Cast-in-Place Concrete Connections for Precast Deck Systems (2011)

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326 Chapter 10 Flange/Deck Connection: Numerical Studies to Determine Forces to be Applied in Large-Scale Tests 10.1. Investigation of Maximum Forces in the Longitudinal Joints 10.1.1. Introduction The objective of the numerical study described in this chapter was to develop a database of maximum forces for determination of the loading demand on the longitudinal joints due to service live loads. This information was subsequently used in the large-scale laboratory investigations to evaluate the performance of the joints. The effects of individual variables were researched by performing parametric studies using ABAQUS. The following variables were considered: • Girder geometry including depth, span, and spacing • Single-lane loading and multi-lane loading • Bridge Skew • Impact of cracking of joints The decked bulb-T (DBT) girder was chosen for this study. Table 10.1.1 summarizes the practical span ranges for typical girder sections (i.e., girder depths of 41, 53 and 65 in.). The girder section was named by the girder depth, such as section “DBT41” referring to a DBT girder with 41 in. depth. For each girder section, there were three different girder spacings investigated: 4, 6 and 8 ft. Figure 10.1.1 shows the cross section of the DBT girder. Table 10.1.1: Practical span ranges for optimized DBT girders Section Spacing (ft) Span (ft) Minimum Maximum DBT41 4 84 124 6 72 130 8 64 118 DBT53 4 98 150 6 84 156 8 76 148 DBT65 4 108 172 6 94 180

327 8 84 176 Figure 10.1.1: Cross section of optimized DBT girder 10.1.2. Description of Bridge Parameters Table 10.1.2 summarizes the seven bridge models with different girder geometry and bridge skew developed for the parametric study. Bridges A, B, C and D were straight bridges with various girder geometry (depth, spacing and span). Bridges D, E, F and G had the same girder geometry with different bridge skews. Table 10.1.2: Summary of the seven bridge models Bridge Girder Span (ft) Skew (degree) Depth (inch) Spacing (ft) A 65 8 134 0 B 65 8 84 0 C 65 4 108 0 D 41 8 118 0 E 41 8 118 45 F 41 8 118 30 G 41 8 118 15 4 ', 6 ' or 8 ' 41 '', 5 3' ' o r 65 '' 3 '- 6 '' 6' ' 6 '' 9. 5 '' Deck of Girder Bottom Bulb Sub-Flange Stem of Girder

328 All seven bridges were simply supported. The use of diaphragms between adjacent girders, as shown in Figure 10.1.2, would decrease the load transferred across the longitudinal joint. Consequently, only a single diaphragm (i.e., the minimum diaphragm configuration that would be used in practice) was assumed in the models to maximize the loads on the longitudinal joint. The single intermediate steel diaphragm (ISD) was assumed at midspan of the bridge to connect the web and bottom flange of the girders. Both the inclined member and horizontal member of the ISD used L 3x3x3/8 in. steel angles which had a cross-sectional area of 2.11 in2. The deck of the adjacent girders was connected by the proposed continuous longitudinal joint shown in Figure 10.1.3 as discussed in Chapter 9. Figure 10.1.2: Steel diaphragm connecting adjacent girders at midspan longitudinal joint top flange of decked girder (Typ.) longitudinal bar (Typ.) U bar (Typ.) A A A-A longitudinal joint (Typ.) top flange of decked girder (Typ.) Figure 10.1.3: Proposed continuous longitudinal joint Longitudinal Joint

329 All of the bridge models in Table 10.1.2 had the same bridge width of 40 ft; a modified version of bridge model B was later added to investigate the effect of bridge width. Figure 10.1.4-(a) to Figure 10.1.4-(d) show the cross-sectional views of the four straight bridges and Figure 10.1.5-(a) to Figure 10.1.5-(c) show the plan views of the three skew bridges. The joints between girders were labeled as “Joint 1”, “Joint 2” and so on from left to right. Because of the symmetry of each bridge in the width direction, the forces in the joints located in the left half of each bridge were studied. The metal railing was not shown in these sketches because only the live load was considered in the study, and the railing was assumed to have a negligible effect on the bridge stiffness. (a) Bridge A (65 in. deep; 96 in. spacing; 134 ft span) (b) Bridge B (65 in. deep; 96 in. spacing; 84 ft span) (c) Bridge C (65 in. deep; 48 in. spacing; 108 ft span) (d) Bridge D (41 in. deep; 96 in. spacing; 118 ft span) Figure 10.1.4: Cross section of bridge models

