Recommendations for the shear design provisions for segmental box girder bridges of the AASHTO-LRFD Bridge Design Specifications, 4th Edition, 2008 Interim (2008)
Alejandro R. Avendano and Oguzhan Bayrak, University of Texas at Austin
In an effort to contribute to the development of a new family of prestressed concrete girders, full-scale Tx-Girders were fabricated and tested in the Phil M. Ferguson Structural Engineering Laboratory of the University of Texas at Austin (Fig. 13). Performance of the new girders was found to be superior to that of previously existing cross sections while allowing for greater bridge span to girder depth ratios. As part of this study, an extensive database of shear test was gathered and examined in depth, resulting in the recommendations presented in this article.
Shear design provisions for segmental box girder bridges included in the AASHTO-LRFD Bridge Design Specifications were used to estimate the shear strength of specimens from the University of Texas Prestressed Concrete Shear Database. Shear strength ratios (Experimental maximum shear divided by the calculated shear strength) were obtained for all specimens using the shear design provisions for segmental box girder bridges as well as other current shear design provisions.
After examining shear strength estimates from the shear design provisions for segmental box girder bridges, a great degree of conservatism was observed throughout the database. Shear design provisions for segmental box girder bridges were carefully examined. Specifically, the limitation on K = 1 for members in which the tensile stress on the outer most fiber exceeds 0.9√f'c (where f'c is given in ksi or 6√f'c when f'c is given in psi), introduced with the rational of covering flexure shear related failures, and the limitation on the value of √f'c to 3.16 for all cases (or 100 when f'c is given in psi), regardless of the amount of shear reinforcement provided in the member.
When Ramirez and Breen (1983) first proposed the shear strength equations for segmental box girder bridges found today in the AASHTO-LRFD Bridge Design Specifications, they evaluated a database of shear tests available at that time. Ramirez and Breen (1983) obtained unconservative shear strength estimates for two specimens tested by MacGregor et al. (1960). As a result of this, the limit on K was then introduced and conservative shear strength estimates were obtained for MacGregor et al.’s (1960) two specimens. Shear strength ratios for these two specimens are presented in Table 1.
Upon re-examining the data from Ramirez and Breen’s (1983) database and examining the University of Texas Prestressed Concrete Shear Database, it was found that for the two specimens in question, all other currently accepted shear design provisions evaluated (except for shear design provisions for segmental box girder bridges) yield unconservative shear strength estimates.
This fact led the researchers to believe that (i) shear design provisions for segmental box girder bridges without the limit on K for members with flexural tension cracks are as conservative as other currently accepted shear design provisions; (ii) Failure of the two specimens tested by MacGregor et al. (1960) was possibly related to an unaccounted phenomenon in order for all design provisions to provide unconservative strength estimates; (iii) Setting a limit for the value of K in order to obtain conservative shear strength estimates for the two mentioned specimens is not justified.
Limiting √f'c to 3.16 (or 100 when f'c is given in psi) was meant to cover an expected decrease in the ultimate shear strength of beams fabricated with high strength concretes. It is believed that given than the shear crack surface in high strength concrete beams is smoother than that of normal strength concrete, the quality of aggregate interlock decreases, resulting in lower ultimate strengths. It is also believed that as shear cracks grow wider, aggregate interlock ceases to contribute to shear strength. The University of Texas Prestressed Concrete Shear Database was further examined in an effort to validate these ideas.
The University of Texas Prestressed Concrete Shear Database contains information from 30 references regarding shear strength of prestressed concrete beams published between 1954 and 2008. A total of 506 tests are included in the database, from which our main focus was devoted to a group of 153 specimens complying with the following criteria:
1. The failure mode is shear related, including specifically: (i) Diagonal web crushing, (ii) Flexure shear, (iii) Diagonal Tension, (iv) Shear Tension (anchorage failure or rupture of stirrups), (v) Strand Slip/Bond failure, and (vi) Sliding Shear (Horizontal Shear)
2. The overall depth of the member is greater than 12 inches
3. Some transverse reinforcement is included
Items 2 and 3 above were established to exclude test specimens that are not representative of the actual bridge girders. With the increasing availability of shear tests on full-scale specimens, it seems appropriate to statistically evaluate current design provisions using more representative tests. As part of this filtering process, the specimens tested by MacGregor et al. (1960) are not included in our analysis, given than they are only 12 inches deep and have no shear reinforcement.
