 10RA, 10RB, 10RC, and 10RD. Specimen 10RA had no corrosion damage. Specimens 10RB, 10RC, and 10RD had light, moderate, and severe damage states, respectively. Typically, cracks were observed adjacent to locations of the corroded stirrups, along the stem face to top and bottom of the beams, and near the location of the longitudinal steel, even though the flexural steel was not corroding.