Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections (2022)

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30 C H A P T E R 2 2.1 Introduction To meet the objective of the research, the analytical phase primarily focused on connection details between DBT girders using UHPC as an option. A number of past and ongoing studies have evaluated different connection details between slabs. Slabs in these tests are expected to behave similarly to flanges in DBTs. As part of meeting the overall objective, additional factors were considered: 1. The live load continuity at the transverse connections between DBT girders and applicability of the AASHTO 2020 LLDFs. 2. The fabrication, control of camber, stability, and erection of DBT girders using conventional and lightweight concrete. 3. The effects of span length, girder spacing, skew, diaphragm effects, differential camber and associated locked-in stresses, and provisions for bridge widening. Various models with different parameters and levels of detail were evaluated to determine connection designs for the DBT girders using UHPC. Figure 2.1 depicts details of the analytical modeling process in stages. Bridges were designed using commercial software to ensure they were practical (stage 1). Detailed finite element method (FEM) models with three beams were then used to assess the joint performance (stage 2). Finally, complete bridges with joint details were modeled and analyzed (stage 3). 2.2 Bridge Models: Stage 1 The primary purpose of stage 1 of the analytical modeling was to determine the girder section necessary for a given span. All bridge designs were five girders wide; the girder sizes varied with span. The concrete compressive strengths were taken as 7.5 ksi for the initial concrete compressive strength, f ′ci, and 10 ksi for the 28-day concrete compressive strength, f ′c. The girders were designed based on the AASHTO 2017a specifications under HL-93 live loading and self-weight. No other loading (e.g., barriers, braking, wind, earthquake) was considered in this stage. Software packages LEAP Bridge V8i and PGSuper were used in this stage. Detailed longitudinal joint information was not necessary in the models for this stage. Other parameters considered included: • Span: The shortest span was 55 ft. This span was used in order to start with a bridge system that matched the span in the full-scale experimental testing. Spans of 100, 150, and 200 ft. were also considered. The larger spans required a deeper DBT, which could affect behavior of the joint because taller webs with the same web thickness are a less rigid support for the flanges. In addition, the longer spans may have larger camber, which could come into play for differential camber considerations. Analytical Approach and Results

Analytical Approach and Results 31   • Concrete unit weight: The shorter span members were not very deep. Therefore, lightweight concrete (LWC) may not be as necessary for the girder section to deal with overall weight. The longer spans with larger girder sections cause an increase in weight so LWC was considered. • Skew: The majority of bridges have skews under 30°. Therefore, three different skews were investigated: 0°, 15°, and 30°. The case with 0° skew was expected to have the simplest behavior. According to AASHTO 2017a Article 9.7.1.3, the primary reinforcement in the deck may be placed in the direction of the skew if the skew angle does not exceed 25°. Reinforcement in the joint, and thus primary reinforcement in the flanges, was placed perpendicular to the web to meet AASHTO requirements. However, skew cases required fanning of the reinforcement near the ends. • Girder section: The girder section depended on design requirements such as the span and girder spacing. The PCEF DBT section was used as a starting point because the experimental testing used this section. The other primary sections available are the Precast/Prestressed Concrete Institute Northeast (PCINE) and WSDOT wide-flange deck bulb tees (WFDBTs). All three sections have differences in basic geometry. Both the PCINE and WSDOT sections have options for 60-in.- and 96-in.-wide flanges. WSDOT sections also come in 72-in. and 84-in. flange widths. The PCINE uses an 8-in.-thick flange while the WSDOT girders can have a flange thickness as small as 6 in. Since the WSDOT girders can be deeper and have large flange widths and thin flanges, this section was used along with the PCEF section. The PCINE section was not used. • Cross slope: The cross slope on DBT girder bridges can be obtained various ways. An overlay can be added with varying thickness, the girders can be set with their webs out of plumb, or the DBT flanges can be sloped to achieve the cross slope. Most cross slopes do not exceed 2%, and therefore this was investigated using the methods of placing the girders 2% out of plumb and sloping the DBT flanges 2%. Table 2.1 provides a summary of the sections considered along with the number of 0.6-in. grade 270 low-relaxation strands necessary for the exterior and interior girders. The exterior Stage 1: Bridge Models (LEAP Bridge V8i, PGSuper) Camber Stability (PCI, PGSTABL) Span Ranges Joint Details Stage 2: Joint Detail Models w/ 3 Girders (Abaqus) Joint Performance (Load and Temperature) Live Load Distribution Stage 3: Bridge Models w/ Joint Details (Abaqus) Bridge Performance (Load and Temperature) Input (Span(s), Skew, Diaphragms, Flange Thickness, Beam Spacing, etc.) Figure 2.1. Modeling process.

*The flanges of the girders were sloped to achieve bridge cross slope, but thickness remained constant. Case Span (ft.) Concrete Type Section Flange Width (in.) Flange Thickness (in.) Section Depth (in.) Skew (deg.) Girder Exterior 0.6-in. Strands Interior 0.6-in. Strands Harped Straight Total Harped Straight Total NWC PCEF 70.625 5.75 Plumb 10 12 10 12 NWC PCEF 70.625 5.75 15 Plumb 10 12 10 12 NWC PCEF 70.625 5.75 30 Plumb 10 12 10 12 4 NWC PCEF 70.625 5.75 2% 10 12 10 12 NWC PCEF 70.625 5.75 30 2% 10 12 10 12 6 55 55 55 55 55 55 NWC PCEF 70.625 2% slope* Plumb 10 12 10 12 7 100 NWC PCEF 70.625 5.75 Plumb 22 26 18 22 8 100 NWC PCEF 70.625 5.75 15 Plumb 22 26 18 22 9 1 2 3 5 100 NWC PCEF 70.625 5.75 30 Plumb 22 26 18 22 10 100 NWC PCEF 70.625 5.75 2% 22 26 18 22 11 100 NWC PCEF 70.625 5.75 30 2% 22 26 18 22 12 100 NWC PCEF 70.625 2% slope* Plumb 2 2 2 2 2 2 4 4 4 4 4 6 22 28 2 2 2 2 2 2 4 4 4 4 4 4 18 22 13 150 NWC PCEF 70.625 5.75 Plumb 10 32 42 10 24 34 14 150 NWC PCEF 70.625 5.75 15 Plumb 10 32 42 10 24 34 15 150 NWC PCEF 70.625 5.75 30 Plumb 10 32 42 10 24 34 16 150 NWC PCEF 70.625 5.75 2% 10 32 42 10 24 34 17 150 NWC PCEF 70.625 5.75 30 2% 10 32 42 10 24 34 18 150 NWC PCEF 70.625 2% slope* 39 39 39 39 39 39 47 47 47 47 47 47 63 63 63 63 63 63 Plumb 10 32 42 10 24 34 19 200 NWC WF103DG 103 Plumb 16 32 48 10 32 42 20 200 NWC WF103DG 103 Plumb 16 38 54 12 34 46 21 200 NWC WF103DG 103 30 Plumb 16 38 54 12 34 46 22 200 NWC WF103DG 2% slope* 103 Plumb 10 32 42 10 30 40 23 200 LWC WF103DG 103 Plumb 10 28 38 10 24 34 24 200 LWC WF103DG 103 30 Plumb 10 28 38 10 22 32 25 200 LWC WF103DG 103 30 Plumb 12 32 44 10 26 36 26 200 LWC WF103DG 6 6 6 6 6 6 6 103 Plumb 12 34 46 10 28 38 27 200 LWC WF103DG 60 96 96 60 60 60 96 96 60 2% slope* 103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Plumb 12 34 46 10 28 38 Table 2.1. Designs for stage 1.

