**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

**Suggested Citation:**"Appendix B - Finite Element Analyses." National Academies of Sciences, Engineering, and Medicine. 2023.

*Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems*. Washington, DC: The National Academies Press. doi: 10.17226/27029.

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35Â Â A P P E N D I X B Finite Element Analyses After completing the literature review, the researchers proposed several analytical models to assess the shear key performance. The purpose of the analytical modeling was: 1. To assess the stresses in various shear key configurations under temperature movements. 2. To assess the stresses in various shear key configuration under live load application. 3. To determine parameters that affect shear key performance. Parameters considered were: a. Span length b. Girder depth c. Skew d. Deck type e. Amount of lateral post-tensioning f. Keyway reinforcement girders varied. Decks, either asphalt or concrete, were taken as 6 inches thick. Figure B-1. Cross section of bridge used in the analytical models. The material properties, unless noted otherwise, are listed in Table B-1. Table B-1. Material properties used in analytical models. Girder Concrete Compressive Strength 6 ksi Modulus of Elasticity 4,500 ksi Poisson Ratio 0.2 Tensile Strength 590 psi Coefficient of Thermal Expansion 5.5 x 106/oF Deck Concrete Compressive Strength 4.5 ksi The model cross section consisted of seven 48-inch-wide box girders (Figure B-1). The depth of the

36 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Modulus of Elasticity 3,800 ksi Poisson Ratio 0.2 Tensile Strength 500 psi Coefficient of Thermal Expansion 5.5 x 106/oF Grouta Compressive Strength 3 ksi at one day 8 ksi at 28 days Modulus of Elasticity 3,000 ksi Poisson Ratio 0.2 Tensile Strength 600 psi Coefficient of Thermal Expansion 5.5 x 106/oF (assumed same as concrete) Steel Modulus of Elasticity 29,000 ksi Coefficient of Thermal Expansion 6 x 106/oF Bearing Pads 9 in. x 6 in. x 1 in. thick 9 in. dimension placed transverse to the bridge span a Grout properties were determined as typical properties of non-shrink grout materials listed on the Ohio Department of Transportation Approved Product list in flowable condition. B.1 Temperature Analysis B.1.1 Temperature Analysis of the Shear Keys The weight of evidence is that temperature effects crack the shear keys. Field data show that the cracks tend to start near the ends of the girders (Miller, et al. 1999; Attanayake and Aktan 2015). This may be due to some restraint from the end bearings. Table B-2 shows the analytical cases performed for the temperature effects. The shapes of the shear keys noted in Table B-2 are shown in Figure B-2. The temperature modeling was handled as follows: 1. The bridge was modeled. The shear keys and concrete deck (for models with a concrete deck) were present but were âturned offâ to allow the elements to follow the deformations of the girders. 2. The temperature gradient from the AASHTO LRFD Specifications, Article 3.12.3 (2017) was applied to the box girders. The worst case of Solar Radiation Zone 1 was used. This caused the top of the boxes to expand. 3. The shear key and deck material were then âturned onâ to simulate the casting of the shear keys and deck. For asphalt decks, the asphalt was not modeled but the weight was added. 4. The temperature gradient was then removed from the girder to simulate cooling of the girders. 5. Stresses in the girders and keys were then assessed after cooling. Field observations, detailed in the literature review, showed that cracking tends to begin at the ends of the girders. This indicates that restraint due to support conditions may be important. Model 1 (45-foot span, 27-inch-deep girder, no skew, concrete deck) was initially run as a test model without end diaphragms in the boxes and a pinned end and a roller end for boundary conditions. The results showed higher stresses in the shear keys near the ends of the girders, consistent with field observations. Real girders often have end diaphragms and there was concern that end diaphragms may affect the results due to stiffening of the beam ends. Therefore, 18-inch-thick diaphragms were then added to the girder ends of the model. The first row