330 (a) Bridge E (b) Bridge F (c) Bridge G Figure 10.1.5: Plan view of skewed bridge models 10.1.3. Description of Loadings The AASHTO LRFD Bridge Design Specification HL-93 live load was used in the study. The HL-93 live load consisted of a design vehicle load and lane load. The design vehicle was either a design truck or design tandem whichever could produce the larger forces. Figure 10.1.6 shows the dimensions and wheel weights of the HL-93 live load. The tire contact area for the design vehicle was 10 by 20 in. The dynamic load allowance was applied to the design vehicle load but not to the lane load. The length of the lane load was varied to produce the largest load effects. The distance between middle wheel and rear wheel of the truck load could vary from 14 ft to 30 ft to produce the largest load effects. In the parametric study, multiple presence factors of 1.2 and 1.0 were used for single-lane loading and multi-lane (i.e., two-lane) loading, respectively. 135¡ ã 120¡ ã 105¡ ã

331 Figure 10.1.6: Dimensions and wheel weights of the HL-93 live load 10.1.4. Development of Finite Element Models Three-dimensional (3D) finite element (FE) modeling was completed using ABAQUS 6.7.1. The bridge modeling consisted of three main components: intermediate steel diaphragms at midspan, DBT girders, and the continuous longitudinal joint connection between the top flanges of adjacent girders (Figure 10.1.7). The inclined members of the steel diaphragm were modeled using 3D two-node truss elements (T3D2); the horizontal member was modeled using 3D two-node beam elements (B31) as shown in Figure 10.1.7-a. The angle between the inclined member and horizontal member was dependent on the depth and the spacing of the girder. The major portion of the DBT girder, including the bottom bulb, stem, sub-flange, and the deck directly above the sub-flange, was modeled using 3D twenty-node solid elements (C3D20) as shown in Figure 10.1.7-b. The remainder of the model consisted of the longitudinal joint that provided continuity of the deck between the DBTs by connecting the outer edges of the girder flanges shown in Figure 10.1.2. This was the main area of interest in this study. Sensitivity analyses were carried out to compare results using various modeling approaches for this area of the deck. Shell elements were used in lieu of solid elements in the sensitivity analyses to facilitate the determination of moments and shear forces in the longitudinal joint. Based on the results of the analyses (i.e., moments and shears compared at the longitudinal joints of bridges assuming only one interior transverse diaphragm at midspan), this area of the deck, including the continuous longitudinal joint connection, was modeled using 3D eight-node thick shell elements (S8R), as shown in Figure 9.1.7-c. 10 ft 0.444 psi 14 f t 6 ft 14 f t t o 30 f t 20 psi 80 psi 80 psi 20 psi 80 psi 80 psi 6 ft 4 ft62.5 psi 62.5 psi 62.5 psi 62.5 psi V ar ia bl e Truck Load Tandem Load Lane Load Rear Wheel Middle Wheel Front Wheel

332 (a) Intermediate steel diaphragm (b) Decked bulb-T (DBT) girder (c) Continuous longitudinal joint connection Figure 10.1.7: Bridge components modeled by 3D finite elements

333 Different material properties were assigned to different bridge components. The Young’s modulus for the stem of the girder including the bottom bulb and sub-flange was 4,769 ksi (based on 7 ksi compressive strength), the modulus for the deck of the girder was 3,605 ksi (based on 4,000 psi compressive strength), and the modulus for the steel diaphragm was 29,000 ksi. The Poisson’s ratios for the concrete and steel were taken as 0.18 and 0.3, respectively. A sufficiently refined mesh was used to ensure the results from the 3D FE models were adequate. The bridge models were assumed to be simply supported at the ends. In the 3D FE models (Figure 10.1.8), a roller support was modeled at one end by restraining the vertical movement (direction 3) of the bottom flange of the girders. The pinned support at the other end was modeled by restraining the movements of girder bottom flanges in both the girder length and vertical directions (direction 2 and 3). In the transverse direction (direction 1), both end sections of the girder were restrained to simulate concrete end diaphragms. The developed 3D FE models were calibrated and discussed in detail by Ma et al. 2007. Figure 10.1.8: Boundary conditions at pinned end 10.1.5. Parametric Study Based on the bridge models and vehicle loading discussed above, parametric studies were conducted to determine the maximum forces in the longitudinal joint. The following parameters were considered: different loading locations, effect of bridge width, combination of design truck and lane loading versus combination of design tandem and lane loading, girder geometry (depth, spacing and span), bridge skew, single-lane loading versus multi-lane loading, and impact of cracking of the joints. The maximum bending moment and maximum vertical shear in the longitudinal joints were the focus of the study. 10.1.5.1. Effect of Loading Locations Lane Loading. The effect of the extent of the lane loading on the maximum moments and shear in Joint 1 were studied with bridge model A (see Figure 10.1.4), considering its wider girder spacing and longer span.