Analytical Approach and Results 33   girders often required more strands due to their higher distribution factors. The designs were completed in the PGSuper software, with all plumb designs checked with the LEAP Bridge V8i software. The span-to-depth ratios of the girders are provided in Table 2.2. The 55-ft. span had a lower than typical ratio for DBT sections, but this span was chosen due to limitations on DBT length for testing in the laboratory. The smallest DBT section was selected for the 55-ft. span and analyses were performed to obtain results comparable to the proposed testing plan. 2.2.1 Distribution Factors The LLDFs provided by AASHTO 2020 for the precast prestressed concrete DBTs are based on case (j), which is specific for the precast prestressed concrete tee section with shear keys and with or without transverse post tensioning. It was assumed that the use of a UHPC joint was sufficient to connect the elements. Thus, the distribution factors for a bridge “sufficiently connected to act as a unit” were used. It is not clear how to apply the LRFD definition of the Kg term for a section like the DBT. Since I and A are defined as applying to the noncomposite beam and e is the distance between the deck and “basic” beam center of gravities, it is not clear how to calculate Kg for a monolithic section. One option is to assume the upper flange as the “deck” and everything beneath it as the beam. Another option is to use I and A for the entire beam and take es from the center of the flange to the centroid of the DBT. Table 2.3 shows the results for the 39-in. PCEF (case 1) and the 103-in. WSDOT (case 19) sections. While the difference can be significant for Kg, the distribution factor (DF) uses Kg within a term that is raised to the 0.1 power and its effect is minimal. Table 2.4 provides the distribution factors from the design cases considered. The exterior girders have higher distribution factors than the interior girders, which often occurs in design under AASHTO 2020. However, the difference between the interior and exterior MDFs gener- ally becomes higher as the span becomes larger. Span (ft.) Depth (in.) Span/Depth 55 39 16.9 100 47 25.5 150 63 28.6 200 103 23.3 Table 2.2. Span/depth ratios. Property 39-in. PCEF 103-in. WSDOT Not Separated Separated Not Separated Separated n 1 I (in.4) 186,153 A (in.2) 920 ybeam (in.) ydeck (in.) e (in.) Kg 342,214 S (ft.) L (ft.) 55 ts (in.) DF (1) 23.10 36.125 13.0 6.39 5.75 0.4835 1 699,301 1,297 100.00 6,060,908 200 6 35.70 64.3 5.50 0.3594 Difference 1 60,789 514 12.80 36.125 23.3 340,334 6.39 55 5.75 0.4833 0.048% 1 429,838 937 28.00 100.00 72.0 5,286,209 5.50 200 6 0.3554 1.13% Table 2.3. Longitudinal stiffness parameter, Kg.

34 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections An issue that arises due to the fairly large differences in the MDF for the exterior and interior DBT girders is that the exterior girders may have up to eight additional strands. Designers often design the interior girders the same as the exterior controlling girder even though this increases the cost of the strand used in the girder. If the exterior girder is designed differently from the interior girder, excessive differences may occur in camber between interior and exterior girders, leading to further difficulties during construction. In addition, fabrication of girders with dif- ferent strand patterns for interior and exterior girders increases cost of fabrication, causes addi- tional shop drawings, and prolongs the review process. These costs typically exceed the cost of additional strands. Therefore, designs used the same strand pattern for all girders within a span. 2.2.2 Camber Table 2.5 provides the cambers in the girders determined by the PGSuper software. The erec- tion (Δ1) camber was the amount of camber expected at the time of girder erection, which was assumed to occur at 90 days from girder fabrication. The longitudinal joints were assumed to be cast 31 days after girder erection (121 days after fabrication), which caused the additional camber growth from creep 1 (Δ2). The creep 2 (Δ4) camber provided was due to the additional creep Case Span (ft.) Concrete Type Section Type Flange Width (in.) Flange Thickness (in.) Section Depth (in.) Skew (deg.) Web Exterior Girder Interior Girder +M V +M V NWC PCEF 70.625 5.75 Plumb 0.813 0.813 0.656 0.698 NWC PCEF 70.625 5.75 15 Plumb 0.814 0.847 0.657 0.728 NWC PCEF 70.625 5.75 30 Plumb 0.772 0.886 0.625 0.761 NWC PCEF 70.625 5.75 2% 0.770 0.884 0.624 0.760 NWC PCEF 70.625 5.75 30 2% 0.770 0.884 0.624 0.760 55 55 55 55 55 55 NWC PCEF 70.625 2% slope* Plumb 0.813 0.813 0.661 0.698 100 NWC PCEF 70.625 5.75 Plumb 0.814 0.814 0.580 0.699 100 NWC PCEF 70.625 5.75 15 Plumb 0.814 0.848 0.580 0.728 1 2 3 4 5 6 7 8 9 100 NWC PCEF 70.625 5.75 30 Plumb 0.785 0.887 0.560 0.762 10 100 NWC PCEF 70.625 5.75 2% 0.814 0.814 0.580 0.699 11 100 NWC PCEF 70.625 5.75 30 2% 0.785 0.887 0.560 0.762 12 100 NWC PCEF 70.625 2% slope* Plumb 0.814 0.814 0.584 0.699 13 150 NWC PCEF 70.625 5.75 Plumb 0.814 0.814 0.555 0.699 14 150 NWC PCEF 70.625 5.75 15 Plumb 0.814 0.844 0.556 0.725 15 150 NWC PCEF 70.625 5.75 30 Plumb 0.788 0.879 0.538 0.755 16 150 NWC PCEF 70.625 5.75 2% 0.814 0.814 0.555 0.699 17 150 NWC PCEF 70.625 5.75 30 2% 0.788 0.879 0.538 0.755 18 150 NWC PCEF 70.625 2% slope* 39 39 39 39 39 39 47 47 47 47 47 47 63 63 63 63 63 63 Plumb 0.814 0.814 0.558 0.699 19 200 NWC WF103DG 103 Plumb 0.814 0.814 0.569 0.699 20 200 NWC WF103DG 103 Plumb 1.059 1.059 0.696 0.849 21 200 NWC WF103DG 103 30 Plumb 1.017 1.123 0.669 0.901 22 200 NWC WF103DG 2% slope* 103 Plumb 0.655 0.655 0.514 0.634 23 200 LWC WF103DG 103 Plumb 0.814 0.814 0.569 0.699 24 200 LWC WF103DG 103 30 Plumb 0.786 0.864 0.550 0.742 25 200 LWC WF103DG 103 30 Plumb 1.017 1.123 0.669 0.901 26 200 LWC WF103DG 6 6 6 6 6 6 6 103 Plumb 1.059 1.059 0.696 0.849 27 200 LWC WF103DG 60 96 96 60 60 60 96 96 60 2% slope* 103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Plumb 1.059 1.059 0.882 0.882 *The flanges of the girders were sloped to achieve bridge cross slope, but thickness remained constant. **Assumes type j bridge with girders transversely sufficient to act as a unit. Table 2.4. Distribution factors for designs.**