Finite Element Analyses 37 in Table B-3 shows the results of test Model 1 without diaphragms and the pinned and roller boundary conditions. The next row in Table B-3 shows the increase in the stresses in the shear key with the addition of end diaphragms. These stresses are significant enough to easily crack the shear keys and show that modeling the end diaphragms was necessary. Subsequent models then utilized 8-inch-thick end diaphragms. An 8-inch diaphragm may be small, so a few cases were rerun with an 18-inch-thick diaphragm and there was almost no difference in the results. Thus, the presence of a diaphragm appears to matter, but the thickness appeared less important. Table B-2. Models to study temperature effects. Model Span (ft) Girder Depth (in.) Shear Key Deck Skew (Â°) 1 45 27 Standard Type III Concrete 0 2 60 27 Standard Type III Concrete 0 3 60 42 Standard Type III Concrete 0 4 80 42 Standard Type III Concrete 0 5 45 27 Thin Full-Depth Type IV Concrete 0 6 60 27 Thin Full-Depth Type IV Concrete 0 7 60 42 Thin Full-Depth Type IV Concrete 0 8 80 42 Thin Full-Depth Type IV Concrete 0 9 45 27 Thick Full-Depth Type V Concrete 0 10 60 27 Thick Full-Depth Type V Concrete 0 11 60 42 Thick Full-Depth Type V Concrete 0 12 80 42 Thick Full-Depth Type V Concrete 0 13 45 27 Mid-Depth Concrete 0 14 60 27 Mid-Depth Concrete 0 15 60 42 Mid-Depth Concrete 0 16 80 42 Mid-Depth Concrete 0 17 60 27 Standard Type III Asphalt 0 18 60 27 Thin Full-Depth Type IV Asphalt 0 19 60 27 Thick Full-Depth Type V Asphalt 0 20 60 27 Mid-Depth Asphalt 0 21 60 27 Standard Type III Concrete 30 22 60 27 Thin Full-Depth Type IV Concrete 30 23 60 27 Thick Full-Depth Type V Concrete 30 24 60 27 Mid-Depth Concrete 30 25 80 42 Standard Type III Concrete 30 26 80 42 Thin Full-Depth Type IV Concrete 30 27 80 42 Thick Full-Depth Type V Concrete 30 28 80 42 Mid-Depth Concrete 30

38 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-2. Shear key configurations. (Horizontal dimensions are exaggerated for clarity.) Table B-3. Max shear key stress due to diaphragm and bearing pad effect for Model 1. Case Maximum Transverse Stress (ksi) Maximum Longitudinal Stress (ksi) w/o Diaphragm w/o Bearing Pads 3.4 1.7 w/ 18 in. Diaphragm w/o Bearing Pads 8.9 2.5 w/ 18 in. Diaphragm w/ Longitudinal Bearing Pads 2.1 0.53 w/ 18 in. Diaphragm w/ Transverse Bearing Pads 0.7 0.54 Initially, the boundary conditions were modeled as pinned and roller conditions. This was done to assure the model would run and that no problems were caused by improper boundary conditions. It also provided information on âideal, theoreticalâ supports. Once the model was running properly, the theoretical support conditions were replaced by the more realistic 9-inch by 6-inch by 1-inch-thick bearing pads. The 9-inch dimension was first placed in the longitudinal direction of the girders. This positioning was then changed so the 9-inch dimension was transverse to the bridge span. In addition, one end of the girders had two bearing pads and the other ends of the girders had a single centered bearing pad. This was done to investigate the effects of using a single center-bearing pad compared to using two bearing pads placed near the edges of the girder. As shown by the last three rows of Table B-3, the stresses decrease when using the bearing pads in comparison to the theoretical pinned and roller boundary conditions. Placement of the larger dimension of the bearing pad transverse to the bridge span, which is more common, also reduced the stress. Therefore, the remaining models investigated for temperature included 8-inch end diaphragms and 9-inch by 6-inch by 1-inch-thick bearing pads with the 9-inch dimension placed transverse to the bridge span. The maximum shear key stresses for Models 1â28 are provided in Table B-4. The maximum stresses typically occurred at the end of the girders supported with two bearing pads (location II) compared to the end with a single bearing pad (location I). In most cases, the difference in the stresses on each end was minor. The transverse stresses in the shear keys were higher than the longitudinal direction. This is

