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26 ing shear Vcw governs. (Example, when f c = 10,000 psi, These members were selected from the larger shear database the LRFD stress limit is 2,500 psi while the AASHTO so that members in which significant arch action or flexural Standard Specifications limit is 1,000-1,400 psi). failures were suspected were removed from the database. Although the authors have concluded that the LRFD Most of the RC members had rectangular cross sections and stress level is sufficient to prevent web crushing in were simply supported using bearings positioned underneath regions where there is a uniform field of diagonal com- the member. Of these, 718 did not contain shear reinforce- pression, they are concerned that this limit may be ment and 160 did. The PC members consisted of rectangular, unconservative near supports where there is a signifi- T-shaped, and I-shaped sections and most of the members cant magnification of the stress as the diagonal com- were simply supported, again on bearings positioned under- pression funnels into the support. neath the member. Of these, 321 did not contain shear 6. The approach by Tureyen and Frosch is not sufficiently reinforcement and 160 did. About 80 percent of both the mature for the complete design of reinforced through members in the RC and PC components of the database had prestressed concrete members of all shapes and load- depths less than 20 inches. ings. In addition, this approach is a significant depar- Table 4 presents an examination of the Shear Strength ture from how most of the research community views Ratios (Vtest /Vcode) and Coefficients of Variation (COV) for the transfer of shear, even in web-shear regions. Since ACI 318-02, AASHTO LRFD Bridge Design Specifications the publication of this method, members of the research (2001), CSA A23.3-04, JSCE Code (1986), Eurocode EC2 community have responded with experimental evi- 2003, and the German Code (DIN, 2001). The code calcu- dence that suggests that for beams with shear rein- lated strengths are nominal capacities and therefore all resis- forcement most of the shear carried by the concrete tance and strength reduction factors are set to 1.0. As a result, could not be transmitted in the uncracked compression the calculated strengths by ACI 318-02 would be equivalent zone suggested by Tureyen and Frosch. to the calculated strengths by the AASHTO Standard Speci- fications (16th edition). In this table, the mean and COV are presented for seven segments of the database, all members, 2.3 EVALUATION OF SHEAR DESIGN all RC members, all RC members without shear reinforce- METHODS USING TEST DATABASE ment, all RC members with shear reinforcement, all PC To evaluate the accuracy of different national codes of prac- members, all PC members without shear reinforcement, and tice, a large experimental database was used to evaluate the all PC members with shear reinforcement. shear strength ratio (Vtest /Vcode) for six different Codes for From Table 4, the following observations can be made: 1,359 selected beam tests results. Following a brief description of the experimental database, the results of this evaluation are · The AASHTO LRFD and CSA approaches were best summarized. More detailed information on the database and able to predict the capacity of the members in this data- an evaluation of Codes is presented in Appendixes C and D, base. The mean of the strength ratios for both of these which are part of NCHRP Web-Only Document 78. approaches was very consistent across the different cat- The 1,359-member database consists of 878 reinforced egories of selected members and of a value (1.19-1.46) concrete (RC) and 481 prestressed concrete (PC) members. that would be expected to result in conservative designs TABLE 4 Code assessment for RC and PC members
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27 that made reasonably efficient use of shear reinforce- parallel chord truss model is used in calculating the con- ment. The small COV was particularly impressive for tribution of the shear reinforcement. PC members with shear reinforcement. · Both the EC2 and DIN Codes were considerably less · The close correlation between the means and COV for successful in predicting the capacity of members in the the AASHTO LRFD and CSA methods indicates that shear database. There was a surprisingly large variation these two methods would yield similar designs in terms in the means across the different categories of members. of the amount of required shear reinforcement. As a result, it is concluded that the equations for calculating , This large database of shear test results is also useful for , and x in CSA A23.3-04 are reasonable replacements examining minimum required amounts of shear reinforce- for the tables and the old equation for x of AASHTO ment in codes of practice. In Figure 19, the shear strength LRFD that could result in an iterative design approach. ratio (Vtest /VAASHTO-STD) is examined for reinforced concrete · Although the overall COV for the ACI (AASHTO Stan- beams that contain reasonably light amounts of shear rein- dard Specifications) approach is about 40 percent forcement. The results illustrate that traditional amounts of greater than the least overall COV, this results princi- minimum shear reinforcement, v fy = 40-60 psi, were insuf- pally from the poor performance of these design provi- ficient to ensure that code provisions were conservative. This sions in predicting the capacity of RC members that do illustrates why the larger amounts of minimum shear rein- not contain shear reinforcement. Both the mean and forcement required by AASHTO LRFD Sectional Design COV of the ACI (AASHTO Standard Specifications) Model are appropriate. method for RC and PC members with shear reinforce- This database is also useful for evaluating the maximum ment were quite good. Regarding the prediction of RC shear stress design limit. The LRFD Sectional Design Model members without shear reinforcement, given the mea- enables the design of members for up to 2.5 times the maxi- sured shear capacity of many of the members, the ACI mum shear design stress permitted in the AASHTO Standard (AASHTO Standard Specifications) approaches would Specifications. Figure 20 reveals that the AASHTO Standard frequently have required designs with minimum shear Specifications are unduly conservative. However, the authors reinforcement because of the rule that Av,min is required are concerned that the LRFD limit of 0.25 f c may be too high. when Vu Vc / 2. As observed in NCHRP Project 12-56, in the end regions of · The JSCE code was somewhat better than the ACI prestressed concrete bulb-tee girders, the funneling of the (AASHTO Standard Specifications) approach at calcu- diagonal compressive stresses into the support results in lating the shear strength of RC members, but very con- stresses that are significantly higher than those assumed in servative at calculating the shear strength of prestressed the LRFD Sectional Design Model which was developed for concrete members. This conservatism results from a regions of members in which the diagonal compression field limitation in the Japanese code of only doubling Vc due is parallel. However, most available test results are for beams to the effect of prestressing and because a 45-degree simply supported on bearings positioned underneath the 3.00 v f y Value 40-60 psi 2.50 60-80 psi 80-100 psi 2.00 100-120 psi 120-140 psi Vtest > 140 psi 1.50 VACI 1.00 0.50 0.00 0 5000 10000 15000 f c ( psi ) Figure 19. Strength ratio versus concrete compressive strength for RC members.