Analytical Approach and Results 35   another 27 days from casting of the longitudinal joints in the software. The values were provided to determine the change in camber of the girders after the UHPC longitudinal joints were cast. This could be critical to the longitudinal joints as the UHPC is gaining strength during this period. The change in camber increased with span length but was not significantly affected by skew. The largest difference occurred for the lightweight concrete models with large flanges. This was likely due to the lower self-weight of the girders to reduce camber from the prestressing. The timeline used for the calculations was very long, especially if considering accelerated bridge construction (ABC). However, a larger camber growth after the placement of the UHPC in the longitudinal joint would occur if the timeline were longer before the addition of other loads from barriers, overlay, sidewalk, etc. The larger camber growth would cause a higher longitudinal tensile stress in the UHPC, which would be more critical. Analyses were performed for cases 1, 7, 13, 19, and 20 using 2 days for longitudinal joint placement after girder erection and an additional 10 days after closure pour placement until the placement of barriers, overlay, sidewalk, etc. This resulted in changes of camber by at least a factor of 5 less than those provided in Table 2.5. 2.2.3 Deck and Longitudinal Joint Design AASHTO 2020 Article 5.12.2.3.3b notes that decks with flexural shear joints should be modeled as continuous plates and the empirical design procedure of Article 9.7.2 should not be used. Case Span (ft.) Concrete Type Section Type Flange Width (in.) Flange Thickness (in.) Section Depth (in.) Skew (deg.) Web Midspan Camber (in) Erection (Δ1) Creep 1 (Δ2) Creep 2 (Δ4) Change (Δ4−Δ2) NWC PCEF 70.625 5.75 Plumb 0.314 0.39 0.502 0.112 NWC PCEF 70.625 5.75 15 Plumb 0.306 0.381 0.49 0.109 NWC PCEF 70.625 5.75 30 Plumb 0.302 0.376 0.484 0.108 NWC PCEF 70.625 5.75 2% 0.309 0.384 0.494 0.11 NWC PCEF 70.625 5.75 30 2% 0.309 0.384 0.494 0.11 55 55 55 55 55 55 NWC PCEF 70.625 2% slope* Plumb 0.304 0.378 0.487 0.109 100 NWC PCEF 70.625 5.75 Plumb 1.322 1.644 2.117 0.473 100 NWC PCEF 70.625 5.75 15 Plumb 1.321 1.644 2.117 0.473 1 2 3 4 5 6 7 8 9 100 NWC PCEF 70.625 5.75 30 Plumb 1.319 1.642 2.113 0.471 10 100 NWC PCEF 70.625 5.75 2% 1.322 1.644 2.117 0.473 11 100 NWC PCEF 70.625 5.75 30 2% 1.319 1.642 2.113 0.471 12 100 NWC PCEF 70.625 2% slope* Plumb 1.419 1.766 2.273 0.507 13 150 NWC PCEF 70.625 5.75 Plumb 2.339 2.91 3.746 0.836 14 150 NWC PCEF 70.625 5.75 15 Plumb 2.341 2.913 3.75 0.837 15 150 NWC PCEF 70.625 5.75 30 Plumb 2.349 2.923 3.763 0.84 16 150 NWC PCEF 70.625 5.75 2% 2.339 2.91 3.746 0.836 17 150 NWC PCEF 70.625 5.75 30 2% 2.349 2.923 3.763 0.84 18 150 NWC PCEF 70.625 2% slope* 39 39 39 39 39 39 47 47 47 47 47 47 63 63 63 63 63 63 Plumb 2.279 2.835 3.65 0.815 19 200 NWC WSDOT 103 Plumb 1.223 1.522 1.959 0.437 20 200 NWC WSDOT 103 Plumb 1.791 2.231 2.875 0.644 21 200 NWC WSDOT 103 30 Plumb 1.81 2.254 2.905 0.651 22 200 NWC WSDOT 2% slope* 103 Plumb 0.911 1.133 1.459 0.326 23 200 LWC WSDOT 103 Plumb 2.66 3.31 4.261 0.951 24 200 LWC WSDOT 103 30 Plumb 2.681 3.335 4.293 0.958 25 200 LWC WSDOT 103 30 Plumb 3.479 4.33 5.584 1.254 26 200 LWC WSDOT 6 6 6 6 6 6 6 103 Plumb 3.825 4.765 6.141 1.376 27 200 LWC WSDOT 60 96 96 60 60 60 96 96 60 2% slope* 103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Plumb 3.698 4.600 5.922 1.322 *The flanges of the girders were sloped to achieve bridge cross slope, but thickness remained constant. Table 2.5. Cambers for designs.

36 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections Therefore, the deck, which was the upper flange of the DBT section, was designed using the strip method, which was incorporated and assessed in the LEAP Bridge V8i software. This required entering the DBT sections with an upper flange that consisted of only the nonprismatic sec- tion and using the thinner portion of the upper flange as the thickness of the “deck.” Figure 2.2 depicts the deck design model for case 20 (which is a WSDOT girder with 96-in. flange). The design of the top flange, which served as the deck for the DBT bridge system, was impor- tant to the research as it provides the transverse reinforcement near the longitudinal UHPC joints between girders. Currently, there are no design specifications in the United States for UHPC. To date, the most helpful document for UHPC connection design was covered in tech note FHWA-HRT-14-084 (Graybeal 2014b). This document provided guidance and associated commentary for the design of the UHPC connection details. Embedment length (ld) of straight bars No. 8 or smaller bars with yield strength not greater than 75 ksi should be taken as 8db, where db is the nominal bar diameter. This recommendation assumes the field cast UHPC has 2% steel fibers by volume, and cover is not less than 3db. If cover is less than 3db but greater than or equal to 2db, ld increases to 10db. Lap splice lengths (ls) of reinforcement should be at least 0.75ld. The clear spacing of the lap splice bars should not exceed ls, but should exceed the minimum spacing of reinforcing bars. The minimum spacing of bars is 1.5 times the length of the longest fiber reinforcement in the UHPC. Table 2.6 provides the UHPC connection design recommendations for No. 4, No. 5, and No. 6 bars. Since the No. 6 bars require a fairly large embedment length, the width of the longitudinal joint would have to be increased. In addition, cover requirements increase, leaving the bars less effective in flexure. Therefore, No. 5 bars were chosen for the top and bottom transverse reinforcement. The consistent top and bottom spacing simplifies fabrication and reduces the chance of bar interference in the joint during girder placement. Figure 2.2. Deck modeling in LEAP Bridge V8i. Bar Size Criteria Cover (in.) ld (in.) ls (in.) Spacing (in.) No. 4 UHPC ≥1.5 4.0 3.0 ≤3.0 ≥1.0 but <1.5 5.0 3.75 ≤3.75 No. 5 UHPC ≥1.875 5.0 3.75 ≤3.75 ≥1.25 but <1.875 6.25 4.69 ≤4.69 No. 6 UHPC ≥2.25 6.0 4.50 ≤4.5 ≥1.5 but <2.25 7.5 5.63 ≤5.63 Table 2.6. UHPC connection design recommendations.

Analytical Approach and Results 37   Table 2.7 provides the joint details for several DBT bridges that have UHPC longitudinal joint connections. Using No. 5 top and bottom bars in the experimental portion of the research was consistent with current UHPC joint designs. Table 2.8 provides the reinforcement results from the deck designs using the LEAP Bridge V8i software. Using No. 5 bars spaced at 6 in. top and bottom in the longitudinal joint works for the deck design. The design is also consistent with spacing used in other girders. The PCINE uses No. 4 at 6 in. in the flange. WSDOT uses No. 6 at 8 in. in the interiors girders and No. 6 at 5 in. for exterior girders. Although outside the scope of this research, it should also be noted that the top transverse reinforcement for the exterior girders is typically controlled by the design of the overhang, which supports the barrier or railing. The impact loads from vehicular collision often require additional reinforcement compared to that provided in Table 2.8. This additional reinforcement can be bundled with the transverse reinforcement or placed between the 6-in. spaced transverse reinforcement and terminated at the longitudinal joint. A difficulty with using the LEAP Bridge V8i software for the deck (top flange) design was that the changing depth of the flange (deck) could not be incorporated into the software. In addition, any change in the slope of the deck or girder could not be performed for the deck design. The differences in the material properties of the UHPC longitudinal joint could not be accounted for either. The increased depth of the flange (deck) near the web increases stiffness and causes more load to transfer toward the web/flange interface, as opposed to the midspan between adjacent DBT girders. This would reduce the moment at the location of the longitudinal joint. However, using UHPC in the joint increases stiffness at the joint and has an opposite effect as the chang- ing flange thickness. To investigate the effects of the UHPC stiffness in the longitudinal joint and the changing flange depth, simple beam models were constructed in another program, SAP2000; the cases considered included: 1. A model with members of constant cross section and material properties, similar to LEAP Bridge V8i. 2. A model with members of constant cross section but different material properties for the girder and UHPC joint. 3. A model with members of constant material properties but with changes in the flange thick- ness modeled as average cross-sectional depth between transitions. 4. A model with members of an average cross-sectional depth between changes in the flange thickness and different material properties for the girder and UHPC. Only cases 1 and 21 in Table 2.1 were investigated. Case 1 was investigated because it was the girder for the testing phase of the project; case 21 was considered because of the long span, deep girders, and wide flanges. All four spans between the five girders were modeled. For clarity, Bridge Name or Route Location Year Joint Girder Flange Reinforcement SR 31 (Forgham Street) Lyons, NY 2009 6 in. No. 6s (top) at 4.5 in. and No. 4s (bottom) at 9 in. Fingerboard Road Staten Island, NY 2011 6 in. No. 6s (top) and No. 4s (bottom) at 6 in. SR 248 Greenwood, NY 2011 6 in. No. 5s (top interior and bottom) and No. 7s (top exterior) at 6 in. SH 97 Coeur d’Alene, ID 2016 6 in. No. 5s (top and bottom) at 6 in. Table 2.7. Existing UHPC designs.

