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1 LRFD Minimum Flexural Reinforcement Requirements The main purpose of minimum flexural reinforcement requirements for load and resistance factor design (LRFD) is to ensure that a structural member possesses sufficient strength and ductility so that it will not fail in a brittle manner without sufficient warning or redistribution of load when it reaches the flexural cracking limit state. The minimum reinforcement requirement in design codes is addressed by ensuring a minimum value for the ratio between the flexural nominal moment capacity and the flexural cracking moment at the section level. The ductility of the member is addressed outside of the minimum reinforcement requirement by requiring a minimum value for the net tensile strain in the reinforcement, as this is required for all flexural members. Use of unnecessarily high amounts of minimum reinforcement is not preferred because doing so will lead to inefficient and expensive design and possible reinforcement con- gestion. Further, an excessive amount of reinforcement may cause the member to fail in compression-controlled mode, thereby defeating the purpose of specifying the minimum flexural reinforcement requirement. In some cases, requiring an unnecessarily high amount of minimum reinforcement may lead to a design process that is iterative yet without con- vergence, especially for unbonded segmental members, which makes it impossible to satisfy the design requirement. Therefore, NCHRP Project 12â94 was devised to verify the current minimum flexural reinforcement requirements in the AASHTO LRFD Bridge Design Specifi- cations, 8th edition (AASHTO 2017), and improve their effectiveness. Unlike its predecessor, NCHRP Project 12â80, this research study included several large-scale tests on bridge girders designed with less than the current minimum reinforcement requirements. In the current edition of the AASHTO LRFD Bridge Design Specifications (AASHTO 2017), the minimum flexural reinforcement is mainly dictated by the cracking moment, Mcr, which is a function of the modulus of rupture, fr, among others. Typically, fr has been based on test data from 6-in.-deep modulus of rupture beams, which do not reflect the effect of typical bridge girder depths. Fracture mechanics theory and a limited number of tests conducted on large-scale concrete beams suggest that the modulus of rupture is a function of the depth of the beam. Taking the depth into account in calculating fr will lead to a more realistic estimation of Mcr, which in turn will lead to lower minimum flexural reinforcement requirements. In a study of the influence of member depth on fr, Shioya et al. (1989) reported that fr is proportional to h-0.25, where h is the depth of the member. Carpinteri and Corrado (2011) suggested that fr should be taken as proportional to h-0.15. Several researchers have cor- roborated this phenomenon of expressing fr as a function of h through fracture mechanics theory (e.g., Hillerborg et al. 1976; Bosco et al. 1990; Hawkins and Hjorteset 1992; BaÅ¾ant 1999; Ince et al. 2003). In the current AASHTO LRFD Bridge Design Specifications, fr is defined as 0.24 â²fc (ksi), independent of the height of the member. In other design codes S U M M A R Y
2 around the world, it is also found to be the common practice to have the minimum flexural reinforcement requirement equation merely as a function of â²fc , with the exception of the Norwegian Standard (Norwegian Standards Associ ation 2003), which includes a function of depth, although this code is no longer used in practice because of the adoption of the Eurocode. On the basis of the recommendations from NCHRP 12â80, determination of the minimum reinforcement in the AASHTO LRFD Bridge Design Specifications is based on the greater of either 1.33 Mu, where Mu is the ultimate moment demand obtained from the load combinations, or an Mcr equation that is a function of several factors, namely, the flexural cracking variability factor (Î³1), prestress variability factor (Î³2), and a factor con- sidering the ratio of specified minimum yield strength to ultimate tensile strength of the reinforcement (Î³3). The Mcr equation, however, does not account for the effect of the depth of the member. In addition, it was found that the minimum reinforcement calculated with different design codes varied noticeably, which suggests that a more reliable approach to calculating the minimum reinforcement is required. The objective of this research project was, therefore, to examine the current requirements regarding minimum flexural reinforcement in the AASHTO LRFD Bridge Design Specifica- tions and improve their effectiveness, in compliance with the LRFD design philosophy. The following work was completed in this project: 1. A critical review of relevant specifications, technical literature, and owner/industry experiences worldwide; 2. Large- or full-scale testing of selected reinforced, pre-tensioned, unbonded post- tensioned segmental, and bonded post-tensioned segmental concrete girders, most of which were designed with reinforcement less than the current minimum reinforce- ment requirements; 3. Development and validation of analytical models with which to further evaluate the behavior of girders with minimum reinforcement; 4. Development of recommendations for the specifications and commentary language for proposed revisions to the AASHTO LRFD Bridge Design Specifications; and 5. Demonstration of the proposed revisions with some representative design examples and quantification of the potential economic impact of the proposed revisions. Past experimental tests on lightly reinforced concrete beams (i.e., with relatively small reinforcement) suggested that as long as there was sufficient strength after the cracking moment was reached (i.e., the load resistance was not dropped after the beam cracked), the members would have some ductility capacity. These tests were generally carried out under displacement-controlled protocols. While this approach is acceptable, it should be acknowl- edged that displacement-controlled tests will not usually cause a sudden failure when sufficient minimum reinforcement is not provided. Instead, these tests will allow the beams to fail gradually following a negative post-cracking stiffness. This loading scheme also does not account for the possible dynamic effects from the onset of flexural cracking. Nine large-scale girder tests were completed as part of this project. In all cases, tests results confirmed that the concrete girders had sufficient strength and ductility capacities beyond the cracking limit state, although several of them were designed with less than the currently required minimum reinforcement. This further showed that an adequate level of safety can be ensured with less than the currently required minimum reinforcement. While the behav- ior of the tested girders generally followed the ordinary beam flexural theory, it is important to note that for lightly reinforced unbonded post-tensioned segmental concrete girders, the response was dominated by a hinging mechanism instead of the flexural mechanism after cracking occurred and a concentrated crack had formed. This hinge was located approxi- mately at the centroid of the compression zone. Validation of the analyt ical models showed good agreement with the experimental results. On the basis of the test observations and
3 results, a set of recommendations was established to revise the current minimum flexural reinforcement requirements in the AASHTO LRFD Bridge Design Specifications. These rec- ommendations include taking the depth of the member into account in the Mcr calculation and introducing the ultimate moment amplification factor, Î±, as a function of the net tensile strain, et, similar to the net tensile strain currently used in determining the strength reduc- tion factor, Ï. That means that the constant value of 1.33 is no longer used; thus, members in the compression-controlled regime are not doubly penalized. The validated analytical mod- els were then used to illustrate that, by providing the proposed minimum reinforcement for concrete members, a satisfactory performance in terms of strength and ductility capacities can still be achieved fairly uniformly for different depths of the member. Implementing the proposed recommendations will result in a more efficient flexural design of concrete members. In particular, the prescribed amount of minimum reinforce- ment will be substantially reduced for deeper members. This will translate to a lower cost associated with members designed with minimum reinforcement. The design pro- cess will also be more rational, since members in the compression-controlled regime will not require excessive reinforcement. These proposed recommendations will also lead to a more uniform and consistent level of safety for all concrete members designed according to the AASHTO LRFD Bridge Design Specifications.