Finite Element Analyses 39 consistent with what has often been observed in the field with cracking occurring longitudinally due to transverse stress. The maximum transverse stress in the shear keys increased with the span length and girder depth for the standard Type III and thick full-depth Type V shear keys. However, the maximum transverse shear key stresses decreased with the span and beam depth for the thin full-depth Type IV shear key. There was little change for the mid-depth shear key. When the concrete deck was replaced with an asphalt wearing surface, the maximum transverse stress in the shear keys increased for all type of shear keys except the thick full-depth Type V which had negligible change. Of note was the large increase in stress in the mid-depth shear key. It appeared this key is more vulnerable to stresses when the deck is not present. Increasing the skew of the bridge to 30Â° resulted in maximum transverse stress increases for the thin full- depth Type IV and mid-depth shear keys but reductions in maximum transverse stresses in the shear keys for the standard Type III and thick full-depth Type V shear keys. Though the maximum stresses provided valuable information, it is important to get a more complete picture of the behavior of the joints when they are subjected to heating and cooling. To illustrate typical behavior, Figure B-3 provides the transverse shear stress in the exterior and first two interior standard Type III shear keys near the end of Case 2 (60-foot span, 27-inch-deep girder, no skew, concrete deck). Note that the figure and following figures only show the shear keys and no girders for clarity. As shown in Figure B- 3, high transverse tensile stress exists near the top of the key at the ends. This stress is in the range of 900 psi which is sufficient to crack the shear key. Also, the transverse stress remains tensile throughout the depth of the shear key at the ends. Moving away from the ends toward midspan shows the transverse stress becoming compressive. Again, this is consistent with field observations of cracking starting near the end of the girders.

40 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Table B-4. Maximum stress in shear key due to temperature. Model Span (ft) Girder Depth (in) Shear Key Deck Skew (Â°) Maximum Transverse Stress*(ksi) Maximum Longitudinal Stress*(ksi) 1 45 27 Standard (Type III) Concrete 0 0.73 II 0.54 II 2 60 27 0.96 II 0.60 I 3 60 42 1.00 II 0.75 II 4 80 42 1.00 II 0.75 II 5 45 27 Thin Full (Type IV) Concrete 0 0.97 II 0.72 II 6 60 27 0.74 II 0.54 II 7 60 42 0.69 II 0.55 II 8 80 42 0.69 II 0.60 II 9 45 27 Thick Full (Type V) Concrete 0 0.82 II 0.64 II 10 60 27 0.82 II 0.63 I 11 60 42 0.93 II 0.52 II 12 80 42 1.02 II 0.63 II 13 45 27 Mid-Depth Concrete 0 0.83 II 0.24 II 14 60 27 0.87 II 0.28 II 15 60 42 0.82 II 0.20 II 16 80 42 0.76 II 0.22 II 17 60 27 Standard Asphalt Wearing Surface 0 1.25 I 0.37 I 18 60 27 Thin Full 1.13 II 0.63 II 19 60 27 Thick Full 0.78 II 0.43 II 20 60 27 Mid-Depth 2.13 II 0.40 II 21 60 27 Standard Concrete 30 0.69 II 0.60 II 22 60 27 Thin Full 0.94 II 0.77 II 23 60 27 Thick Full 0.63 II 0.56 II 24 60 27 Mid-Depth 1.13 II 0.30 II 25 80 42 Standard Concrete 30 0.67 II 0.60 II 26 80 42 Thin Full 0.93 II 0.78 II 27 80 42 Thick Full 0.55 II 0.53 II 28 80 42 Mid-Depth 1.19 II 0.35 II *End Location of Maximum Stress: I near single bearing pad end; II near two bearing pad end.

Finite Element Analyses 41 Figure B-3. Case 2 transverse shear key stresses for standard (Type III) key. Figure B-4 shows the transverse shear key stresses for the thin full-depth (Type IV) key for Case 6 (60- foot span, 27-inch-deep girder, no skew, concrete deck). As shown, the stresses were high in the throat of the key in excess of 700 psi. However, the stresses decreased with depth of the key and compressive stresses existed at the bottom of the key near the end. This implied that cracking was still likely to occur near the top but may not fully penetrate through the full depth of the key. In addition, tensile stresses less than approximately 300 psi existed at the base of the throat of the key. Figure B-5 provides the results for the transverse shear key stresses of the thick full-depth (Type V) key. Similar to the thin full-depth key, the stresses were high near the top and exceed 800 psi. However, the transverse stresses at the bottom of the key were compressive even at the very end of the key. This suggests that the full-depth shear key may be successful because cracking will not penetrate the entire depth of the shear key, and this may prevent leakage. Figure B-4. Case 6 transverse shear key stresses for thin full-depth (Type IV) key.