Case Span (ft.) Concrete Girder Section Flange Width (in.) Flange Thickness (in.) Girder Depth (in.) Skew (deg.) Web Longitudinal Deck Rebar Transverse Deck Rebar Top Bottom Top Bottom Bar Spacing (in.) Bar Spacing (in.) Bar Spacing (in.) Bar Spacing (in.) 1 NWC PCEF 70.625 5.75 0 Plumb #5 16 #6 12 #5 6 #5 6 2 NWC PCEF 70.625 5.75 15 Plumb #5 16 #6 12 #5 6 #5 6 3 NWC PCEF 70.625 5.75 30 Plumb #5 16 #6 12 #5 6 #5 6 4 NWC PCEF 70.625 5.75 0 2% #5 16 #6 12 #5 6 #5 6 5 NWC PCEF 70.625 5.75 30 2% #5 16 #6 12 #5 6 #5 6 6 55 55 55 55 55 55 NWC PCEF 70.625 2% slope 0 Plumb #5 16 #6 12 #5 6 #5 6 7 100 NWC PCEF 70.625 5.75 0 Plumb #5 16 #6 12 #5 6 #5 6 8 100 NWC PCEF 70.625 5.75 15 Plumb #5 16 #6 12 #5 6 #5 6 9 100 NWC PCEF 70.625 5.75 30 Plumb #5 16 #6 12 #5 6 #5 6 10 100 NWC PCEF 70.625 5.75 0 2% #5 16 #6 12 #5 6 #5 6 11 100 NWC PCEF 70.625 5.75 30 2% #5 16 #6 12 #5 6 #5 6 12 100 NWC PCEF 70.625 2% slope 0 Plumb #5 16 #6 12 #5 6 #5 6 13 150 NWC PCEF 70.625 5.75 0 Plumb #5 16 #6 12 #5 6 #5 6 14 150 NWC PCEF 70.625 5.75 15 Plumb #5 16 #6 12 #5 6 #5 6 15 150 NWC PCEF 70.625 5.75 30 Plumb #5 16 #6 12 #5 6 #5 6 16 150 NWC PCEF 70.625 5.75 0 2% #5 16 #6 12 #5 6 #5 6 17 150 NWC PCEF 70.625 5.75 30 2% #5 16 #6 12 #5 6 #5 6 18 150 NWC PCEF 70.625 2% slope 39 39 39 39 39 39 47 47 47 47 47 47 63 63 63 63 63 63 0 Plumb #5 16 #6 12 #5 6 #5 6 19 200 NWC WSDOT 103 0 Plumb #5 16 #6 12 #5 6 #5 6 20 200 NWC WSDOT 103 0 Plumb #5 16 #6 12 #5 6 #5 6 21 200 NWC WSDOT 103 30 Plumb #5 16 #6 12 #5 6 #5 6 22 200 NWC WSDOT 2% slope 103 0 Plumb #5 16 #6 12 #5 6 #5 6 23 200 LWC WSDOT 103 0 Plumb #5 16 #6 12 #5 6 #5 6 24 200 LWC WSDOT 103 30 Plumb #5 16 #6 12 #5 6 #5 6 25 200 LWC WSDOT 103 30 Plumb #5 16 #6 12 #5 6 #5 6 26 200 LWC WSDOT 6 6 6 6 6 6 6 103 0 Plumb #5 16 #6 12 #5 6 #5 6 27 200 LWC WSDOT 60 96 96 60 60 60 96 96 60 2% slope 103 0 Plumb #5 16 #6 12 #5 6 #5 6 Table 2.8. Deck reinforcement.

Analytical Approach and Results 39   Figure 2.3 shows a portion of the SAP2000 elements for model 4 of case 1 above a cross section for one of the girders. The beam elements in the SAP2000 model had different prismatic sections to account for some of the changing depth of the flanges, as well as the difference in material. Table 2.9 provides the data for the beam elements used in the case 1 model. For all models, the webs were assumed to be simple supports. Each model was loaded with a unit load at the middle of the first longitudinal joint. Table 2.10 provides the results of the positive and negative moments and percentage difference with the basic constant material and thickness model. As can be seen from the results, the positive moment can decrease approximately 10–20% when the effect of the UHPC properties and the changing flange thickness are included in the analyses. Therefore, the positive design moments for the longitudinal joint between girders are conser- vative if constant flange depth and material properties are considered. The negative moment increased over 20% for the two cases investigated. This should be considered when designing the top flange for transverse behavior. Figure 2.3. SAP2000 model. Element E (ksi) Depth (in.) Length (in.) C1 5,755 5.875 11.875 C2 5,755 6.75 18.0 C3 5,755 8.5 3.0 C4 5,755 9.5 3.4375 UHPC 7,268 5.75 6.0 Table 2.9. SAP2000 elements for case 1. Case Model +M % Change −M % Change 1 1 9.412 - −8.028 - 2 9.557 1.5 −7.882 −1.8 3 8.367 −11.1 −10.351 28.9 4 8.539 −9.3 −10.155 26.5 21 1 12.725 - −11.263 - 2 12.874 1.2 −11.115 −1.3 3 10.413 −18.2 −13.849 23.0 4 10.302 −19.0 −13.689 21.5 Table 2.10. SAP2000 model results.

40 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections Case Spans(ft.) −Mu (k-ft.) Section Flange Width (in.) Flange Thickness (in.) Depth (in.) Cover (in.) Required As (in.2) 1 55 1,152 PCEF 70.625 5.75 39 2.5 7.9 7 100 3,002 PCEF 70.625 5.75 47 2.5 16.8 19 200 8,368 WF103DG 60 6 103 2.5 20.6 20 200 10,883 WF103DG 96 6 103 2.5 26.8 Table 2.11. Deck continuity connection for negative moment. Case Girder Depth (a) Diaphragm Width (b) Bar Spacing Cover (c) Minimum Embedment (d) Minimum Lap Splice UHPC Depth (e) (in.) (in.) (in.) (in.) (in.) (in.) (in.) 1 39 7.5 No. 6 2 Rows of 9 @ 8 2.5 6 4.5 5.75 7 47 12.5 No. 6 2 Rows of 20 @ 3 2.5 6 4.5 6 19 103 14.0 No. 8 2 Rows of 14 @ 4 2.5 10 7.5 6.5 20 103 14.0 No. 8 2 Rows of 17 @ 4 2.5 10 7.5 6.5 Table 2.12. Negative moment continuity reinforcement. 2.2.4 Continuity Connection To initiate the design of the continuity connection over the pier, four cases were examined to determine the negative moment at the pier using the PGSuper software. Table 2.11 provides the details of the designs. For simplicity, bridges with two spans of equal length were considered and the case number corresponds to the simple-span designs from stage 1. The design moments only account for live load. Assumptions for the designs included HL-93 loading and distribution factors per AASHTO. The required reinforcement area was determined assuming grade 60 steel. Table 2.12 provides the reinforcement details for the UHPC continuity connection as well as the required dimensions per Figures 2.4 and 2.5. UHPC exists only in the upper portion of the diaphragm to save on material costs and deal with the higher negative moment. The lower portion of the diaphragm is assumed to be conventional concrete. The details for the reinforce- ment (cover, embedment, and lap splice) are based on tech note FHWA-HRT-14-084 (Graybeal 2014b). The recommendations from this reference assume straight bars No. 8 or smaller with yield strength not greater than 75 ksi, and the field-cast UHPC has 2% steel fibers by volume. The spacing of the bars is based on the requirements to meet the maximum negative moment requirements. The diaphragm width ensures the lap splice is sufficient for the minimum embed- ment. Transverse clear spacing of the lap splices shall not exceed the lap splice lengths. The continuity diaphragm is designed for restraint moments generated by time-dependent effects in addition to the negative moments from loads. For slab-girder bridges, differential shrinkage between the deck and girders determined analytically is believed to reduce the positive moment formation, but shrinkage between the deck and girders is not a consideration for DBT girders because the top flanges of the DBT girders are the deck. The age of the girder when conti- nuity is established affects the restraint moments. Article 5.12.3.3.4 of AASHTO 2020 mentions that simplifications can be made if the minimum age of the girder is 90 days. The simplifications include that calculation of restraint moments is not required, and the positive moment connec- tion capacity needs to exceed 1.2Mcr. The positive moment reinforcement needs to be developed in the girder and continuity diaphragm according to AASHTO 2020 Article 5.12.3.3.9. The reinforcement can be mild reinforcement or pretensioning strands embedded in the girders

Analytical Approach and Results 41   Figure 2.4. Continuity detail elevation. Figure 2.5. Plan view of continuity detail.

