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13 fs = service load stress in reinforcing bar; Indeed, AASHTO LRFD Commentary C5.7.3.4 provides dc the following third alternative: s = 1 + ; and 0.7 ( h - dc ) The crack width is directly proportional to the d factor, there- h = overall depth of the concrete section. fore, if the individual Authority with jurisdiction desires an alter- nate crack width, the d factor can be adjusted directly. This equation can therefore also be rearranged in a man- ner similar to Equation 4, resulting in the same conclusions Thus a value of d > 1.0 may be permitted as appropriate. and implications. This approach is additionally deemed to be appropriate for deck slabs since the value of fs will be appreciably lower. It w is also noted that deck slabs designed using the empirical s 1.34 d - 2dc (Eq. 6) s s approach of AASHTO LRFD 9.7.2 are not required to sat- isfy 5.7.3.4. For Class 1 exposure, Equation 5 is calibrated, through d = 1, for a crack width of 0.017 in.; for Class 2 (d = 0.75) 1.3.7.3 "Acceptable" Crack Widths or other exposures, the de facto crack width is d 0.017. In the commentary to 5.7.3.4, AASHTO describes the use of ACI Committee 224 (2001) suggests that crack widths the d term to calibrate Equation 5 for any desired crack exceeding 0.016 in. may be unacceptable from the standpoint of aesthetics. Similarly, Halvorsen (1987) states that a case width limitation. could be made that crack widths ranging from 0.006 to 0.012 in. It is well established that crack control is improved by could be considered unacceptable for aesthetic reasons as using a larger number of well-distributed, smaller diameter they are visible to the naked eye; hence, generating a sense of bars to make up the required area of flexural reinforcing insecurity about structural distress. Beyond this, there is little steel. The number of bars that can be provided, however, is consensus as to acceptable crack widths. restricted by minimum spacing requirements (AASHTO LRFD 5.10.3). Thus, if the area of flexural steel is provided using the greatest number of bars that may be placed in a 1.3.7.4 Analytical Assessment of Crack Widths section, such a section, theoretically, should exhibit the best Soltani (2010) conducted a detailed analytical assessment control of crack widths. This relationship is manifested in of expected crack widths. This approach accounted for non- Equations 4 and 6 where the crack width (w) is propor- linear stress transfer between the bar and surrounding con- tional to the flexural bar spacing (s). Ward (2009) shows crete along the development length and nonlinear bar slip that for fs = 36 ksi (appropriate for bars having fy = 60 ksi), relationships associated with the stress transfer. Soltani con- Class 1 and 2 exposure crack width limits (0.017 in. and sidered a range of bar sizes and reinforcement ratios and used 0.0128 in., respectively) are met for all permissible designs experimentally determined R-O stress-strain relationships to (see Appendix I). model the steel reinforcement. Figure 2 provides a represen- As seen in Equations 4 and 6, crack width (w) is also pro- tative result showing anticipated average crack widths at the portional to reinforcing bar stress (or strain, in this case, location of the reinforcing steel for a concrete tension zone s). Therefore, if fs = 60 ksi (appropriate for bars having having a reinforcing ratio of 2%. Soltani concluded that fy = 100 ksi), crack widths are expected to increase. In this through reinforcing bar stresses of 72 ksi, average crack case, Ward (2009) shows that while the Class 1 exposure widths (it is only possible to consider average crack widths in crack width limit (0.017 in.) is met for all practical beam an analytical context) remain below 0.016 in. for all but the design cases, the Class 2 limit (0.0128 in.) is generally only largest bars considered (#10). The results were relatively met with #5 bars and smaller (see Appendix I). The impli- insensitive to changes in reinforcing ratio. Finally, it is noted cation of this is that accepted crack width limits may not be that crack widths expressed at the surface of a concrete mem- met with higher permitted reinforcing bar stress. Ward ber may be amplified from those at the reinforcing bar loca- (2009) proposes the following two alternatives to addressing tion due to the depth of concrete cover and/or the curvature crack control for beam design in the context of AASHTO of the member. LRFD (5.7.3.4): Limit fs 50 ksi in order to satisfy present Class 2 require- 1.3.8 Corrosion Performance of Reinforcing Steel Grades ments; or Limit fs 60 ksi and remove the Class 2 limit when consid- The quantification of corrosion resistance is beyond the ering high-strength reinforcing steel. scope of the present work but is summarized here in the