42 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-5. Case 10 transverse shear key stresses for thick full-depth (Type V) key. B.1.2 Temperature Analysis of Keys Where the Throat Is Cracked or Not Grouted The research team (RT) also investigated removing the grout material within the throat. This simulates two cases: Either the throat is cracked and unable to transfer load or the throat is simply not grouted. The results for Case 6 without the throat are shown in Figure B-6. The transverse stresses were highly tensile near the top but dropped significantly and quickly with depth, eventually turning to compression. This was consistent with previous research by Huckelbridge et al. (1995, 1997) that cracking starts in the throat and that removal of the throat grout (as is done in the mid-depth shear key) may prevent cracking. In the configuration, the throat could be filled with a filler or sealer material which may help prevent leakage. Figure B-7 shows the transverse shear key stresses for the mid-depth key (which was originally proposed without a grouted throat). Similar to the thick full-depth key, the stresses were high at the top of the key (about 900 psi) and dropped quickly with depth. By the midpoint of the key, the tensile stresses were nearly zero and small compressive stresses developed at the bottom of the mid-depth shear key. As with the full- depth shear keys, the results suggested these keys may crack near the top, but the cracks may not propagate the entire depth of the shear key. Although not explicitly modeled, Figure B-5 suggested that thick full-depth (Type V) key would have little or no tensile stress if the key were not completely filled with grout or if cracking occurred at the top of key. Figure B-3 suggested that removing the grout from the throat of standard (Type III) key would be ineffective since the entire key is in tension.

Finite Element Analyses 43 Figure B-6. Case 6 without throat transverse shear key stresses for thin full-depth (Type IV) key. Figure B-7. Case 14 transverse shear key stresses for mid-depth key. B.2 Post-Tension Analysis B.2.1 Cases Examining Post-Tensioning Stresses Only Table B-5 provides models investigated for post-tensioning (PT) analysis. PT loads were applied to provide an average force of 11kâ12k per linear foot of girder. PT models were assembled as shown, with the deck, shear keys, and diaphragms hidden for clarity. Model 29 is shown in Figure B-8, Model 32 in Figure B-9, Model 35 in Figure B-10, and Model 38 in Figure B-11. PT analysis was performed where the girders were heated, shears keys placed, PT applied, deck placed, and the model cooled. As noted in the literature, PT was most beneficial near the application location and dropped off rapidly away from the PT locations. This was also observed in the PT models. Figure B-12 shows this effect for PT application at model ends and midspan. PT at model ends and third points results are shown in Figure B-13 and Figure B-14 shows results for PT application at model ends and quarter points. The figures show the compressive transverse stresses at the point of application of the PT and prior to cooling. As can be seen in the figures, the compressive stresses are high at the application of the PT (ends, midspan, third and quarter points), but decrease away from the PT application. In general, the stress condition shown in the

44 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-8. Model 29 assembly (deck, shear keys, and diaphragms hidden). Figure B-9. Model 32 assembly (deck, shear keys, and diaphragms hidden). Figure B-10. Model 35 assembly (deck, shear keys, and diaphragms hidden). figures is very similar to the condition found in analysis by Lopez de Murphy et al. (2010) and is consistent with field measurements (Miller et al. 2009) and laboratory measurements (Graybeal 2017a). Table B-5. Proposed models to study post-tensioning in joints. Model Span (ft) Girder Depth (in) Shear Key Deck Skew (Â°) PT Locations PT Force per Point (k) 29 45 27 Standard (Type III) Concrete 0 Ends/Midspan 165 30 60 27 Ends/Thirds 180 31 80 42 Ends/Quarters 187 32 45 27 Thin Full (Type IV) Concrete 0 Ends/Midspan 165 33 60 27 Ends/Thirds 180 34 80 42 Ends/Quarters 187 35 45 27 Thick Full (Type V) Concrete 0 Ends/Midspan 165 36 60 27 Ends/Thirds 180 37 80 42 Ends/Quarters 187 38 45 27 Mid-Depth Concrete 0 Ends/Midspan 165 39 60 27 Ends/Thirds 180 40 80 42 Ends/Quarters 187 41 60 27 Standard Asphalt Wearing Surface 0 Ends/Thirds 180 42 60 27 Thin Full Ends/Thirds 180 43 60 27 Thick Full Ends/Thirds 180 44 60 27 Mid-Depth Ends/Thirds 180

Finite Element Analyses 45 Figure B-11. Model 38 assembly (deck, shear keys, and diaphragms hidden). Figure B-12. Model 29 PT transverse stresses (end and midspan PT). Figure B-13. Model 30 PT transverse stresses (end and third points PT).