42 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections and developed into the continuity diaphragm. AASHTO also allows for any connection shown by analysis, testing, or approved by the owner to provide adequate positive moment capacity. If the simplifications mentioned above are not used, the positive moment connection has to resist the larger of the restraint moment or 0.6Mcr. The issue with the positive moment continuity designs is that they are based on the assump- tion that 1.2Mcr was conservative if the girder age was 90 days or more. The 1.2Mcr criterion was developed for conventional girder-deck bridges where the deck counteracts the positive moment formation (Mirmiran et al. 2001). In addition, the timeframes of many projects do not allow girders to be cast and then be erected 90 days or more. Therefore, the positive moment was investigated in more detail. Determination of the positive restraint moment is dependent on many variables and can lead to a wide range of results. The primary variables, which create the positive restraint moment, are creep and shrinkage. However, creep is affected by the magni- tude of stress caused by prestress and dead load. The magnitude of prestress is affected by elastic shortening, shrinkage of the concrete, relaxation of prestressing strands, and creep. Additional variables such as time, relative humidity, and volume to surface ratio also affect the prestress loss values. The percentage of creep and shrinkage losses that have occurred by the time the girder continuity connections have been created are provided in Table 2.13; these values use the refined method of prestress loss calculations in Article 5.9.3.4 of AASHTO 2020. Other assumptions include a relative humidity of 70%, low relaxation strands, age at release of 1 day, and a total time of 20,000 days. As shown in Table 2.13, approximately 50% of the creep and shrinkage have occurred if continuity is established at 28 days and over 75% has been completed if continuity is established after 90 days. 2.3 Joint 3D FEM Models: Stage 2 Stage 2 of the analytical work involved creating models of the bridges designed in stage 1. These models consisted of only three girders, but included details of the longitudinal joints such as geometry and reinforcement within the joint. The primary purpose of this stage of the model- ing was to assess the performance of the longitudinal joint under load and temperature gradient. Figure 2.6 shows the cross section and longitudinal joint detail for PCEF 39 used in models 1–6. The PCEF 47 and 63 sections are similar and only differ by web height. The WSDOT 103 used in models 19–27 uses a 6-in. flange at the tips, a 6.125-in. web, and a bottom flange width of 38.375 in. Figure 2.7 shows the joint detail for the WSDOT 103 section. Though the shape of the key does affect performance of the joint as noted by optimization of the keyway geometry performed by Hussein et al. (2018), the joint was not changed from the standard configuration. Optimization of the joint does not necessarily provide a significant performance enhancement. Case Girder Age when Continuity Established (days) 14 28 60 90 1 30.0 47.4 67.0 76.0 7 30.2 48.0 68.1 77.2 19 30.4 48.3 68.7 77.9 Table 2.13. Percentage of total creep and shrinkage losses completed before establishing continuity.

Analytical Approach and Results 43   Material properties used in stage 2 modeling were consistent with materials used in stage 1 modeling and are provided in Table 2.14. 2.3.1 Loading The loading applied in the models consisted of a single 16-kip wheel load applied over a contact area of approximately 10 in. × 20 in. The load was placed at midspan of the models and at the edge of the longitudinal face to create a worst case for the longitudinal joint. In some cases, the load was moved near the support in order to investigate skew effects. 2.3.2 Tied versus Cohesion Interface There are various ways to perform modeling of the interface of the UHPC and DBT concrete. In the case of the interface between the UHPC within the longitudinal joint and the flanges of the high-strength prestressed concrete DBTs, a tied constraint and cohesive constraint were investigated. A tied constraint condition forces the elements to remain connected at the interface between the UHPC and DBT flanges. This allows for transfer of loading and reduces (b) (a) Figure 2.6. PCEF 39 (a) cross section and (b) joint detail.

44 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections computation time in the model. However, it does not allow for separation at the interface, which would simulate cracking. The cohesive constraint condition allows separation to occur at the interface and simulate cracking. However, using cohesive constraints becomes more computa- tionally intensive and requires information on the behavior between the materials to be known. The information required is related to the shear and tensile bond behavior between the materials. Further details can be found in Appendix A. 2.3.3 Longitudinal versus Transverse Behavior Often modeling is done on reduced sections to save computational time and expense. For the longitudinal joints, the transverse behavior of the flanges is considered critical. Often, only a longitudinal section of the DBTs is considered. As an alternative, the girders are considered “supports” and only the flanges are modeled. The problem with these reduced models is the longitudinal behavior of the girders is often overlooked in whole or in part. The longitudinal bending behavior creates compressive strains and stresses in the top flanges and the UHPC longitudinal joints. These compressive strains cause expansion in the transverse direction from Poisson’s effect. The transverse expansion is resisted by the longitudinal joint and the transversely expanding adjacent girder flanges. This causes compression in the transverse Figure 2.7. WSDOT 103 joint detail. Element Strength (ksi) Poisson’s Ratio, µ E (ksi) Coefficient of Thermal Expansion, α (/°F) Girder NWC f ć = 10 0.20 6,164 6.0E−06 Girder LWC f ć = 10 0.20 3,393 6.0E−06 UHPC f ć = 22 0.18 8,520 9.4E−06 Strands fu = 270 0.30 28,500 7.0E−06 Reinforcement fy = 60 0.27 29,000 7.0E−06 Table 2.14. Stage 2 material properties.

Analytical Approach and Results 45   direction that reduces tensile strains and stresses from flexure in the transverse direction, however the net stress remains tensile. In addition, localized dishing at the concentrated wheel load causes longitudinal stresses and strains in the UHPC longitudinal joint. Figure 2.8 shows the deflection of case 1 from the end of the model, where the girders deflect longitudi- nally. Figure 2.9 shows the deflection of case 1 at midspan where the loading exists. This figure shows the exaggerated local transverse deflection of the flanges and girder rotations from the loading. The results for the cohesive models are provided in Table 2.15. For the models with the cohesive interface, the longitudinal stresses in the joint are typically higher than the transverse stresses. In addition, the dowels are stressed higher compared to the tied models. The largest longitudinal tensile stress in the joint (0.245 ksi) occurs in case 20 for the 96-in. flange WSDOT section. Nearly all the transverse tensile stresses in the joints are less than 0.1 ksi, with the largest (0.1050 ksi) occurring in case 25 when the flanges of the WSDOT 103-in.-deep section are 96 in. wide, and the section is made of LWC. The tied model results were similar to the cohesive interface models. 2.3.4 Skew The reinforcement doweled into the joint from the flanges for skewed ends was fanned to allow for placement without interference. The 16-kip load was placed near the end of models 1–3 to evaluate the effect of skew on the longitudinal joint. The results from this load placement for the models are shown in Table 2.16. The placement of the load near the end of the span increased the maximum transverse stress in the joint for all the models investigated compared to loading at midspan. The maximum longitudinal stress in the joint only increased for the models with skews (models 2 and 3) but slightly decreased for the model without skew (model 1). The stress in the dowels decreased for all the models loaded near the support compared to midspan load- ing. In addition, there was no clear effect from the skew for the models. The 15° model showed an increase in stresses in the joint in both the transverse and longitudinal directions compared to the unskewed model. The 30° skewed model had lower stresses compared to the 15° model. The 30° model also had lower transverse joint and dowel bar stresses compared to the unskewed model but higher longitudinal joint stress. Figure 2.8. End view of deflection for case 1. Figure 2.9. Midspan view of deflection for case 1.