334 The combination of design truck load and lane load was chosen to produce the maximum forces in the joint, the extreme condition of the design truck load with 14 ft between the middle wheel and rear wheel was applied in the study. Figure 10.1.9 shows the loading positions for the study of bending moment in Joint 1. The design truck was positioned at the same location in the two cases. In the longitudinal direction, the truck was located to produce the maximum moment in the bridge, and in the transverse direction, the center of the left wheels of the truck was located directly on top of Joint 1 to produce the maximum bending moment in the joint according to the influence line analysis. The length of lane load was varied. In case (a), the lane load was terminated at the center of the rear wheel of the truck while in case (b), the lane load was fully applied along the bridge in the longitudinal direction. The maximum bending moments with the corresponding vertical shear in the Joint 1 are shown in Table 10.1.3. Table 10.1.3: Forces in Joint 1 due to loads applied in accordance with Figure 10.1.9 Load Positions Forces in Joint 1 Maximum Moment (kip-ft/ft) Corresponding Shear (kip/ft) Case (a) 5.34 0.09 Case (b) 5.50 0.11 As shown in Table 10.1.3, the maximum moment in the two cases were very close which meant the position of lane load had little effect on the moment in the joint. The values of the corresponding vertical shear were very small and close to zero indicating that there was almost no shear while the maximum moment was produced in the joint.

335 Case (a) Case (b) Detail A Figure 10.1.9: Lane loading positions for moment Figure 10.1.10 shows the loading positions for the study of vertical shear. In the longitudinal direction, the design truck load was located at the same position as for the case of the moment study. In the transverse direction, the left edge of left wheels was located directly on top of Joint 1 to produce the maximum vertical shear in the joint according to the influence line analysis. There were three different lane loads investigated as shown in cases (a) through (c), respectively: fully along the bridge; terminated at the center of the middle wheels; and terminated at the center of the rear wheels. The maximum shear with the corresponding moment for each load case is presented in the Table 10.1.4. See Detail A Joint 1Joint 1 Rear WheelRear Wheel 14 f t Middle Span Joint 1 10 ft 6 ft 14 f t Lane Load Truck Load (Typ.)

336 Case (a) Case (b) Case (c) Detail A Figure 10.1.10: Lane loading positions for shear Joint 1 Joint 1 Middle Span Joint 1Joint 1 Detail A

337 Table 10.1.4: Forces in Joint 1 due to loads applied in accordance with Figure 10.1.10 Load Positions Forces in Joint 1 Corresponding Moment (kip-ft/ft) Maximum Shear (kip/ft) Case (a) 3.76 4.93 Case (b) 3.60 5.92 Case (c) 3.72 6.02 From Table 10.1.4, it can be seen that cases (b) and (c) produced larger maximum shears than case (a); however, the difference was not significant. As long as the lane load was terminated at the heavy truck wheel (middle wheel or rear wheel), the difference of the maximum shear in the two cases was negligible. In summary, the lane load which was fully applied along the bridge length direction produced the largest moment in the joint while the lane load that terminated at the center of the rear truck wheel produced the largest shear in the joint. Truck/Tandem Loading Positions The effects of the truck and tandem loading positions on the maximum moments and shear generated in Joint 1 were also studied with the bridge model A. Figure 10.1.11 shows the loading positions for the study of bending moment. In all six cases, the lane load was fully applied along the bridge length direction. For the truck load, the center of the left wheel was located directly on top of Joint 1 (Figure 10.1.9-detail A) in the transverse direction. In the longitudinal direction, the truck positions were specified by the distance between the center of the front wheel and the midspan of the bridge. The results of maximum moment in Joint 1 and the corresponding shear are given in Table 10.1.5.

338 Case (a) Case (b) Case (c) Case (d) Case (e) Case (f) Figure 10.1.11: Truck load positions for moment Joint 1 Middle Span 36 f t 9 ft 14 f t Joint 1 Joint 1 16 f t 23 f t 63 f t Joint 1 Joint 1 Joint 1

339 Table 10.1.5: Forces in Joint 1 due to loads applied in accordance with Figure 10.1.11 Load Positions Forces in Joint 1 Maximum Moment (kip-ft/ft) Corresponding Shear (kip/ft) Case (a) 5.39 0.04 Case (b) 5.50 0.05 Case (c) 5.50 0.09 Case (d) 5.50 0.11 Case (e) 5.49 0.14 Case (f) 5.49 0.07 As shown in Table 10.1.5, all six cases produced approximately the same maximum moment in Joint 1. Truck loads with heavy wheels (middle wheels and rear wheels) located near midspan (Cases b-e) produced 2% more moment than the truck loads with heavy wheels located farthest from midspan (Cases a and f). Consequently, while load case (d) produced the largest maximum moment, the influence of the truck load position on the maximum moment was negligible. Figure 10.1.12 shows the loading positions for the study of vertical shear. In all four cases, the lane load was terminated at the center of truck rear wheel. For the truck load, the left edge of the left wheel was located directly on top of Joint 1 (Figure 10.1.10-detail A) in the transverse direction. In the longitudinal direction, the truck positions were specified by the distance between the center of the front wheel and the midspan of the bridge. The maximum shears and corresponding moments obtained in Joint 1 are given in Table 10.1.6.