46 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-14. Model 31 PT transverse stresses (end and quarter points PT). Figure B-15 shows the left exterior key and two interior keys and how the PT compresses the Type III key when PT is applied at the model ends and midspan. The interior keys develop slight compressive stresses throughout the key, while the exterior key develops slight tensile stresses at locations between PT application points. The highest magnitude of compressive stresses develops at the bottom of the key and at points of PT application. Figure B-15. Model 29 shear key (Type III) transverse compressive stresses after PT application. Figure B-16 presents how the PT compresses the Type IV key when PT is applied at the model ends and midspan. Compressive stresses develop in most key locations, except at the mid-depth edges of the key where slight tensile stresses develop. The compressive stresses are greatest at PT application points, and rapidly decrease between PT points.

Finite Element Analyses 47 Figure B-16. Model 32 shear key (Type IV) transverse compressive stresses after PT application. Figure B-17 shows how the PT compresses the Type V key when PT is applied at the model ends and midspan. The distribution of developed compressive stresses is similar to the compressive stress distribution of the Type IV key. However, the stresses are less in magnitude and tensile stresses are not developed in the key. Figure B-17. Model 35 shear key (Type V) transverse compressive stresses after PT application. Figure B-18 presents how the PT compresses the mid-depth key when PT is applied at model ends and midspan. Compressive stresses are developed at most locations along the key, except at locations between PT application points where slight tensile stresses develop at the top of the key. The highest compressive stresses develop at points of PT application.

48 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-18. Model 38 shear key (Mid-Depth) transverse compressive stresses after PT application. The maximum shear key stresses for Models 29â44 are presented in Table B-6 after the PT was applied, deck placed, and the model cooled. The maximum transverse stresses occurred at the end of the girders, except for the Mid-Depth shear key in which maximum stresses occurred at midspan. In all cases, the stresses in the transverse direction of the shear keys were higher than those of the longitudinal direction. This is consistent with what has often been observed in the field with cracking occurring longitudinally due to transverse stress. It was observed that the maximum transverse stress in the shear keys increased with the span length and girder depth for the standard Type III shear keys. However, the maximum transverse shear key stresses decreased with the span and beam depth for the thin full-depth Type IV and thick full Type V shear keys. There was little change for the mid-depth shear key. When the concrete deck was replaced with an asphalt wearing surface, the maximum transverse stress in the shear keys decreased for all type of shear keys with the exception of the Standard Type III key. B.2.2 Combining Temperature and Post-Tensioning Stresses Though the maximum stresses provide valuable information, it is important to get a more complete picture of the behavior of the joints when subjected to the heating and cooling. To illustrate typical behavior, Figure B-19 provides the transverse shear key stress in the exterior and first two interior standard Type III shear keys near the end of Case 30 (60-foot span, 27-inch-deep girder, no skew, concrete deck). The transverse tensile stresses exist at the top of the key and gradually decreased throughout the shear key depth until stresses convert to compression. The maximum tensile stress is in the range of 883 psi, which is sufficient to crack the shear key. Figure B-20 shows the transverse shear key stresses for the thin full-depth (Type IV) key for Case 33 (60-foot span, 27-inch-deep girder, no skew, concrete deck). As shown, the stresses are high in the throat of the key, in excess of 600 psi. However, the stresses decrease with depth of the key and compressive stresses exist at the bottom of the key. This indicates that cracking is still likely to occur near the top but may not fully penetrate through the full depth of the key. This is consistent with previous research by Huckelbridge et al. (1997) that cracking starts in the throat and that removing the throat grout (as is done in the mid-depth shear key) may prevent cracking. Figure B-21 provides the results for the transverse shear key stresses of the thick full-depth (Type V) key for Case 36 (60-foot span, 27-inch-deep girder, no skew, concrete deck). Similar to the thin full-depth key,