46 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections Case Span (ft.) Concrete Girder Section Flange Width (in.) Flange Thickness (in.) Girder Depth (in.) Skew (deg.) Web Stress (ksi) Shear Key Dowels Longitudinal Transverse NWC PCEF 70.625 5.75 Plumb 2.165 0.0848 11.40 NWC PCEF 70.625 5.75 15 Plumb 2.176 0.4027 18.30 NWC PCEF 70.625 5.75 30 Plumb 2.030 0.3359 47.22 NWC PCEF 70.625 5.75 2% 2.166 0.1572 10.57 NWC PCEF 70.625 5.75 30 2% 2.055 0.3759 41.14 55 55 55 55 55 55 NWC PCEF 70.625 2% slope Plumb 2.194 0.2482 2.50 100 NWC PCEF 70.625 5.75 Plumb 1.864 0.7057 7.15 100 NWC PCEF 70.625 5.75 15 Plumb 2.179 0.2365 14.92 1 2 3 4 5 6 7 8 9 100 NWC PCEF 70.625 5.75 30 Plumb 2.195 0.3598 18.85 10 100 NWC PCEF 70.625 5.75 2% 1.997 0.1678 10.87 11 100 NWC PCEF 70.625 5.75 30 2% 2.162 0.3391 16.19 12 100 NWC PCEF 70.625 2% slope Plumb 2.175 0.1206 6.27 13 150 NWC PCEF 70.625 5.75 Plumb 1.774 0.3619 4.94 14 150 NWC PCEF 70.625 5.75 15 Plumb 2.172 0.2509 12.02 15 150 NWC PCEF 70.625 5.75 30 Plumb 2.196 0.2782 12.18 16 150 NWC PCEF 70.625 5.75 2% 2.170 0.2167 3.68 17 150 NWC PCEF 70.625 5.75 30 2% 2.191 0.3132 17.09 18 150 NWC PCEF 70.625 2% slope 39 39 39 39 39 39 47 47 47 47 47 47 63 63 63 63 63 63 Plumb 1.720 0.0499 19 200 NWC WSDOT 103 Plumb 2.202 0.3570 20 200 NWC WSDOT 103 Plumb 2.241 0.3567 21 200 NWC WSDOT 103 30 Plumb 2.233 0.2900 22 200 NWC WSDOT 2% slope 103 Plumb 2.202 0.3370 23 200 LWC WSDOT 103 Plumb 2.093 0.3401 24 200 LWC WSDOT 103 30 Plumb 2.754 0.2198 25 200 LWC WSDOT 103 30 Plumb 2.150 0.2642 26 200 LWC WSDOT 6 6 6 6 6 6 6 103 Plumb 2.157 0.3459 27 200 LWC WSDOT 60 96 96 60 60 60 96 96 60 2% slope 103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Plumb 2.091 0.3383 6.03 5.76 5.21 8.71 5.02 5.54 7.73 7.63 4.84 4.91 Table 2.15. Maximum tensile stresses from loading. Case Span (ft.) Girder Section Flange Width (in.) Flange Thickness (in.) Girder Depth (in.) Skew (deg.) Stress (ksi) Shear Key Dowels Longitudinal Transverse 1 55 PCEF 70.625 5.75 39 0 0.0884 0.0528 3.69 2 55 PCEF 70.625 5.75 39 15 0.1240 0.0567 4.05 3 55 PCEF 70.625 5.75 39 30 0.1115 0.0434 1.03 Table 2.16. Maximum tensile stresses from end loading.

Analytical Approach and Results 47   2.3.5 Lightweight versus Normal-Weight Concrete LWC was used in the 200-ft. spans with the WSDOT 103-in.-deep sections to compare the effects with the normal-weight concrete. The LWC was used in this large section as it would likely require LWC for shipping purposes. The use of LWC increased stresses in the longitudinal joint in both directions and also in the dowel bars for all cases with the one exception of the longitu- dinal stress for the 96-in. flange with no skew. The increase in stresses in the longitudinal joint is likely due to the lower assumed stiffness of the girders when using LWC compared to normal- weight concrete. This would lead to more force being transferred to stiffer sections such as the UHPC longitudinal joint. It should also be noted that the literature does not contain informa- tion on the bond characteristics between an exposed aggregate LWC finish and UHPC. Some work has been performed on UHPC and LWC but this was for connections with very different geometries (Banta 2005). Therefore, the models used assumed the same parameters as with the normal high-strength concrete. 2.3.6 Temperature AASHTO 2020 accounts for uniform temperature change in a bridge by one of two proce- dures. Procedure A or B can be used for bridges with concrete decks and concrete or steel girders. Procedure A involves a specified maximum and minimum extended temperature based on material and a climate condition of moderate or cold. The thermal deformation effects are based on the difference of the specified maximum or minimum temperature and the base construction temperature assumed in design. Procedure B involves taking the difference in a maximum and minimum temperature determined from contour figures in AASHTO 2020. The maximum and minimum temperatures determined from procedure A or B are then used to determine the design’s thermal movement range, ΔT, as noted in AASHTO 2020 Article 3.12.2.3. In addition to the uniform temperature change, AASHTO specifies a thermal gradient through the depth of the bridge. The thermal gradient depends on the zone location of the bridge, the depth of the bridge, and the material type. Both positive and negative temperature gradients should be considered. Both the uniform and thermal gradient temperature effects are thought of in terms of expan- sion and contraction of the bridge and the associated forces and stresses that may be generated if restraint resists the movements. However, temperatures can also change during construction of the bridge and affect connections such as the longitudinal joint in the DBT bridges. Increases in temperature after bridge completion cause expansion of the girders longitudi- nally and transversely. Adjoining girders and longitudinal joint expansion resist the transverse expansion. This creates compression in the longitudinal joints. However, if the expansion of the girders occurs during construction before the longitudinal joint is cast and cured, subsequent cooling of the joints and girders can create detrimental tensile strains and stresses in the joint. Therefore, analyses were performed assuming a uniform temperature drop of 80°F (procedure A for cold regions). The results of the uniform temperature analyses are provided in Table 2.17. The stresses are much higher than the loading condition investigated. Longitudinal stresses in the joint were higher than the transverse stresses. This is likely due to the higher coefficient of thermal expansion used for the UHPC relative to the girders. The stresses in the dowel bars were high, especially for the models with skews. Very high stresses were obtained in the dowel bars for the high-skewed short spans (cases 3 and 5). In addition, a temperature gradient can occur in the girders before longitudinal joint UHPC placement and curing. Therefore, a drop in temperature gradient approximately equal to the

48 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections Case Span (ft.) Concrete Girder Section Flange Width (in.) Flange Thickness (in.) Girder Depth (in.) Skew (deg.) Web Stress (ksi) Shear Key Dowels Longitudinal Transverse NWC PCEF 70.625 5.75 Plumb 2.165 0.0848 11.40 NWC PCEF 70.625 5.75 15 Plumb 2.176 0.4027 18.30 NWC PCEF 70.625 5.75 30 Plumb 2.030 0.3359 47.22 NWC PCEF 70.625 5.75 2% 2.166 0.1572 10.57 NWC PCEF 70.625 5.75 30 2% 2.055 0.3759 41.14 55 55 55 55 55 55 NWC PCEF 70.625 2% slope Plumb 2.194 0.2482 100 NWC PCEF 70.625 5.75 Plumb 1.864 0.7057 100 NWC PCEF 70.625 5.75 15 Plumb 2.179 0.2365 14.92 1 2 3 4 5 6 7 8 9 100 NWC PCEF 70.625 5.75 30 Plumb 2.195 0.3598 18.85 10 100 NWC PCEF 70.625 5.75 2% 1.997 0.1678 10.87 11 100 NWC PCEF 70.625 5.75 30 2% 2.162 0.3391 16.19 12 100 NWC PCEF 70.625 2% slope Plumb 2.175 0.1206 13 150 NWC PCEF 70.625 5.75 Plumb 1.774 0.3619 14 150 NWC PCEF 70.625 5.75 15 Plumb 2.172 0.2509 12.02 15 150 NWC PCEF 70.625 5.75 30 Plumb 2.196 0.2782 12.18 16 150 NWC PCEF 70.625 5.75 2% 2.170 0.2167 17 150 NWC PCEF 70.625 5.75 30 2% 2.191 0.3132 17.09 18 150 NWC PCEF 70.625 2% slope 39 39 39 39 39 39 47 47 47 47 47 47 63 63 63 63 63 63 Plumb 1.720 0.0499 19 200 NWC WSDOT 103 Plumb 2.202 0.3570 20 200 NWC WSDOT 103 Plumb 2.241 0.3567 21 200 NWC WSDOT 103 30 Plumb 2.233 0.2900 22 200 NWC WSDOT 2% slope 103 Plumb 2.202 0.3370 23 200 LWC WSDOT 103 Plumb 2.093 0.3401 24 200 LWC WSDOT 103 30 Plumb 2.754 0.2198 25 200 LWC WSDOT 103 30 Plumb 2.150 0.2642 26 200 LWC WSDOT 6 6 6 6 6 6 6 103 Plumb 2.157 0.3459 27 200 LWC WSDOT 60 96 96 60 60 60 96 96 60 2% slope 103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Plumb 2.091 0.3383 2.50 7.15 6.27 4.94 3.68 6.03 5.76 5.21 8.71 5.02 5.54 7.73 7.63 4.84 4.91 Table 2.17. Maximum tensile stresses from uniform temperature. AASHTO temperature gradient, as shown in Figure 2.10, was applied in models to determine effects on the longitudinal joint. Some of the models were investigated using the temperature gradient; results are shown in Table 2.18. The results from the temperature gradient were similar to the uniform temperature results: the stresses were higher for skewed models and much more significant than loading. 2.3.7 Diaphragms Diaphragms were not included in the analyses to save computing time and costs. Review of the results for cases 3 and 5 subjected to the uniform temperature revealed transverse bending of the girders, which led to higher flexure in the flanges. Adding diaphragms to the ends of the girders reduced the stress in the dowel bars. The results for the addition of the end diaphragms is shown in Table 2.19: the stresses in the dowels reduced to less than 10 ksi for both cases 3 and 5 once the end diaphragms were included in the models. Intermediate dia- phragms were also added to the midspans of the primary cases 1, 7, 13, and 19. The stresses in the shear key and dowel bars were reduced for the intermediate diaphragm cases when the wheel loading was applied at midspan. However, the stresses in the shear key and dowel

