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37 sion of the accuracy of proposed changes. In this section, the Figure 24 presents the trends in the strength ratios for the strength ratios are evaluated briefly. CSA method as a function of: (a) f c; (b) depth, d; (c) per- Table 5 compares the strength ratios for the 64 selected centage of longitudinal reinforcement, l; and (d) strength of reinforced concrete and 83 selected prestressed concrete test shear reinforcement provided, v fy. The results illustrate no results. From this table, the following observations can be trend in the strength ratio with any of these parameters for the made about how well these four design provisions predicted range of values shown. the capacity of members in the selected databases: The results presented in Table 5, Figure 23, and Figure 24 give the impression that the proposed simplified provisions 1. The LRFD and CSA methods provided the most accu- are less accurate than the current AASHTO standard meth- rate and very similar estimates of the shear capacity of ods for prestressed members and are significant less accurate both the RC and PC members. With Mean strength ratios than the CSA method. This may be misleading for, as previ- ranging from 1.1 to 1.24 and coefficients of variation ously mentioned, the types of members tested in laboratories (COV) for these ratios that range from 0.13 to 0.18, the do not represent well the types of members built in the field. fit with the test data is considered to be excellent. Additionally, most members tested in laboratories were 2. For the 64 RC members, the proposed simplified pro- designed to fail near a support while a member in the field visions were slightly less accurate than the LRFD and must be designed for shear over its entire length. For this rea- CSA approaches but far more accurate than the son, the fit with experimental test data should only be viewed AASHTO standard approach. The proposed simplified as one evaluation metric. Another is a comparison of the provisions and the STD approach had similar Mean required amount of shear reinforcement by multiple meth- values, but the STD approach had a significantly larger ods, including analytical results, for a large number of design COV. This result implies that there are likely to be sections that represent the types of sections designed in prac- many more situations in which the STD provisions tice. This comparison is presented in the next section. are less conservative than the proposed simplified provisions. 3.5 COMPARISON OF REQUIRED STRENGTH 3. For the 83 PC members, the proposed simplified provi- OF SHEAR REINFORCEMENT IN DESIGN sions had a larger Mean and a slighter larger COV than DATABASE the STD specifications. To further assess the safety and efficiency of the two Figure 23 presents the trends in the strength ratios for the change proposals, the required amount of shear reinforce- proposed simplified provisions as a function of: (a) f c; (b) ment (v fy) by these two methods, the LRFD and AASHTO depth, d; (c) percentage of longitudinal reinforcement, l; standard methods, and program Response 2000 (Response and (d) strength of shear reinforcement provided, v fy. The 2000) are compared for a large number of design sections. A results illustrate a slight trend in strength ratio with the per- summary of these results is presented following a description centage of longitudinal reinforcement. Some of the most of the design database. A more complete presentation of the conservative results are for members that contain high lev- results and the design database is presented in Appendix H, els of shear reinforcement. This result is to be expected as which is included in NCHRP Web-Only Document 78. the proposed simplified provisions limit the shear strength The design database was developed to cover practical conservatively to guard against brittle diagonal compressive design sections. The database included prestressed and non- failures. prestressed sections, composite and non-composite, as well TABLE 5 Evaluation of approaches for selected RC and PC members
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38 3.0 3.0 2.5 2.5 Vtest/Vn,Prop 2.0 Vtest/Vn,Prop 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 5000 10000 15000 20000 0 5000 10000 15000 20000 f'c (psi) f'c (psi) 3.0 3.0 2.5 2.5 2.0 2.0 Vtest/Vn,Prop Vtest/Vn,Prop 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 10 20 30 40 0 20 40 60 80 100 d (in) d (in) 3.0 3.0 2.5 2.5 2.0 2.0 Vtest/Vn,Prop Vtest/Vn,Prop 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0.0 5.0 10.0 15.0 20.0 0.0 2.0 4.0 6.0 8.0 l (%) p l (%) 3.0 3.0 2.5 2.5 2.0 2.0 Vtest/Vn,Prop Vtest/Vn,STD 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 v fy (psi) v fy (psi) (a) 64 RCmembers (b) 83 PCmembers Figure 23. Comparison of simplified approach predictions and test results. as simply-supported and continuous members. All members from the support. The sections selected for shear design of supported a uniformly distributed load and were designed continuous members were at "d", 0.1L, 0.2L, 0.3L, 0.4L, for flexure to satisfy the requirements of the LRFD specifi- 0.8L, 0.9L and L-d from the simple support. In order to cations. The sections selected for shear design of simply- obtain a range of shear design stress levels and M/V ratios supported members were at "d", 0.1L, 0.2L, 0.3L, and 0.4L at each of these sections, each member was designed for