340 Case (a) Case (b) Case (c) Case (d) Figure 10.1.12: Truck load positions for shear Table 10.1.6: Forces in Joint 1 due to loads applied in accordance with Figure 10.1.12 Load Cases Forces in Joint 1 Corresponding Moment (kip-ft/ft) Maximum Shear (kip/ft) a 3.82 5.81 b 3.72 6.02 c 3.61 5.95 d 2.80 5.39 As shown in Table 10.1.6, truck loads with heavy wheels (middle wheels and rear wheels) located near midspan (Cases a- c) produced larger shear forces than truck loads with the heavy wheels located further away from midspan (Case d). For truck loads with the heavy wheels located near midspan, the variation in maximum shear force in the joint was only 3%. As for the investigation of the truck load position, bridge model A was also used to investigate the effect of the tandem loading position on the maximum moment and shear in Joint 1. Figure 10.1.13 shows the locations of the tandem load combined with the lane load to produce the maximum moment or shear in Joint 1 14 f t 16 f t 23 f t 63 f t Joint 1 Joint 1 Joint 1

341 the joint. In Figure 10.1.13-a, the tandem was located to produce maximum moment in the longitudinal direction of the bridge, while in the transverse direction, the center of left wheels of the tandem was located directly on top of Joint 1. The lane load was applied fully along the bridge length. In Figure 10.1.13-b to determine maximum shear, the tandem was positioned at the same location in the longitudinal direction, while in the transverse direction; the left edge of the left wheels was located directly on top of Joint 1. The lane load terminated at the center of the rear tandem wheel. In summary, the influence of truck load position in the longitudinal direction on the maximum moment and shear in the joint was not significant while truck loads with heavy wheels located near midspan produced the largest maximum moment and shear. In summary, the influence of the location of the vehicle load (truck or tandem) in the longitudinal direction on the maximum forces in the joint was not significant. The truck with heavy wheels (middle wheel or rear wheel) or the tandem located around midspan of the bridge produced a slightly larger moment and shear than the other locations.

342 (a): Maximum Moment (b): Maximum Shear Figure 10.1.13: Tandem load positions for maximum moment and shear 6 ft 4 ft Middle Span Joint 1 10 ft Tandem Load (Typ.) Joint 1 See Detail A Detail A Lane Load Middle Span Joint 1 10 ft 6 ft 4 ft Tandem Load (Typ.) Lane Load Joint 1 See Detail B Detail B

343 10.1.5.2. Effect of Bridge Width Figure 10.1.14 shows the effect of the bridge width on the maximum negative moment in Joint 2 of bridge model B. Joint 2 was studied because joints closer to the middle of the bridge deck will experience larger negative moments when loads are applied closer to the edge of the deck. The position for the left loading was the same for all three cases (i.e., the left edge of the left lane loading was 2 ft away from the left edge of the bridge based on the requirement specified in the AASHTO LRFD (2010)). The position of the right loading was varied. The right edge of the right lane loading was 10, 6 and 2 ft away from the right edge of the bridge for Cases (a) through (c), respectively. Table 10.1.7 summarizes the results for the maximum negative moment under the three loading cases. Case (a) Case (b) Case (c) Figure 10.1.14: Load positions for negative moment on bridge model B Table 10.1.7: Negative moment in Joint 2 due to loads applied in accordance with Figure 10.1.14 Load Positions Maximum Negative Moment (kip-ft/ft) Case a -0.66 Case b -1.00 Case c -1.03 Joint 2 10' 6' 2' Joint 2 Joint 2 2'2'2'

344 As shown in Table 10.1.7, it appeared that the maximum negative moment increased with the increase in distance between the two loadings in the transverse direction such that a larger negative moment would be expected to be produced in a wider bridge. In order to study the impact of bridge width on the negative moment, a “modified bridge B” (adding one more girder) was developed in the study. Figure 10.1.15 shows the cross section of the modified bridge model B. Figure 10.1.15: Cross section of Modified Bridge B Figure 10.1.16 shows the multi-lane loading positions on the modified bridge model B to produce negative moment in Joints 2 and 3. The left edge of the left lane loading was 2 ft away from the left edge of the bridge while the right edge of the right lane loading was 2 ft away from the right edge of the bridge. The maximum negative moments in Joints 2 and 3 are summarized in Table 10.1.8. Figure 10.1.16: Loading positions for negative moment on modified bridge model B Joint 1 Joint 2 Joint 3 Joint 2 2'2' Joint 3