Analytical Approach and Results 49   bars increased slightly for some of the intermediate diaphragm cases when the uniform and linear temperature loading conditions were applied. This is likely because of the restriction from the intermediate diaphragm. 2.3.8 Camber The camber growths determined in stage 1 (see Table 2.5) were investigated further in stage 2. This was done by increasing the upward camber after the UHPC joints had been placed in the models. The results of these analyses for various cases are provided in Table 2.20; the transverse stresses in the shear keys are not significant. The longitudinal stresses from the camber growth Figure 2.10. Applied temperature gradient. Case Span (ft.) Concrete Girder Section Flange Width (in.) Flange Thickness (in.) Girder Depth (in.) Skew (deg.) Web Stress (ksi) Shear Key Dowels Longitudinal Transverse NWC PCEF 70.625 5.75 39 Plumb 2.075 0.2366 10.39 NWC PCEF 70.625 5.75 39 15 Plumb 2.109 0.2473 10.59 NWC PCEF 70.625 5.75 39 30 Plumb 2.068 0.2538 25.04 55 55 55 55 NWC PCEF 70.625 5.75 39 30 2% 2.610 0.1984 16.28 100 NWC PCEF 70.625 5.75 47 Plumb 1.897 0.3237 100 NWC PCEF 70.625 5.75 47 15 Plumb 2.015 0.2170 1 2 3 5 7 8 9 100 NWC PCEF 70.625 5.75 47 30 Plumb 1.684 0.4378 11 100 NWC PCEF 70.625 5.75 47 30 2% 2.534 0.6074 13 150 NWC PCEF 70.625 5.75 63 0 0 0 Plumb 1.737 0.3737 14 150 NWC PCEF 70.625 5.75 63 15 Plumb 1.976 0.1704 15 150 NWC PCEF 70.625 5.75 63 30 Plumb 1.982 0.1605 17 150 NWC PCEF 70.625 5.75 63 30 2% 2.734 0.1583 2.98 9.11 7.61 9.55 4.17 7.55 6.43 7.31 19 200 NWC WSDOT 60 6 103 0 Plumb 2.478 0.2194 11.37 Table 2.18. Maximum tensile stresses from gradient temperature.

50 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections Case Span (ft.) Girder Section Flange Width (in.) Girder Depth (in.) Skew (deg.) Web Condition No Diaphragm End Diaphragms Stress (ksi) Stress (ksi) Shear Key Dowels Shear Key Dowels Longitudinal Transverse Longitudinal Transverse 1 55 PCEF 70.625 39 0 Plumb Load 0.0930 0.0505 0.1110 0.0666 Uniform Temp 0.0848 0.1147 Gradient Temp 0.2366 0.2500 12.11 2 55 PCEF 70.625 39 15 Plumb Load 0.0868 0.0456 0.1041 0.0507 Uniform Temp 0.4027 0.3468 Gradient Temp 0.2473 0.2201 11.98 3 55 PCEF 70.625 39 30 Plumb Load 0.0957 0.0368 0.0984 0.0380 Uniform Temp 0.3359 0.1925 Gradient Temp 0.2538 0.2047 17.06 5 55 PCEF 70.625 39 30 2% Load 0.0725 0.0342 - - - Uniform Temp 0.3759 0.1068 Gradient Temp 0.1984 4.44 11.40 10.39 18.30 10.59 47.22 25.04 41.14 16.28 - - - 7 100 PCEF 70.625 47 0 Plumb Load 0.1007 0.0599 0.1387 0.1069 Uniform Temp 0.7057 0.8645 Gradient Temp 0.3237 0.6669 13 150 PCEF 70.625 63 0 Plumb Load 0.1351 0.0335 0.1664 0.0496 Uniform Temp 0.3619 0.3695 Gradient Temp 0.3737 0.4243 12.72 19 200 WSDOT 60 103 0 Plumb Load 0.0737 0.0279 0.0750 0.0277 Uniform Temp 0.1402 2.682 0.1751 Gradient Temp 0.2243 2.164 2.084 2.159 2.124 2.244 2.340 2.141 2.653 2.109 2.630 2.025 2.211 2.464 0.1345 20 200 WSDOT 96 103 0 Plumb Load 0.2447 0.0496 0.2380 0.0494 4.72 4.10 5.96 9.21 2.87 9.86 8.69 3.19 6.41 9.05 4.39 4.94 4.01 2.50 8.88 6.25 Uniform Temp 2.165 2.075 2.176 2.109 2.030 2.068 2.055 2.610 1.864 1.897 1.774 1.737 2.207 2.465 2.236 0.0807 5.46 3.02 3.83 2.84 7.15 2.98 5.48 4.94 4.17 4.06 6.64 6.38 2.96 1.066 0.3303 4.18 Table 2.19. End diaphragm effects on maximum tensile stresses from loading and temperature (cohesion models). Case Span (ft.) Skew (deg.) Longitudinal Shear Key Stress (ksi) Transverse Shear Key Stress (ksi) 1 55 0 0.2652 0.0053 7 100 0 0.3141 0.0079 13 150 0 0.4600 0.0099 19 200 0 0.3011 0.0014 20 200 0 0.3478 0.0054 23 200 0 0.5992 0.0034 26 200 0 0.8786 0.0040 Table 2.20. Shear key stresses from camber growth.

Analytical Approach and Results 51   can be fairly high. However, this assumed significantly long time periods, as noted in section 2.2.2 prior to the results of Table 2.5. Differential camber between members can also be perceived as an issue when leveling proce- dures are employed. Semendary et al. (2018) noted that leveling of differential camber could use approximately 20% of the capacity of the UHPC in the joint of DBT girders. Cases 1 and 19 were performed in a manner similar to that employed by Semendary et al. Case 1 analyzed a 0.5-in. camber differential and case 19 analyzed a 1-in. camber differential. The results of the analyses are provided in Table 2.21. As noted, the longitudinal stresses can be significant compared to the transverse stresses in the UHPC. 2.3.9 Ultimate Joint Capacity Loading the joint with a single wheel load did not produce very high stresses in the joint. The effects of uniform and gradient temperature changes were more critical. To investigate the longitudinal joint capacity, the load in the model for case 1 was increased until failure of the joint occurred. The ultimate load at failure of the joint was 340 kips. However, other aspects of the model showed issues well before this magnitude of loading, such as yielding of the reinforce- ment in the joint, longitudinal cracking of the girder’s top flanges, and transverse cracking of the girder’s bottom flanges. 2.3.10 Continuity Connection To estimate the positive moment, a model of the continuity connection consisting of the diaphragm and two girders was created in the finite element software Abaqus for cases 1, 7, and 19. The girders were then subjected to the effects of creep and shrinkage based on the age when continuity was established using AASHTO refined creep and shrinkage losses. The restraint moments were then determined from the generated stresses (see Table 2.22). The strand designs are based on continuity being established at 28 days. The positive restraint moments are much lower than the 1.2Mcr moments. Analyses were performed on models of the continuity connections to investigate the positive restraint moment effects. The traction-separation failure model was used to determine cracking (see Appendix B). Values greater than 1 indicate a crack. Figure 2.11 shows the results from the traction-separation failure model at the interface of the diaphragm with the girder for case 1. Case Span (ft.) Skew (deg.) Longitudinal Shear Key Stress (ksi) Transverse Shear Key Stress (ksi) 1 55 0 0.8341 0.2307 19 200 0 0.4288 0.0611 Table 2.21. Shear key stresses from differential camber leveling. Case Girder Age when Continuity Established (days) Number of 0.6-in. Strands Vertical Embedment of Strands (in.) 1.2Mcr 1 2 12 412 7 90 43 30.3 2 12 553 19 28 78 122 274.6 negative 5 14 1,809 Table 2.22. Positive restraint moment (kip-ft.).