The limit on K is aimed at providing a similar provision to the Vci and Vcw approach used in AASHTO Standard and LRFD Specifications and ACI 318 by making Vc the lesser of Vci and Vcw. For this reason, the 153 specimens included in the evaluation database were grouped into 23 specimens governed by flexure-shear (Vci < Vcw) and 130 specimens governed by web-shear (Vcw < Vci). Results of this analysis are shown in Table 2.
Furthermore, if the upper limit of 3.16 on √f'c is waived for sections with at least the minimum amount of shear reinforcement indicated in the AASHTO-LRFD Bridge Design Specifications, no significant loss of conservativeness was observed as can be seen by comparing columns 3 and 6 of Table 2. In effect, this analysis would imply that the current shear provisions for segmental box girder bridges can be extended to high strength concrete without compromising the conservativeness of the provisions.
The results of this analysis indicate that shear design provisions for segmental box girder bridges are not only conservative but remarkably accurate in the estimation of shear strength when no limit on K is imposed for members with flexural-tension cracks, both for cases governed by flexure-shear or web-shear (Tables 2 and 3).
Figure 14 illustrates the distribution of the Shear Strength Ratio versus concrete strength for the current shear provisions for segmental box girder bridges with and without the limits on K and √f'c for the 153 tests. It can be observed how the removal of the limits on K and f'c results in consistently safe strength estimations without being overly conservative. Additionally, no pronounced trend is observed in Fig. 14, hence, a limit on √f'c seems unjustified for beams with at least a minimum amount of shear reinforcement.
In conclusion, it is recommended that:
i For shear design, the stress variable K shall be given by:
K = stress variable K shall not be taken greater than 1.0 for any section where the stress in the extreme tension fiber, calculated on the basis of gross section, due to factored load and effective prestress force after losses exceeds 0.9√f'cin tension.
ii The value √f'c is allowed to be taken greater than 100 psi (or 3.16 when f'c is given in ksi) as long as the requirements for Minimum Transverse Reinforcement from section 220.127.116.11 are satisfied.
The easy-to-use shear design provisions for segmental box girder bridges will be as accurate as or more accurate than other shear design provisions upon implementation of the proposed changes. It is also important to note that the conservative nature of these provisions is not compromised with these proposed changes (Table 3.)
Oguzhan Bayrak is Associate Professor at Department of Civil, Environmental and Architectural Engineering, and holds Charles Elmer Rowe Fellowship in Engineering at the University of Texas at Austin. He serves as Director of the Phil M. Ferguson Structural Engineering Laboratory.
Alejandro Avendano is a research assistant at the University of Texas at Austin. He received his Bachelors in Civil Engineering from the Technological University of Panama and his Masters in Structural Engineering from The University of Texas at Austin. His research interests include the behavior of prestressed concrete elements.
1. AASHTO, LRFD Bridge Design Specifications, 4th Edition, 2008 Interim Revisions, American Association of State Highway and Transportation Officials, Washington, D.C., 2008.
2. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-08), American Concrete Institute, Farmington Hills, MI, 2008.
3. Avendaño, A., Bayrak, O., “Shear Strength and Behavior of Prestressed Concrete Beams”, Technical Report for TxDOT IAC-88-5DD1A003-3, The University of Texas at Austin, Austin, Texas, 2008. 180 pp.
. 4. MacGregor, J. G., Sozen, M. A., and Siess, C. P., “Effect of Draped Reinforcement on Behavior of Prestressed Concrete Beams,” Journal of the American Concrete Institute, V. 32, No. 6, December 1960, pp. 649-677.
5. Ramirez, J. A., and Breen, J. E., “Experimental Verification of Design Procedures for Shear and Torsion in Reinforced and Prestressed Concrete,” Research Report 248-3, Center of Transportation Research, University of Texas at Austin, Austin, Texas, November 1983.