345 Table 10.1.8: Negative moment in Joints 2 and 3 due to loads applied in accordance with Figure 10.1.16 Modified Bridge B Maximum Negative Moment (kip-ft/ft) Joint 2 -0.67 Joint 3 -0.87 The maximum negative moment in modified bridge model B, given in Table 10.1.8, was less than that of bridge model B, given in Table 10.1.7. The maximum positive moment and shear were also studied between bridge B and modified bridge B. The maximum forces under different loading locations are presented in Table 10.1.9. Table 10.1.9: Maximum positive moment and shear comparison between bridge B and modified bridge B Bridge B Modified Bridge B Moment (kip-ft/ft) Shear (kip/ft) Moment (kip-ft/ft) Shear (kip/ft) Joint 1 5.03 5.65 5.03 5.63 Joint 2 5.23 5.90 5.15 5.69 Joint 3 5.10 5.69 From Table 10.1.9, the maximum positive moment and shear in the modified bridge model B were less than those found for bridge model B; however, the difference was negligible. In summary, increasing the bridge width decreased the maximum negative moment in the joints while it had a negligible effect on the maximum positive moment and the maximum shear. 10.1.5.3. Truck and Lane Loading versus Tandem and Lane Loading The HL-93 live load has two different loading combinations: one combination was truck load plus lane load; the other combination was tandem load plus lane load. Generally, the truck and lane load combination produce larger forces on long-span bridges; while the tandem and lane load combination produce larger forces on short-span bridges (where the span of the bridge is comparable to the distance from the front wheel to the rear wheel of the truck). In order to determine the effect of different loading combinations on the maximum forces in the joint for practical span ranges of DBT girders, the maximum forces under two

346 loading combinations both for the long-span bridge (bridge model A) and the short-span bridge (bridge model B) were studied. Figure 10.1.17 shows a comparison of the maximum moment and shear in Joints 1 and 2 produced by different loading combinations in the long-span bridge (bridge model A). The label “Truck” means truck and lane load combination while “Tandem” refers to the tandem and lane load combination. (a) Moment (b) Shear Figure 10.1.17: Moment and shear comparison in long-span bridge (A) Figure 10.1.18 shows a comparison of the maximum moment and shear in Joints 1 and 2 produced by different loading combinations in the short-span bridge (bridge model B).

347 (a) Moment (b) Shear Figure 10.1.18: Moment and shear comparison in short-span bridge (B) It can be seen that the truck and lane load combination produced larger maximum forces than the tandem and lane load combination in both the long- and short-span bridges investigated. This occurred because the practical span range of DBT girders is much longer than the truck length which makes the truck and lane load dominate the loading. 10.1.5.4. Effect of Girder Span The effect of girder span on the maximum forces in the joints was studied between bridge model A and bridge model B. Both bridge models had the same girder cross-sectional geometry. Bridge model A had a long girder span while bridge model B had a short girder span. Figure 10.1.19 compares the maximum forces in the joint between the long-span bridge model A and the short-span bridge model B.

348 (a) Positive Moment (b) Shear (c) Negative Moment Figure 10.1.19: Span effect on forces in joint

349 It can be seen that the girder span had some effect on the maximum positive moment in the joint. The longer span produced larger positive moments. However, the influence was not significant. For the shear and negative moment, there was little difference between the results of the two models which means the span had a negligible effect on the maximum shear and negative moment in the joint 10.1.5.5. Effect of Girder Depth The DBT girder family investigated had three different girder depths: 41, 53, and 65 in. The effect of girder depth on the maximum forces in the joint was studied by comparing the results for the 41 in. girder depth using bridge model D and the 65 in. girder depth using bridge model A. The results are shown in Figure 10.1.20.

350 (a) Positive Moment (b) Shear (c) Negative Moment Figure 10.1.20: Effect of girder depth on forces in joint

351 The girder depth had an influence on the maximum forces in both joints. The influence was found to be larger on the moment than on the shear. Decreasing the girder depth caused an increase in the magnitude of the positive and negative moments of up to 58 and 120%, respectively, while the shear decreased 4%. 10.1.5.6. Effect of Girder Spacing The DBT girder family investigated had three different girder spacings: 4, 6, and 8 ft. The effect of girder spacing on the maximum forces in the joint was studied by comparing the results for the 4 ft girder spacing using bridge model C and the 8 ft girder spacing using bridge model A. The results are shown in Figure 10.1.21 where it can be seen that the girder spacing had a significant influence on the forces in the joints. Decreasing the girder spacing reduced both the moment and shear. For the bridges with the same width, decreasing the girder spacing meant adding more girders to resist the loading. The bridge with more girder members produced less force in the joint but might cost more.