52 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections This figure shows cracking is expected to occur near the junction of the web and top of the bottom flange when subjected to the positive restraint moment. The negative moment effects were also investigated for cases 1, 7, and 19 under service and ultimate loading. Table 2.23 provides the moments and stresses in the top mild reinforcement and the UHPC for both loading conditions. 2.4 Bridge 3D FEM Models: Stage 3 Stage 3 models included a total of five girders to simulate a full bridge and included the cohe- sive modeling of the interface for the longitudinal joints. These bridges had a minimum width exceeding 31 ft. to allow for at least two lanes. The primary objective of stage 3 modeling was to evaluate the LLDFs for comparison to AASHTO while incorporating behavior of the UHPC longitudinal joint. HL-93 loading was applied to the models as shown in Figures 2.12 and 2.13. The HL-93 truck loading was positioned, as shown in Figure 2.12, to produce the largest moment along the span. The lane loading is not shown in Figure 2.12 for clarity. The HL-93 loading was positioned transversely on the bridge, as shown in Figure 2.13, to produce the largest effect for the distribution factors. Figure 2.14 shows the longitudinal stresses at midspan for case 1 under the HL-93 loading. The live load MDFs have been determined in a variety of ways over the years. Ghosn et al. (1986) assumed each LLDF for a girder was equal to the ratio of the static strain in the girder Figure 2.11. Positive moment traction separation model for case 1. Case Service Moment (kip-ft.) Max Tensile Ultimate Stress in UHPC (ksi) Max Tensile Ultimate Stress in Mild Steel (ksi) Ultimate Moment (kip-ft.) Max Tensile Ultimate Stress in UHPC (ksi) Max Tensile Ultimate Stress in Mild Steel (ksi) 1 655 0.498 2.87 1,152 0.877 5.01 7 1,713 1.184 5.22 3,002 2.074 9.15 19 4,777 1.203 5.08 8,368 2.101 8.90 Table 2.23. Continuity stresses from negative service and ultimate moments.

Analytical Approach and Results 53   Figure 2.14. Longitudinal stresses in case 1 from HL-93 loading. Figure 2.13. HL-93 loading along bridge width. Wheel Load Wheel Load Lane Load 6 ft. 1 ft. 16 kips 16 kips 4 kips 14 ft2.3 ft11.67 ft L/2 Figure 2.12. HL-93 loading along span. over the total of the strains on all the girders. Stallings and Yoo (1993) used weighting factors to account for differences in the section modulus of exterior girders with interior girders. Since the girders in the models used for this research had the same section modulus for exterior and interior girders, the weighting factors are equal to 1. In addition, the modulus of elasticity of each girder is the equivalent. Therefore, each LLDF was determined by dividing the stress in each DBT girder from the FEM analysis by the sum of all the girder stresses as shown in Equation 1. The LLDF results of these analyses for moment in the interior and exterior girders under 1 and 2 lane loadings are provided in Table 2.24. As the results show, the moment live load distribution factors (MLLDFs) from the analyses are lower than those determined by AASHTO as provided in Table 2.4 for the exterior girders. For the interior girders, the MLLDFs from the analyses Case Interior Girder Exterior Girder 1 Lane Loaded 2 Lanes Loaded 1 Lane Loaded 2 Lanes Loaded 1 0.364 0.515 0.591 0.522 7 0.328 0.483 0.516 0.521 13 0.320 0.518 0.456 0.559 19 0.389 0.661 0.530 0.560 20 0.315 0.578 0.614 0.637 Table 2.24. LLDFs for moment.

54 Design and Construction of Deck Bulb Tee Girder Bridges with UHPC Connections are comparable and conservative based on AASHTO with the exception of case 19, which had a large span and closely spaced girders. ∑ ∑ = ε ε = σ σ LLDF (1) 1 1 w w i i i i i k i i k where: LLDFi = live load moment distribution factor for girder i εi = static strain in girder i wi = ratio of section modulus for girder i to interior girder σi = stress in girder i from live loading k = number of girders in the bridge To determine the distribution factors for shear, the truck loading was moved longitudinally to the support. The shear in each girder was then divided by the total shear for the end of the bridge to determine the LLDF for shear. The LLDFs for the shear at the end that was loaded are more critical and are shown in Table 2.25. As the results show, the LLDFs from the analyses are lower than those determined by AASHTO as provided in Table 2.4 for the interior girders. However, the analyses show higher shear LLDFs than AASHTO for the exterior girders. 2.5 Summary of Analytical Results Based on the analytical results, the following observations and general conclusions were made: 1. For the interior girder MLLDF calculations, assuming girders are sufficiently connected to act as a unit, AASHTO is not clear about the definition of the Kg term for a section like the DBT. The terms I and A are based on the noncomposite beam, and e the distance between the deck and beam center of gravities. One option is to assume the upper flange as the “deck” and everything beneath it as the beam. Another option is to use I and A for the entire beam and take es from the center of the flange to the centroid of the DBT. While the difference between the methods can be significant for Kg, the MLLDF uses Kg within a term raised to the 0.1 power and the effect is therefore minimal. 2. The higher stiffness of a longitudinal UHPC joint in a DBT bridge is offset by the changing cross section of the flanges such that the moment in the joint can be conservatively deter- mined assuming a constant-depth flange. However, the negative moment in the DBT flange at the web interface can be as much as 20% higher when a constant-depth flange is assumed. 3. Longitudinal bending behavior from live loading of DBT bridges creates compressive strains and stresses in the top flanges and the UHPC longitudinal joints. These compressive strains cause expansion in the transverse direction from Poisson’s effect. The transverse expansion is resisted by the longitudinal joint and the transversely expanding adjacent girder flanges. This causes compression in the transverse direction that reduces tensile strains and stresses from Case Interior Girder Exterior Girder 1 Lane Loaded 2 Lanes Loaded 1 Lane Loaded 2 Lanes Loaded 1 0.378 0.512 0.936 0.568 7 0.350 0.519 0.942 0.659 13 0.351 0.513 0.887 0.667 19 0.372 0.432 0.787 0.555 20 0.178 0.714 1.138 0.889 Table 2.25. LLDFs for shear.

Analytical Approach and Results 55   flexure in the transverse direction, but the net stress remains tensile. In addition, localized dishing at the concentrated wheel load causes longitudinal stresses and strains in the UHPC longitudinal joint. Stresses from live loading are not significant. 4. Both uniform and gradient temperature effects can change during construction of the bridge and affect connections such as the longitudinal joint in DBT bridges. If thermal expansion of the girders occurs during construction before the longitudinal joints are cast and cured, subsequent cooling of the joints and girders can create detrimental tensile strains and stresses in the joint. The analyses of a uniform 80°F temperature drop (procedure A for cold regions) resulted in stresses much higher than the live loading conditions investigated. Longitudinal stresses in the joint were higher than transverse stresses. This was due to the larger coefficient of thermal expansion for the UHPC relative to the girders. High stresses were also determined in the dowel bars for the high-skewed short spans. 5. A large uniform temperature change is less likely to occur during construction than a tem- perature gradient. Analyses from a gradient temperature drop equivalent to AASHTO zone 1 resulted in stresses much higher than the live loading conditions investigated. Longitudinal stresses in the joint were higher than transverse stresses. This was due to the larger coefficient of thermal expansion for the UHPC relative to the girders. High stresses were also determined in the dowel bars for the high-skewed short spans. 6. The addition of end diaphragms reduced stress in the dowel bars for bridges with skews. 7. Leveling of differential camber can produce significant stresses in the UHPC joints. 8. The use of UHPC in continuity connections between spans of DBTs can reduce the length of the connection due to the bond strength of UHPC. 9. The analytical results showed the moment LLDFs were lower than those determined by AASHTO for the exterior girders. For the interior girders, the MLLDFs from the analyses were com- parable and conservative based on AASHTO with the exception of a large-span and closely spaced girder bridge (case 19). The LLDFs for shear from the analyses are lower than those determined by AASHTO for the interior girders. However, the analyses showed higher shear LLDFs than AASHTO for the exterior girders.