Considerations for the Design and Construction of Bonded and Unbonded Post-Tensioned Concrete Bridge Elements (2025)
Chapter: 5 Summary and Recommendations for Future Research
CHAPTER 5
Summary and Recommendations for Future Research
5.1 Summary of Research Findings
Based on the results of the experimental and analytical research, a summary of the major findings is provided.
5.1.1 Flexure
Flexural behavior is dependent on the bond type (bonded, unbonded, or combination bonded/unbonded) of the prestressing strands. Similar behavior was experienced up until flexural cracking. Following cracking, a divergence in behavior was observed where the flexural stiffness of girders with only unbonded strands was significantly less than that for bonded strands. Specimens with only unbonded strands experienced very few, but extremely wide, cracks. The behavior of girders with a combination of bonded and unbonded prestressing strands was dependent on the ratio of bonded strands to total strands. Specimens with larger ratios of bonded strands to total strands exhibited flexural cracks that were small and well distributed. Specimens with smaller ratios of bonded strands to total strands exhibited flexural cracks that were wider and concentrated. Strand stress development was also influenced by the bond type of the prestressing strands. For unbonded strands, stresses developed at approximately the same rate as deflection increased and were unaffected by flexural cracking. For bonded strands, stresses increased significantly at the cracking load as stress development is based on strain compatibility.
The accuracy of the LRFD BDS (AASHTO 2020) in estimating strand stresses and flexural capacity was also evaluated. Analytical modeling indicated that the LRFD BDS estimates strand stress and flexural capacity for bonded strands well. For members with only unbonded strands, however, the LRFD BDS can provide unconservative estimates of strand stress and flexural capacity. When mild reinforcement is added, the flexural capacity linearly increases with the ratio of the mild reinforcement area to the concrete flexural tension area, Act. For these cases with mild reinforcement, the LRFD BDS (AASHTO 2020) conservatively predicted strand stress and flexural capacity. For the combination of bonded and unbonded strands, flexural capacity linearly increases with the amount of bonded reinforcement. The current LRFD BDS assumes the unbonded strand stress does not increase at ultimate, which results in conservative flexural capacity predictions (AASHTO 2020).
Based on these results, changes are proposed to Article 5.6.3 of the LRFD BDS (AASHTO 2020) for flexural members. Modifications to Article 5.6.3.1.2 provide for use of the current unbonded strand stress expression if a minimum amount of bonded tension reinforcement is provided. The requirement of a minimum amount of bonded reinforcement is intended to avoid unconservative stress calculations that can occur if unbonded strands are used either without any bonded reinforcement or with minimal bonded reinforcement. Modifications to Article 5.6.3.1.3b permit
the use of the approximate stress expression for unbonded strands provided in Article 5.6.3.1.2 and is intended to improve the accuracy of the approximate method of determining the stresses for the unbonded strands. The proposed changes also provide better direction to designers on how to incorporate sections with both bonded and unbonded tendons using the current equations for moment capacity.
5.1.2 Shear
Shear behavior can also be influenced by the bond type of the prestressing strands, especially depending on the location of the tendon (bottom flange or web). For bottom flange strands, the bond type had a significant influence on flexural behavior, which also impacts shear behavior. With bonded bottom strands, flexural cracking occurs in the shear span, and a flexure-shear failure can occur if web-shear failure is prevented. However, a flexure-shear failure cannot occur with only unbonded bottom strands, as flexural cracking cannot occur in the shear span due to the unbonded nature of the strand. Therefore, girders with only unbonded bottom strands can only fail due to web-shear cracking or due to flexural failure. For web tendons, the bond type did not significantly influence shear capacity, and shear failures were generally characterized by concrete crushing at the level of the top duct. The specimens with bonded web tendons produced only a slightly higher shear strength than those with unbonded web tendons. The test results provided several additional conclusions. As the duct diameter to web width ratio increased, the shear capacity decreased. Increasing the transverse reinforcement ratio resulted in an increase in the shear capacity of the girders. Finally, the distribution of internal and external web tendons did not influence the overall behavior or shear capacity of the girders.
The accuracy of the LRFD BDS (AASHTO 2020) in estimating shear capacity was also evaluated for the experimental results and for simply supported and continuous girders analyzed in the parametric investigation. While conservative results were provided, there was significant scatter in the results, and very conservative estimates of shear strength were noted for multiple cases.