352 (a) Positive Moment (b) Shear (c) Negative Moment Figure 10.1.21: Effect of girder spacing on forces in joint

353 10.1.5.7. Effect of Bridge Skew The effect of bridge skew on the maximum forces in the joints was studied using bridge models D through G (Figure 10.1.22). They each had the same girder cross-sectional geometry while the girder skew varied between 0 and 45 degrees. It can be seen that the bridge skew had an influence on the maximum moment in the joints while it had no influence on the shear. For bridge models with different skews, the maximum shear forces were almost the same in each joint. However, the effect of skew on the maximum moment depended on the loading positions related to the joint of interest. To maximize the positive moment in Joints 1 and 2, the single-lane loadings were applied, which made the moment increase with increasing skew. To maximize the magnitude of the negative moment in Joints 1 and 2, multi-lane loadings were applied. The multi-lane loading positioned on the same side of Joint 1 made the magnitude of the negative moment increase with increasing skew. However, the multi-lane loading located on each side of Joint 2 made the magnitude of the negative moment decrease with increasing skew.

354 (a) Positive Moment (b) Shear (c) Negative Moment Figure 10.1.22: Effect of bridge skew on forces in joint

355 10.1.5.8. Single-lane Loading versus Multi-lane Loading Figure 10.1.23 compares the effect of the number of loaded lanes on the maximum forces in the joints among the bridge models. The left column of each model represents the single-lane loading and the right column of each model represents the multi-lane loading. Note that the data includes multiple presence factors of 1.2 and 1.0 for the single- and multi-lane (two-lane) loading, respectively, based on Article 3.6.1.1.2 in AASHTO LRFD 2010. (a) Joint 1-Moment (b) Joint 1- Shear (c) Joint 2-Moment (d) Joint 2-Shear Figure 10.1.23: Effect of number of loaded lanes (single-lane loading (left column bar for each model) versus multi-lane loading (right column bar for each model)) From Figure 10.1.23, it can be concluded that the different number of loaded lanes produced different maximum forces in the joint. Both moment and shear under single-lane loadings were larger than those under multi-lane loading in both joints. So the single-lane loading was observed to dominate the loading.

356 Table 10.1.10 to Table 10.1.14 summarize the maximum forces in the joints of the seven bridge models under different loading locations. Table 10.1.10 to Table 10.1.13 include the maximum positive moment (M) with corresponding shear (CS) and the maximum shear (S) with corresponding moment (CM). Table 10.1.10: Maximum positive moment (+Moment) and shear in Joint 1 under single-lane loading Bridge Models Maximum +Moment Maximum Shear M (kip-ft/ft) CS (kip/ft) CM (kip-ft/ft) S (kip/ft) A 5.50 0.11 3.72 6.02 B 5.03 0.09 3.37 5.65 C 2.24 0.03 1.67 4.75 D 6.30 0.23 4.49 5.77 E 6.71 0.14 5.03 5.70 F 6.51 0.18 4.69 5.72 G 6.40 0.20 4.59 5.75 Table 10.1.11: Maximum positive moment (+Moment) and shear in Joint 2 under single-lane loading Bridge Models Maximum +Moment Maximum Shear M (kip-ft/ft) CS (kip/ft) CM (kip-ft/ft) S (kip/ft) A 6.29 0.11 4.21 5.86 B 5.23 0.05 3.44 5.90 C 3.39 0.30 2.43 4.74 D 7.39 0.35 5.29 5.95 E 7.92 0.42 5.46 6.09 F 7.53 0.36 5.37 6.05 G 7.43 0.35 5.31 6.04

357 Table 10.1.12: Maximum positive moment (+Moment) and shear in Joint 1 under multi-lane loading Bridge Models Maximum +Moment Maximum Shear M (kip-ft/ft) CS (kip/ft) CM (kip-ft/ft) S (kip/ft) A 4.38 0.23 2.96 5.07 B 3.93 0.04 2.62 4.67 C 1.72 0.02 1.25 3.96 D 5.06 0.39 3.52 4.96 E 5.79 0.29 4.36 4.91 F 5.37 0.32 3.80 4.93 G 5.19 0.36 3.60 4.94 Table 10.1.13: Maximum positive moment (+Moment) and shear in Joint 2 under multi-lane loading Bridge Models Maximum +Moment Maximum Shear M (kip-ft/ft) CS (kip/ft) CM (kip-ft/ft) S (kip/ft) A 4.47 0.10 2.83 4.72 B 3.94 0.06 2.53 4.89 C 2.29 0.23 2.20 3.70 D 5.22 0.52 3.49 5.13 E 6.48 0.57 4.07 5.27 F 5.70 0.51 3.76 5.22 G 5.39 0.52 3.58 5.17