Finite Element Analyses 49 the stresses are high near the top and exceed 700 psi. The transverse stresses are highly tensile near the top but drop significantly and quickly with depth, eventually turning to compression. This suggests that the full-depth shear key may be successful because cracking will not penetrate the entire depth of the shear key, and this may prevent leakage. Figure B-22 shows the transverse shear key stresses for the mid-depth shear key. This shear key experienced compressive stress at the end and PT locations, while the rest of shear key experienced tensile stresses. These stresses are high at the top of the key and drop quickly with depth. As with the full-depth shear keys, the results suggest these keys crack near the top, but the cracks may not propagate the entire depth of the shear key. Table B-6. Maximum stress in post-tensioned shear key due to temperature. Model Span (ft) Girder Depth (in.) Shear Key Deck PT Locations Maximum Transverse Stress* (ksi) Maximum Longitudinal Stress* (ksi) 29 45 27 Standard (Type III) Concrete Ends/Midspan 0.60 I 0.55 I 30 60 27 Ends/Thirds 0.88 I 0.69 I 31 80 42 Ends/Quarters 1.32 I 0.87 I 32 45 27 Thin Full (Type IV) Concrete Ends/Midspan 0.88 II 0.72 II 33 60 27 Ends/Thirds 0.61 II 0.52 II 34 80 42 Ends/Quarters 0.59 II 0.55 II 35 45 27 Thick Full (Type V) Concrete Ends/Midspan 0.73 II 0.62 II 36 60 27 Ends/Thirds 0.73 II 0.62 II 37 80 42 Ends/Quarters 0.56 II 0.51 II 38 45 27 Mid-Depth Concrete Ends/Midspan 0.66 MID 0.19 MID 39 60 27 Ends/Thirds 0.68 MID 0.22 MID 40 80 42 Ends/Quarters 0.63 MID 0.19 MID 41 60 27 Standard Asphalt Wearing Surface Ends/Thirds 0.84 II 0.34 MID 42 60 27 Thin Full Ends/Thirds 0.68 II 0.47 II 43 60 27 Thick Full Ends/Thirds 0.72 II 0.36 II 44 60 27 Mid-Depth Ends/Thirds 0.56 II 0.11 II * End Location of Maximum Stress: I near single bearing pad end; II near two bearing pad end; MID at the midspan.

50 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-19. Case 30 transverse shear key stresses for standard (Type III) key. Figure B-20. Case 32 transverse shear key stresses for thin full-depth (Type IV) key.

Finite Element Analyses 51 Figure B-21. Case 36 transverse shear key stresses for thick full-depth (Type V) key. Figure B-22. Case 39 transverse shear key stresses mid-depth key. The PT Type III (standard) key developed lower final maximum transverse tensile stresses compared to the non-PT Type III key for the shorter span lengths and girder depths. The non-PT Type III key developed lower final maximum transverse tensile stresses compared to the PT Type III key at the longer span length and girder depth. Thus, PT was less effective for the traditional Type III keys as the girders got longer and

