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7 Shear capacity exceeds the theoretical value of = f y 3 by ity (COV = 10.3%) whereas stress based on absolute strain a significant margin; and approaches to establishing the yield strength are consistent The tensile capacity of bars is unaffected by the presence of at each strain level considered (COV 7%). standard 90 bends. There is little variation in material properties with bar size. Contrary to conventional wisdom, results from other studies appear to indicate that larger A1035 bars have mar- 1.3.2 Tension Properties of A1035 ginally greater strengths than smaller bars. Results from the Reinforcing Steel present study, however, indicate a marginal reduction in High-strength reinforcing bars often do not have a distinct bar strength with increasing bar size. yield plateau, as shown in Figure 1. For the representative case Regardless of the manner by which yield stress is determined, of an A1035 #5 reinforcing bar shown in this figure, the yield the condition that fu > 1.25fy is satisfied; this relationship is strength is determined to be 93 ksi or 114 ksi depending on implicit in a number of AASHTO design articles including whether the value is determined as that corresponding to a those relating to (1) mechanical couplers (AASHTO LRFD strain of 0.0035 or 0.005. The yield strength is determined to 5.11.5.2.2); and (2) element overstrength (AASHTO LRFD be 123 ksi if the 0.2% offset method is used to determine the Appendix B3). yield point. If a simple definition of 1% strain is used (as is commonly used for prestressing steel, another type of steel For the purposes of modeling steel behavior, some litera- without a well-defined yield plateau), the yield stress is approx- ture proposes "best fit" relationships for A1035 stress-strain imately 140 ksi. Regardless of the method used for determining behavior (Vijay et al. 2002, Rizkalla et al. 2005, Mast et al. yield stress, the value of 68 ksi is found for the representative 2008). In the present study, both Mast et al. (see Appendices A615 #5 bar shown. C and D) and a Ramberg-Osgood (Ramberg and Osgood 1943) A review of tensile test data from 16 previous studies of function are alternately adopted. Ramberg-Osgood (R-O) func- A1035 steel given in Appendix A results in the following tions are commonly used to model prestressing strand and conclusions: post-tensioning steel, and the parameters may be established directly from representative stress-strain curves. (R-O param- Values of yield (fy) and ultimate (fu) strengths and the eters for the A1035 steel tested in this study are provided in strain corresponding to the ultimate stress are relatively Appendix A.) consistent among different test programs. Values of rupture strain vary considerably although this may 1.3.2.1 Modulus of Elasticity, Es be an artifact of the test procedure where strain gages or extensometers typically do not capture ultimate behavior. Regardless of yield or ultimate strength, all steel reinforcing The use of the ASTM A1035-prescribed 0.2% offset method bar grades have a reported modulus of elasticity, Es = 29,000 ksi. for establishing yield strength results in the greatest variabil- At stress levels below about 60 ksi, there is no evidence that the (a) Complete Stress-Strain Curves (b) Various Determinations of fy Figure 1. Representative Stress-Strain Curves for A1035 and A615 Reinforcing Steel.