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6 Â CHAPTER 1 INTRODUCTION AND RESEARCH APPROACH 1.1 PROBLEM STATEMENT Minimum flexural reinforcement is prescribed in the AASHTO LRFD Bridge Design Specifications (also referred to as the âLRFD specificationsâ) for reinforced and prestressed concrete members to reduce the probability of brittle failure (AASHTO, 2007). This minimum reinforcement is based on providing flexural capacity greater than the moment at which cracking of the concrete is anticipated to occur. The intent of providing this additional flexural capacity is to prevent brittle failure without sufficient warning or redistribution of load. It is recognized that there is a wide variability in the cracking moment. Recently, the flexural cracking strength has been increased from 0.24âf'c to 0.37âf'c (ksi) in the LRFD specifications. This increase is to recognize increasing use of high strength concrete and of the wide range of scatter in modulus-of-rupture tests, as shown in experiments by Mokhtarzadeh and French (2000). This recent increase, combined previously incorporated safety factors, has resulted in excessive amounts of reinforcement, especially in segmental concrete bridge box girders. Design examples have demonstrated that a prestressed concrete member may have an amount of reinforcement so large as to cause the member to fail in a compression-controlled mode, while still not satisfying the minimum flexural reinforcement requirement. This anomaly was obviously not intended by the LRFD specifications. Tests have shown that lightly reinforced and prestressed concrete members have significant inelastic strength and ductility when tested with displacement-controlled application devices, as shown in Section 2.1. Figure 1 shows a typical moment-rotation relationship of a reinforced concrete member. If a displacement controlled testing is conducted in a laboratory setting, the entire moment-rotation diagram can be generated. The load is introduced in the form of controlled displacement increments and the hydraulic jacking pressure continues to be applied regardless of whether the load drops at any point or not, which may not be representative of actual bridge loading. However, if these same tests were conducted in load-control mode, a number of these specimens would fail without warning if Mo is smaller than Mcr, where Mo is the moment corresponding to the ultimate (rather than yield) strength of the reinforcement and Mcr is the cracking moment. Based on this observation, minimum flexural reinforcement should be based on the ultimate strength of the reinforcement rather than the yield strength, which
7 Â corresponds to Mn in Figure 1. This observation also implies that minimum reinforcement provisions in the current LRFD specifications applied inconsistently for reinforced compared to prestressed concrete members. For reinforced concrete, Mn is defined in terms of the yield strength of the mild reinforcement, while for prestressed concrete it is defined in terms of the ultimate strength of the prestressing steel. Figure 1. Moment-rotation response of a lightly reinforced concrete member Statically indeterminate structures deserve special considerations because of the ability to internally redistribute loading effects from negative to positive bending. The LRFD specifications restrictions on where redistribution is allowed are related to the net-tensile strain at ultimate, which implies that the section ductility is inversely proportional to the amount of tensile reinforcement. As shown in Figure 2, cracking will typically occur under negative moment first and then positive moment. Circumstances where it is permissible to forgo minimum reinforcement requirements in the negative bending regions for continuous bridges is discussed in Section 2.4.7, along with recommended detailing practice to achieve the required ductility capacity that allows for satisfactory redistribution.
8 Â Figure 2. Load-displacement response of an interior span of a continuous member 1.2 RESEARCH OBJECTIVES The objective of this research is, to develop recommended revisions to the AASHTO LRFD Bridge Design Specifications and Commentary for rational design of minimum reinforcement to prevent brittle failure of concrete sections. This objective is achieved by evaluating the effectiveness of minimum reinforcement provisions on a database of structures that are represented in the LRFD Specifications. A summary of the research is as follows: 1. Review and synthesize U.S. and international practice and research on minimum flexural reinforcement (MFR). 2. Evaluate minimum reinforcement models and select 4 candidates for parametric studies. 3. Develop a database of concrete bridge structures and components where minimum reinforcement provisions apply. 4. Evaluate safety, reliability, and economy by applying minimum reinforcement candidate provisions to the structures listed in the database. 5. Propose revisions to the AASHTO LRFD Bridge Design Specifications. 6. Demonstrate proposed provisions with design examples. 1.3 RESEARCH TASKS To accomplish these objectives, the following research tasks were performed. These tasks are quoted directly from the NCHRP 12-80 project request for proposals.