52 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems deeper. The PT Type IV, Type V, and mid-depth keys developed lower final maximum transverse tensile stresses compared to the non-PT Type IV key for all span length and girder depth combinations. The comparison of maximum transverse tensile stress values between the non-PT and PT models may indicate that PT models generally perform better; however, this may be misleading as the maximum stress for non-PT models occurred at the ends and PT was applied at the ends. Therefore, a more complete assessment was to compare stresses at various locations along the key. Transverse tensile stress comparisons were made at the quarter point of non-PT and PT (midspan and third-point application) models. The results indicated that the PT did not substantially decrease stresses, and in some models actually increased stresses, as shown in Table B-7. Therefore, while PT may be effective in decreasing the maximum transverse stress experienced by the shear key at PT application locations, it was not as effective at decreasing high transverse stresses at locations between the PT application points and may even be detrimental. Table B-7. Maximum transverse stress in key at locations away from PT application points. Model Shear Key Analysis Stress Location (From End with 1 Bearing Pad) (in.) Transverse Stress (ksi) Change in Transverse Stress Due to PT (ksi) 1 Standard (Type III) Temp. Qtr. (135) 0.550 + 0.046 29 PT - Mid. Qtr. (135) 0.596 2 Standard (Type III) Temp. Qtr. (180) 0.734 + 0.098 30 PT - 1/3 Pt. Qtr. (180) 0.832 5 Thin Full (Type IV) Temp. Qtr. (135) 0.831 - 0.019 32 PT - Mid. Qtr. (135) 0.812 6 Thin Full (Type IV) Temp. Qtr. (180) 0.569 - 0.029 33 PT - 1/3 Pt. Qtr. (180) 0.540 9 Thick Full (Type V) Temp. Qtr. (135) 0.712 - 0.006 35 PT - Mid. Qtr. (135) 0.707 10 Thick Full (Type V) Temp. Qtr. (180) 0.711 - 0.019 36 PT - 1/3 Pt. Qtr. (180) 0.692 13 Mid-Depth Temp. Qtr. (135) 0.607 + 0.041 38 PT - Mid. Qtr. (135) 0.648 14 Mid-Depth Temp. Qtr. (180) 0.647 +0.016 39 PT - 1/3 Pt. Qtr. (180) 0.663 Temp. = temperature; Qtr. = quarter; Mid. = midspan; Pt. = point. B.3 Reinforced Joint Analysis Table B-8 provides the reinforced joint (RJ) models which were investigated. The RJ models were subjected to the same temperature cycle as the other models as detailed in the previous sections. The models also utilized the same end diaphragm and bearing pad layouts. The models were assembled as shown for Model 45 in Figure B-23 and for Model 47 in Figure B-24, with shear keys and deck hidden for clarity, and followed the reinforcement layout as shown in Figure B-25.

Finite Element Analyses 53 Table B-8. Models to study reinforcement in joints. Model Span (ft) Girder Depth (in.) Shear Key Skew (Â°) 45 60 27 Standard Type III 46 60 42 Standard Type III 47 60 27 Thick Full- Depth Type V 48 60 42 Thick Full- Depth Type V Figure B-23. Model 45 assembly cross section (shear keys and deck hidden). Figure B-24. Model 47 assembly cross section (shear keys and deck hidden). Figure B-25. Reinforced shear key layout (see Figure B-1 for shear key dimensions). The maximum shear key stresses for Models 45â48 are provided in Table B-9. The maximum stresses typically occurred at the end of the girders supported by two bearing pads (location II), as similarly observed in previous models. Stresses in the transverse direction were once again higher than stresses in the longitudinal direction. Maximum transverse stresses generally occurred in the block out section of the shear key, at the top and away from the geometric center of the key, as shown for Model 45 in Figure B-26. 0 0 0 0

54 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Table B-9. Maximum stress in reinforced shear key due to temperature. Model Span (ft) Girder Depth (in.) Shear Key Deck Skew (Â°) Maximum Transverse Stress* (ksi) Maximum Longitudinal Stress* (ksi) 45 60 27 Standard (Type III) Concrete 0 0.90 II 0.78 II 46 60 42 0.91 II 0.81 II 47 60 27 Thick Full (Type V) 0.94 II 0.79 I 48 60 42 0.92 II 0.82 II Figure B-26. Location of maximum transverse stress in model 45 shear key. Reinforcing the standard (Type III) shear key models (Models 45 and 46) results in a maximum transverse stress decrease of less than 100 psi, while also resulting in an increase of maximum longitudinal stress. Reinforcing the thick full (Type V) shear key models (Models 47 and 48) results in an increase of both maximum transverse and longitudinal stresses, compared to the unreinforced models. Figure B-27 shows the transverse shear key stresses for the standard (Type III) key. Stresses are high near the top of the block out, exceeding 800 psi, and decrease quickly with depth. While the high transverse stresses near the top of the block out would likely create cracking near the top, the rapid drop off of stresses through the depth of the key may indicate that the cracks would not penetrate any farther than the block out. Compressive transverse stresses are present at the bottom of the key but are of a lesser magnitude than was observed in the unreinforced Type III shear key models. The rebar develops higher tensile stresses at the ends of the models, and at locations embedded in the block out, with maximum transverse stresses generally not exceeding 9 ksi. Figure B-27. Case 45 transverse shear key stresses for standard (Type III) key.