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39 3.0 3.0 2.5 2.5 Vtest/Vn,CSA Vtest/Vn,CSA 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 5000 10000 15000 20000 0 5000 10000 15000 20000 f'c (psi) f'c (psi) 3.0 3.0 2.5 2.5 Vtest/Vn,CSA Vtest/Vn,CSA 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 10 20 30 40 0 20 40 60 80 100 d (in) d (in) 3.0 3.0 2.5 2.5 Vtest/Vn,CSA Vtest/Vn,CSA 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0.0 5.0 10.0 15.0 20.0 0.0 2.0 4.0 6.0 8.0 I (%) pI (%) 3.0 3.0 2.5 2.5 Vtest/Vn,CSA Vtest/Vn,CSA 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 v fy (psi) v fy (psi) (a) 64 RCmembers (b) 83 PCmembers Figure 24. Comparison of CSA 2004 predictions and test results. multiple lengths and to support loads that required different specifications. The six different types of members from levels of flexural reinforcement (50%, 75%, or 100% of the which the sections were selected are: maximum allowable flexural reinforcement). This led to some shear design stress levels larger than those commonly 1. A 36-inch Deep Simply-Supported Prestressed I-Beam seen in current design but are still admissible by the LRFD with 7.5-inch Thick Composite Slab
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40 2. A 72-inch Deep Simply-Supported Prestressed Bulb- required. For this evaluation, the required amount of rein- Tee Girder with 7.5 inch Thick Composite Slab forcement, v fy, required by 5 methods (AASHTO Standard 3. A 78-inch Deep Two-Span Continuous Post-Tensioned Specifications), the LRFD Sectional Design Model (LRFD), Box Girder the proposed simplified provisions (p, change proposal 1), 4. A 36-inch Deep Simply-Supported Rectangular Rein- the CSA Method (CSA, change proposal 2) and Response forced Concrete Beam 2000 (Response 2000)). This required amount of shear rein- 5. A 42-inch Deep Simply-Supported T-Shaped Rein- forcement by each design method is given by Equation 34. forced Concrete Beam 6. A 36-inch Deep Two-Span Continuous Reinforced v f y = (Vu - Vs Acv ) (Eq. 34) Concrete Beam where Acv is the area of concrete resisting shear. In comparing required amounts of shear reinforcement by These required amounts are compared for all 473 design the five methods, it is considered particularly important to con- cases in a series of tables, charts and plots in Appendix H. All sider the differences between the amounts required by each of the design sections in this database are representative of design method and the amounts required by using program the types of situations to which the proposed simplified pro- Response 2000. While the required amount by Response 2000 visions would be applicable. In reviewing the results, the is not a replacement for experimental test data, this program has researchers were particularly interested in identifying those successfully proven to provide accurate predictions of the shear conditions under which any of the methods were either capacity for members in the experimental database. Since this unconservative or particularly different than other provi- program is based on a general behavioral model (MCFT) and sions. For each of the prestressed members, the total number not calibrated by this beam test data, it is reasonable to expect of design sections is further divided into web-shear regions, that the program will provide similarly accurate estimates of the transition regions, and flexure-shear regions. A transition capacity of members in this design database as it did for the region is where both web-shear cracking and flexure shear members in the experimental test database. In this use of cracking could be expected to occur and which was numeri- Response 2000, the appropriate ratio of M/V and level of pre- cally considered to be when Vcw was greater than Vci but stressing was input and then the amount of shear reinforcement Mu > Mcr. In many of the design cases, minimum shear rein- was adjusted until the predicted capacity was equal to Vu/. forcement was required. In these cases, the ratio is shown by As stated in the previous section, most experimental test a hollow symbol. Otherwise a solid symbol is used. data is from small-sized member tests and nearly all failures Table 6 summarizes the results of the comparisons by pre- have occurred near simple supports. Thus, an evaluation of senting the mean and COV of the ratios of the requirement the proposed changes in sections away from the support is strength of shear reinforcement by each of the four design TABLE 6 Comparisons of ratios of required strength of shear reinforcement by four design methods to required strength determined by program R2K