358 Table 10.1.14: Maximum negative moment in Joints 1 and 2 under multi-lane loading Bridge Models Joint 1 (kip-ft /ft) Joint 2 (kip-ft/ft) A -0.37 -0.98 B -0.39 -1.03 C -0.08 -0.22 D -0.79 -2.15 E -1.40 -1.56 F -0.94 -1.94 G -0.82 -2.11 In summary, the maximum positive moment, negative moment and shear in the longitudinal joint under the HL-93 live load were 7.92 kip-ft/ft, -2.15 kip-ft/ft and 6.09 kip/ft, respectively. Based on the AASHTO Table A4-1 Deck Slab Design Table, the maximum positive live load moment in the bridge deck supported by girders spaced at 8 ft was 5.69kip-ft/ft. Table A4-1 was used to determine the design moments for the bridge deck. Specified assumptions and limitations were used in developing this table that should be considered when used for design. Among bridge models A, B, D-G, which had 8 ft spacings, models E and F had greater maximum positive moments than those from the AASHTO table. 10.1.5.9. Impact of Cracking Based on the results of the analyses discussed above using uncracked sections for the longitudinal joints, it was anticipated that the joints would be cracked under service loading. Therefore, the forces in the joint would be expected to be reduced compared with the forces calculated assuming uncracked sections. The difference in structural behavior before and after cracking resulted from a change in the joint stiffness. In the FE models where the largest maximum forces in the joint were found, the impact of cracking of the joint was studied by changing the modulus of elasticity (E) in the joint while keeping the moment of inertia (I) the same. The FE model for bridge model E considering cracking of the joint is shown in Figure 10.1.24. In Figure 10.1.24-(a), the lane with the arrows, which are for the lane load, is where the lane load placed; the circles indicate the position of the truck loads. Figure 10.1.25-(a) and Figure 10.1.25-(b) show the impact of cracking on the maximum moment (positive moment and negative moment) and maximum shear, respectively.

359 (a) Loading for the Maximum Positive Moment (b) Cracked Joints Figure 10.1.24: FE Model

360 (a) Moment (b) Shear Figure 10.1.25: Impact of cracking on forces From Figure 10.1.25, it can be seen that cracking had an influence on the maximum forces in the joints. As the section was cracked (modeled as a reduction in stiffness (EI)), the joint forces decrease. The rate of decrease in force increased dramatically for large reductions in stiffness; as the stiffness reduced to zero, the joint resistance would converge to zero. The reduction in stiffness had a greater influence on moment than on shear. At a stiffness reduction of 95%, the moment and shear resisted by the joint were 35% and 76% of the values, respectively, of the values calculated assuming uncracked section properties. To estimate the expected stiffness reduction of the joint as a result of cracking, the theoretical results for flexural specimen WB-1 described in Chapter 9 were used. For this specimen the theoretical reduction in stiffness due to cracking was estimated to be on the order of 84%, as discussed in Section 9.1.5. Based on the estimated 84% reduction in stiffness from the theoretical calculations associated with WB-1 to account for the effects of joint cracking, the maximum positive moment, negative moment and shear in the