Finite Element Analyses 55 Figure B-28 provides the results for the transverse shear key stresses of the thick full-depth (Type V) key. As observed in the unreinforced Type V key, tensile stresses are high near the top of the block out and decrease with depth. The high transverse tensile stresses on the top surface of the block out indicate cracking, however the rapidly decreasing stresses through the depth of the key may indicate that the cracking does not extend past the block out. Minor compressive stresses develop near the mid-depth of the key, but at a lesser magnitude than as observed in the unreinforced Type V key. As observed in the previous models, the embedded rebar develops higher tensile stresses at the model ends and at locations embedded in the block out. However, the rebar stress does not exceed 8 ksi. Figure B-28. Case 47 transverse shear key stresses for thick full (Type V) key. Reinforcing the shear key does not seem to help with temperature effects, but it will transfer load if the keys crack. The problem is that the joint is placed at the point of maximum temperature movement so cracking is likely. Bars do not prevent cracking but simply limit crack width. There is no guarantee that the bars can limit the width enough to prevent leakage. B.4 Live Load Analysis The live load models were run separately to assess the effect of live load only. They were also run with the temperature models. Figure B-29 shows an HL-93 truck loading on the bridge. Table B-10 shows the results of the truck load stresses (without temperature) for certain, representative cases. As seen in Table B-10, the stresses due to live load only are very low, confirming findings from earlier studies that live loads do not cause cracking, but may simply drive existing cracks.

56 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-29. Placement of a truck on the bridge for live load analysis.

Finite Element Analyses 57 Table B-10. Tensile stresses in shear keys due to truck load only (select models). Case No. Shear Key Shape Span (ft) Girder Depth (in.) Skew (Â°) Girder Topping Loading Type SK Maximum Transverse Stress (ksi)* SK Maximum Longitudinal Stress (ksi)* 1 Type III 45 27 0 Concrete LL 0.14 MID 0.03 MID 1 45 27 0 Concrete LL+Temp 0.73 II 0.54 II 2 60 27 0 Concrete LL 0.07 MID 0.04 I 3 60 42 0 Concrete LL 0.04 MID 0.002 II 4 80 42 0 Concrete LL 0.06 MID 0.002 II 5.1 Type IV 45 27 0 Concrete LL 0.15 MID 0.17 MID 6.1 60 27 0 Concrete LL 0.16 MID 0.25 MID 7.1 60 42 0 Concrete LL 0.10 MID 0.15 MID 8.1 80 42 0 Concrete LL 0.14 I 0.23 MID 5.2 Type IV (No Throat) 45 27 0 Concrete LL 0.15 MID 0.17 MID 5.2 45 27 0 Concrete LL+Temp 1.13 II 0.34 I 6.2 60 27 0 Concrete LL 0.16 MID 0.24 MID 7.2 60 42 0 Concrete LL 0.09 MID 0.15 MID 8.2 80 42 0 Concrete LL 0.13 I 0.22 MID 10 Type V 60 27 0 Concrete LL 0.06 MID 0.17 MID 11 60 42 0 Concrete LL 0.04 I 0.10 MID 12 80 42 0 Concrete LL 0.06 I 0.16 MID 14 Mid- Depth 60 27 0 Concrete LL 0.15 MID 0.12 MID 15 60 42 0 Concrete LL 0.06 MID 0.05 MID 16 80 42 0 Concrete LL 0.07 MID 0.07 MID *Location of maximum stresses: I = near end with one bearing pad, II = near end with two bearing pads. Note: MID = midspan, SK = shear key, LL = live load. However, the maximum tensile stresses in the shear keys in Table B-10 are misleading because of where the stresses actually occur. As shown in Figure B-30, the stress in the standard Type III shear key (Case 1) is actually mostly compressive with the tensile stress developing near midspan at the bottom of the shear key. This stress distribution is the opposite of the stress distribution due to temperature. Figure B-31 shows a similar result for the Type IV shear key without the throat grouted (Case 5.2). Since the live load stress for the cases shown were so low and the stress distribution is actually opposite to the temperature stress distribution, the cases shown in Table B-10 were the only live load cases investigated as further analysis was not seen as being beneficial or yielding useful results.

58 Guidelines for Adjacent Precast Concrete Box Beam Bridge Systems Figure B-30. Stress in the Type III shear key (Case 1) due to live load only. Figure B-31. Stress in the Type IV shear key without grout in the throat (Case 5.2) due to live load only.