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98 5.1 Introduction This report has summarized the research completed in NCHRP Project 12â94, which focused on examining the existing minimum reinforcement requirement. This effort included investigating the state of practice within and outside of the United States, conducting nine large-scale tests, com- pleting complementary analytical work, and appropriately revising the current AASHTO provisions. On the basis of this study, the conclusions presented in the following sections have been drawn. 5.2 Review of U.S. and International Practice The review of U.S. and international practices of specifying minimum reinforcement led to the following conclusions: 1. The minimum reinforcement required by codes and stan- dards varies markedly around the world. Some of these requirements include depth as a variable in determining the minimum reinforcement requirement, while others do not include such a requirement. 2. On the basis of fracture mechanics theory, researchers have suggested that flexural cracking strength ( fr) is not an independent material property, but that it is a function of its characteristic length, which depends on the fracture energy per unit area, the elastic modulus of concrete, and the modulus of rupture. This implies that the modulus of rupture of flexural members will decrease as the depth increases. Large-scale tests reported in the literature appear to support this notion. 3. When flexural members are designed with longitudinal reinforcement less than that required by the codes and standards, they still exhibit an adequate safety margin beyond the cracking limit state. 5.3 Experimental Investigation The experimental work included testing of two reinforced concrete girders, three pre-tensioned girders, three unbonded segmental post-tensioned girders, and one bonded segmental post-tensioned girder. They were targeted to be designed with less than the required minimum reinforcement according to the current AASHTO specifications. This approach was used because the preliminary analytical work suggested that the current AASHTO requirement might be excessive. However, the actual amount of minimum reinforcement provided varied from 56% to 130% with respect to the measured material properties. The conclusions drawn from the test observations and analysis of results are as follows: 1. Reinforced concrete members exhibited adequate duc- tility with a minimum overstrength ratio of 2.33 and a maximum net tensile strain of 10.5 me. Both test girders failed in compression. This failure mode was instigated by the application of a concentrated load at the midspan and is unlikely to develop in the real world. This finding implies that the actual overstrength and displacement capacity would be greater. Furthermore, it was suspected that some debonding of the longitudinal reinforcement in the concentrated crack regions around the critical section reduced the demand on the mild steel reinforcement and increased the displacement capacity. 2. All three pre-tensioned concrete members produced sufficient ductility and overstrength moment ratios and caused no concerns for safety during testing. The mea- sured overstrength moment ratios were above 1.8, and the displacement ductility with respect to the cracking limit state was in excess of 20. The measured maximum dis- placements were excessively higher than those expected, owing to strand debonding that progressed during testing over a short distance in the critical section areas. C H A P T E R 5 Conclusions
99 3. Of the three segmental beams with unbonded post- tensioning, two were designed with less than the minimum reinforcement requirement set by AASHTO, while one was designed with more than the current specified require- ment. All three beams performed satisfactorily without exhibiting a response with a negative stiffness following formation of flexural cracking. It was noted that Girder UNB1 would have had limited reserve capacity under load control, but its failure was dictated by the failure of strands at the anchorage. Two of the units, including Girder UNB1, were 3 ft in depth, and their overstrength moment ratio was in the range of about 1.1. The corresponding value for the 4.5-ft-deep beam was 1.6. One reason for the increase in the moment ratio was the increase in member depth, which lowered the modulus of rupture and cracked the member sooner. Therefore, recognizing this phenomenon in the design process will help achieve a more realistic moment ratio in the design calculations. Furthermore, the segmental beam experienced flexural behavior at the beginning, and a hinging mechanism eventually dominated the response following the forma- tion of the flexural cracking. The initiation of the hinging mechanism was associated with a drop in load resistance, which was regained as the displacement was increased. It was found that identifying the formation of a hinging mechanism is imperative to predicting the response of unbonded segmental post-tensioned beams. 4. One bonded segmental post-tensioned girder was tested, and its behavior was more comparable to that of the pre- tensioned beams than to that of the unbonded segmental post-tensioned girders. This is because it experienced dis- tributed cracking rather than the concentrated cracking observed for the segmental beams. The moment ratio and ductility of this girder were also comparable to the those of the pre-tensioned beams. 5. The tests confirmed that the modulus of rupture value established on the basis of standard modulus of rupture beams with 6- Ã 6-in. cross sections can be excessively high. When the depth of the test units was varied, it was seen that the modulus of rupture was dependent on overall member depth, which should be reflected when a more accurate estimate for the modulus of rupture is being evaluated. 5.4 Analytical Study Analytical models were used to estimate the response of the test units, and, subsequently, the measured response of the test units was used to refine the models. The refined models were used to conduct a parametric study based on the proposed AASHTO LRFD minimum reinforcement requirements. The conclusions drawn from this study were as follows: 1. Within the limits of the software used, the analytical models satisfactorily calculated the observed responses of the test units when measured properties were used. 2. The discrepancy between the measured and calculated responses was due to (a) not accurately modeling the debonding behavior of the steel reinforcement; (b) con- vergence issues arising from the nonlinear behavior of concrete; and (c) the assumption of flexural behavior for the entire response of segmental beams with unbonded post-tensioning without giving consideration to formation of a hinging mechanism. The completed parametric study based on the proposed AASHTO specifications found that reinforced concrete and pre-tensioned girders had consistent moment ratios of about 1.75 and 1.64, respectively, thus demonstrating adequate moment ratios. Large variations in the range of 1.06 to 1.44 were observed for the unbonded segmental post-tensioned girders. The lower moment ratios were obtained for shallower beam depths and smaller span-to-depth ratios, as expected. The analyses did not consider the friction between the tendons and the deviators, and, therefore, the actual overstrength moment ratio would be likely to increase. 5.5 Recommended Changes to AASHTO Specifications The current AASHTO specifications were evaluated on the basis of the work completed. Another parametric study involving a variety of sections as well as detailed design examples was completed on the basis of the proposed changes to the specifications. As a result of this effort, the following conclusions were drawn: 1. The influence of the depth on the modulus of rupture should be included in the design equation, as it would provide a more realistic estimate of the moment ratio and produce cost savings. 2. For compression-controlled members, the minimum reinforcement requirement penalizes the design in addition to requiring the use of a reduced resistance factor, which should be corrected. 3. With the method proposed for AASHTO based on the completed study presented in this report, the different beam types produced consistent overstrength moment ratios and required a reduced amount of minimum reinforcement to yield an economic benefit. 4. Completed detailed design examples confirmed the ade- quacy of the proposed changes and potential economic benefits.