Based on the results, changes are proposed to several articles of the LRFD BDS (AASHTO 2020) related to shear. Revisions to Article 5.7.3.3 modify the current shear design expressions regarding the shear contribution of the concrete and transverse steel as well as the upper limit of the nominal shear resistance. It was observed that there is a negligible contribution of the grout in a post-tensioned web duct to the shear strength of a girder. Therefore, to calculate the upper limit of the shear resistance (LRFD BDS Equation 5.7.3.3-2), the entire duct diameter for both grouted and ungrouted ducts should be subtracted from the web width to determine the effective web width. The full web width, however, should be used to calculate the contribution of the concrete in the LRFD BDS Equation 5.7.3.3-3. Stirrups were shown to be capable of achieving their yield strength; therefore, the reduction factor λduct is proposed to be eliminated to reflect the behavior and strength that the transverse reinforcement provides. If very large amounts of shear reinforcement are provided, the shear strength is limited through compression failure of the web, which is accounted by the upper limit of shear resistance (LRFD BDS Equation 5.7.3.3-2). The proposed recommendations result in improved estimates of the shear strength while maintaining conservative results and providing a consistent approach for the design of structures with grouted and ungrouted post-tensioning ducts.
5.1.3 Torsion
The bond type of the prestressing strand had limited influence on torsional behavior. The first observed cracking occurred at the level of the top post-tensioning duct in the webs, followed by torsional cracking in the top flange. Upon the initiation of torsional cracking, specimens with bonded tendons developed a singular torsional crack, while specimens with all unbonded
tendons simultaneously developed multiple torsional cracks across the test regions. The bond type of the tendons, however, did not have a significant influence on the behavior or ultimate torsional capacity of the specimens. The torsional strength of members with grouted ducts was essentially identical to those with ungrouted ducts. The location of the web strands (internal vs external) also did not affect the capacity. Finally, the transverse reinforcement ratio had little effect on the initiation of torsional cracking and did not impact the failure loads of the girders. However, the ultimate capacity of the specimens was limited by concrete compression failure, and yielding of the stirrups in the web was not observed.
The accuracy of the LRFD BDS (AASHTO 2020) in estimating torsional capacity was also evaluated. Analyses indicated that the LRFD BDS provide very conservative estimates of torsional capacity. Excessive conservatism was observed with the use of the λduct factor.
Based on the results, a change is proposed to Article 5.7.3.6.2 of the LRFD BDS (AASHTO 2020) for torsional resistance. The proposed change deletes λduct from the torsional strength equation to provide consistency with behavior and the proposed specification changes for shear strength.
5.2 Recommendations for Future Research
The following suggestions are provided for future research that can further enhance the design and construction of bonded and unbonded post-tensioned concrete bridge elements.
5.2.1 Flexure
The amount of minimum bonded flexural reinforcement recommended in this study is based on research conducted by Mattock et al. (1971), which is the basis of the ACI 318 building code. Use of this minimum reinforcement area was shown as sufficient to allow for use of the current AASHTO expression for calculation of stresses in unbonded tendons. Further research would be useful to investigate if refinement of this minimum is needed, considering girder sections and span lengths used in practice today. In addition, it would be useful to evaluate if the reinforcement type (mild or prestressed strand) of the minimum bonded reinforcement results in differences in behavior.
5.2.2 Shear
Further experimental testing is suggested to provide improved understanding of the shear behavior of unbonded post-tensioned beams. To further evaluate web-shear strength, it is recommended to test girders without transverse reinforcement so that the shear contribution of the concrete can be isolated. The test series should also include girders with increasing amounts of transverse reinforcement. This testing series will enable understanding of the complete range of behavior from girders where only the concrete provides shear resistance to girders where the shear contribution of the transverse reinforcement becomes limited due to compression failure of the web. Further testing is also recommended to provide an improved understanding of the influence of prestress force on web-shear strength. Varying the prestress force can influence shear crack angles and the contribution of the transverse reinforcement. A test series that varies the prestress force while holding all other variables constant can greatly improve understanding.
Additional shear testing is also suggested to evaluate the flexure-shear strength of unbonded post-tensioned beams that contain minimum bonded tension reinforcement. The use of bonded tension reinforcement provides for strain compatibility between the concrete and bonded reinforcement, which produces flexural cracking in the shear span. Fully unbonded beam tests could not produce this failure mode; therefore, these tests will be useful in further understanding the shear behavior of beams incorporating unbonded tendons as the primary flexural reinforcement.
5.2.3 Torsion
Further research examining the torsional behavior of bonded and unbonded tendons with nonuniform stress distributions across the cross section should be conducted. Torsional design expressions for prestressed members are based on a uniform stress distribution across the cross section. Testing has demonstrated that the nonuniform stress distribution due to eccentric prestressing influences torsional cracking. An improved understanding of the effects of eccentric prestressing on torsion is needed to provide improved estimates of torsional strength. Testing should also consider the effects of combined shear and torsional loading. Similar to shear, varying the prestress force can influence torsional crack angles and the contribution of the transverse reinforcement. Therefore, a testing series with varying prestress forces will also be helpful in improving estimates of both torsional cracking and torsional strength. Finally, torsional strength can be limited by concrete crushing. A test series should also be conducted that provides increasing amounts of transverse reinforcement to assist in defining the limiting torsional strength while also providing improved insight regarding the torsional resistance provided by the transverse reinforcement.
