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OCR for page 21
21 Figure 4. Typical measured stress-strain diagram and elastic-perfectly plastic model. capacity. The use of the strain compatibility approach assum- 2.3.2 Tension-Controlled and ing an elastic-perfectly plastic steel stress-strain relationship Compression-Controlled Strain having a yield stress defined at either a strain of 0.0035 or Limits for High-Strength 0.005 ensures that the flexural capacity is computed conserva- ASTM A1035 Reinforcing Bars tively and reliably for the range of reinforcement ratios and concrete compressive strengths encountered in practice. How- 2.3.2.1 Fundamental Concepts ever, for beams with reinforcement ratios exceeding 2.65%, The current steel strain limits of 0.005 defining the lower the definition of the yield stress at a strain of 0.0035 is more bound of tension-controlled behavior and 0.002 or less defin- appropriate. The latter approach is consistent with the currently ing compression-controlled behavior are based on having an prescribed ACI 318 (ACI 2008) approach. The use of the stress adequate change in steel strain from service load to nominal at 0.0035 strain effectively ensures that the steel strain under strength. Nonetheless, the strain limits have been calibrated the design condition is beyond point "b" shown in Figure 4. based on the expected performance of flexural members rein- (Recall that this condition is enforced in the design approach forced with Grade 60 longitudinal bars. Considering that through the definition of Asmax as the steel content that allows A1035 bars could be subjected to larger service level strains a steel strain of 0.004 to be achieved.) and have different stress-strain relationships, the strain lim- its defining tension-controlled and compression-controlled Table 10. Ratios of T-beam and slab flexural capacity behaviors need to be reevaluated. calculated from elastic-plastic analyses to that from fiber model. 2.3.2.2 Development T-Beams The curvature ductility of sections reinforced with A615 Yield Point Average Minimum Maximum Standard Grade 60 reinforcement was computed for the following Deviation cases: concrete compressive strength from 4 to 15 ksi in 1-ksi @ Strain =0.0035 0.741 0.571 0.859 0.091 @ Strain =0.005 0.795 0.659 0.890 0.069 increments; tension longitudinal reinforcement () from 0.2% offset 0.748 0.718 0.764 0.019 0.1% to 6.1% in 0.06% increments; compression longitudi- Deck Slabs nal reinforcement () taken as 0, 0.5, and ; and ratio of Standard Yield Point Average Minimum Maximum Deviation the effective depth of the compression longitudinal bars to @ Strain =0.0035 0.828 0.609 0.953 0.115 the effective depth of the tensile longitudinal bars (d/d) @ Strain =0.005 0.854 0.638 0.971 0.113 equal to 0 or 0.1. The stress-strain relationship of Grade 60 0.2% offset 0.909 0.839 0.951 0.043 was modeled as elastic-perfectly plastic. For the same cases, Note: Ratio less than 1 is conservative. the curvature ductility was recomputed by using A1035

OCR for page 21
22 4 ksi, 0, d/d 0, target t 0.005 Figure 5. Example for f c in ASTM A615. Grade 100 reinforcement. An equation proposed by Mast strain in the tension reinforcement, which improves the duc- (2006) was used to characterize the material properties of tility. As the concrete compressive strength increases, the ten- A1035 reinforcement. Details of the formulation are pro- sion reinforcement strain drops, which is an indication of vided in Appendix C. reduced ductility. The relationship between the strain levels for A615 and A1035 reinforcing bars is illustrated in Figure 5 for one of the 2.3.2.3 Recommendations cases considered. For this example, a singly reinforced mem- = 4 ksi, the strain in the A1035 bars needs to be ber having f c Based on the results shown in Figure 6, the following strain 0.00793 in order to achieve the same implied ductility of the limits are recommended to define tension-controlled and same tension-controlled member reinforced with A615 bars. compression-controlled members that use reinforcement The complete set of results is shown in Figure 6. As expected, with fy = 100 ksi in cases where the service load stresses are lim- the addition of compression bars (i.e., > 0) increases the ited to 60 ksi. Linear interpolation may be used for fy between Figure 6. Equivalent strains for tension-controlled and compression-controlled members reinforced with ASTM A1035.