9 Â Task 1. Review U.S. and international practice, performance data, research findings, specifications, and other information related to minimum reinforcement requirements and flexural cracking of concrete structures. This information shall be assembled from technical literature and from unpublished experiences of engineers, bridge owners, fabricators, and others. Records of brittle flexural failures of laboratory or in-service elements are of particular interest. Task 2. Identify and compare models to determine minimum flexural reinforcement. Models should not be limited to those used in developing the LRFD specifications. The NCHRP will select the models for use in Task 6. Task 3. Assemble a database of concrete structures and components to which the LRFD minimum flexural reinforcement (bonded and unbonded) requirements apply. The database shall be populated with sufficient information to permit calculation of all appropriate cross-section loads and resistances. Task 4. Develop a detailed work plan to use the database structures and components to compare the reinforcement requirements and reliability of not more than three minimum reinforcement models selected by the NCHRP. Task 5. Submit an interim report within four months of the contract start that documents the findings of Tasks 1 through 4. Include a list of proposed design examples to be submitted in Task 7. The contractor will be expected to meet with the NCHRP approximately one month later. Work may not proceed on subsequent tasks without NCHRP approval of the work plan. Task 6. Perform the work plan as approved by the NCHRP. Task 7. Develop specifications with supporting commentary for recommendation to the AASHTO Highway Subcommittee on Bridges and Structures. Provide a minimum of five step- by-step design examples illustrating the application of the specifications. Compare the designs to those produced by the current AASHTO specifications. Task 8. Revise the specifications, commentary, and design examples in accordance with NCHRP review comments (Draft 2). Task 9. Submit a final report that documents the entire research effort.
10 Â 1.4 RESEARCH WORK PLAN The work plan identified in Task 6 was developed to achieve the objectives of this project after the data collection phase of this project. This work plan consisted of the following items: 1.4.1 Refine the Modified LRFD Method A new approach to determine minimum reinforcement is proposed to meet the objectives of the NCHRP 12-80 project. As the name suggests, the Modified LRFD method is based on the minimum reinforcement procedure in the LRFD specifications. In this procedure, variables that influence minimum reinforcement are factored separately to account for differences in variability. Development of these factors is the subject of this task. For concrete flexural cracking, the data presented in Section 2 is used determine a factor that is appropriate. The prestress variability effect on the flexural cracking strength is relatively small regarding the flexural cracking strength. Therefore, a reduced factor, compared to the current 1.2 factor, is warranted, as discussed in Section 2.2. Design methods such as strain compatibility analysis are utilized to develop flexural strength of selected structures within the Concrete Bridge Member Database, to see if any methods in the procedure can be simplified. 1.4.2 Perform the Parametric Study To evaluate candidate minimum reinforcement methods, design calculations were performed on the bridges within the Concrete Bridge Member Database, as described in Section 3.1.1. Design calculations were performed using state-of-the-practice design tools to develop design forces, moments, and shears. The preparation of tables of minimum reinforcement along with appropriate graphs compare each method versus such variables as concrete compressive strength, spacing of girders, depth of members and width and thickness of bottom and top flanges. As a result these methods are easily and directly compared for quick evaluation. 1.4.3 Evaluate the Statistical Parameters of Minimum Flexural Reinforcement To aid in interpretation of applicable test data, a statistical analysis is performed, as described in Section 2.3. The focus of this analysis is on the flexural cracking strength of concrete bridge members.
11  To evaluate the appropriateness of the statistical parameters, the cumulative distribution function (CDF) of the modulus-of-rupture is plotted on the normal probability paper. Any normal CDF on the normal probability paper is represented by a straight line. The methods used to develop CDF plots are described in such references as Nowak and Collins (2000) and in TRB Circular E-C079. 1.5 KEY DEFINITIONS For convenience of the reader, the following definitions are given: ï· fpe - strand stress due to effective prestress. ï· fps - strand stress at ultimate flexure. ï· fy - stress in mild reinforcement at specified yield strain (0.0021 for grade 60 steel). ï· fu - ultimate (peak) stress in mild reinforcement just before rupture. ï· Mcr - theoretical cracking moment. ï· Mo - nominal ultimate moment capacity including the effects of strain hardening, as illustrated in Figure 1. ï· Mn - nominal flexural capacity as defined by the LRFD specifications, excluding strain hardening for conventionally reinforced sections with mild steel reinforcement (see Figure 1) and including strain hardening for sections reinforced with prestressing strands. ï· Mu- ultimate demand moment (or required strength) due to factored applied loads. ï· ï§3 â ratio of yield to ultimate steel stress for non-prestressed steel, (for example, 0.67 for A615 and 0.75 for A706 Grade 60 reinforcement). Note that ï§3 is taken =1.0 for prestressing strands as the codes already utilize the full stress-strain relationship.