361 longitudinal joint under live load HL-93 were expected to be 4.55 kip-ft/ft, -1.40 kip-ft/ft and 5.34 kip/ft respectively. The corresponding moment (CM) occurring with the maximum shear was 3.37 kip-ft/ft. The estimated 84% reduction in stiffness from the theoretical calculations associated with WB-1 was used because: 1) the point when the first crack occurred was not observed in the WB-1 test and calculation of the stiffness change based on the test may not be accurate; 2) the WB-2 test had not yet been performed at the time of the force analysis. 10.1.5.10. Fatigue Loading The Articles in AASHTO LRFD (2010) referenced to the fatigue loading are listed below: 3.4.1 FATIGUE-Fatigue and fracture load combination relating to repetitive gravitational vehicular live load and dynamic responses under a single design truck having the axle spacing specified in Article 3.6.1.4.1 3.4.1 A load factor of 0.75 (Table 3.4.1-1) shall be applied to fatigue load combination 3.6.1.2.1 Vehicular live loading on the roadways of bridges or incidental structures, designated HL-93, shall consist of a combination of the design truck or design tandem, and design lane load. 3.6.1.4.1 The fatigue load shall be one design truck or axles thereof specified in Article 3.6.1.2.2, but with a constant spacing of 30.0 feet between the 32.0-kip axles. 3.6.2.1 The static effects of the design truck or tandem shall be increased by 15% (fatigue and fracture limit state) for dynamic load allowance (Table 3.6.2.1-1). The dynamic load allowance shall not be applied to pedestrian loads or to the design lane load. Revisions to fatigue loading were accepted by AASHTO Bridge Committee, Technical Committees T-5 Loads, and T-14 Steel in May of 2008. The revisions consisted of inclusion of two levels of fatigue load in Table 3.4.1-1. These were Fatigue I and Fatigue II. Fatigue II retained the current Load Factor of 0.75 and was to be applied to represent an effective stress range caused by the fatigue truck with respect to a large but finite number of stress range cycles. Fatigue I had a Load Factor of 1.5 (or 2 times 0.75) and was to be applied to the stress range caused by the fatigue truck with respect to an infinite number of stress range cycles. Using the Load Factor of 0.75 for Fatigue II and not including the Lane Load (i.e., 0.75 [1.15 ( Fatigue Truck Load )], resulted in maximum positive moment, negative moment and shear in the longitudinal joint under fatigue live load HL-93 for finite life of 1.99 kip-ft/ft, -0.35 kip-ft/ft and 2.34 kip/ft, respectively. The forces associated with the Fatigue Load were analyzed using the same FE models discussed in Section 10.1.5.9 with the fatigue load factor and dynamic load allowance considered. These values were used to determine the fatigue loading in the large-scale tests. A separate analytical parametric study was carried out using SAP2000 to determine the shear force assumed to be transferred across the joint due to the leveling of differential camber during construction. Based on that study, a shear force 0.5 kip/ft was determined as a reasonable upper bound to consider in the test specimens. The combination of the fatigue shear of 2.34 kip/ft plus camber leveling shear of 0.5 kip/ft, 2.844 kip/ft, was used to determine the fatigue loading in the large-scale fatigue-shear tests.

362 10.2. Maximum Forces in the Transverse Joints The decked bulb-T girder family was chosen for the study of the live load forces in the transverse joint. This decked bulb-T girder family had the same girder cross sections as those used for the parametric study of the live load forces in the longitudinal joint. Table 10.1.1 summarized the practical span ranges for these girder sections. The transverse joints over the piers experience negative moment under service live load. The maximum negative moment in the transverse joint was studied using QConBridge™, which is a live load (AASHTO LRFD HL-93, 2010) analysis program for continuous bridge frames developed by WSDOT. Two types of bridge systems were developed: (1) two-span continuous bridge and (2) three-span continuous bridge. According to AASHTO LRFD (2010), the HL-93 loading consists of the combination of the design vehicle load and the design lane load. The design vehicle load is either a truck or tandem with dynamic allowance of 1.33. The design truck is specified in Article 3.6.1.2.2 while the design tandem is specified in Article 3.6.1.2.3. The practical span ranges used in the study were much larger than those controlled by the tandem loading, so the truck loading controlled the vehicle load in the analyses. The design lane load was 0.64 kip/ft without dynamic allowance. Based on Article 3.6.1.3.1, for negative moment between points of dead load contra-flexure, and reactions at interior piers only, 90% of the effect of two design trucks spaced at a minimum of 50 ft between the lead axle of one truck and the rear axle of the other truck, combined with 90% of the effect of the design lane load should be considered. The distance between the 32 kip axles of each truck should be taken as 14 ft. Considering the practical span range of the decked bulb-T girder family, Table 10.2.1 lists the bridge span length in each bridge model and shows the maximum negative moment in the transverse joint over the piers for each bridge model under service live load HL-93.

363 Table 10.2.1: Negative moment over piers in bridge models Bridge Model Bridge System Span (ft) Moment (kip-ft) First Second Third Design Load Fatigue Load 1 Two-Span 64 64 -1153 -323 2 180 180 -4700 -1048 3 180 94 -4870 -1377 4 176 84 -4780 -1385 5 Three-Span 64 64 64 -1064 -320 6 176 176 176 -4523 -1091 7 94 180 94 -3786 -1093 8 84 176 84 -3671 -1094 From the analysis results, it can be seen that the span length of the bridge had the largest positive effect on the maximum negative moment in the transverse joint. Generally speaking, the bridge model with the longer span length produced the larger maximum negative moment. For the bridge model with the same span length, the difference of the maximum negative moment between the two-span bridge systems and three-span bridge systems was negligible. In the case of the two-span bridge systems, the bridge model with different span lengths produced larger moments than the bridge model with the same span lengths. The decked bulb-T girder section (DBT65) and the bulb-T girder section (BT72) were chosen for the study of the maximum loads including the design loading and the fatigue loading in the transverse joints. Table 10.2.2 and Table 10.2.3 summarize the maximum moment in the transverse joint over the piers for girder sections DBT65 and BT72, respectively, under the HL-93 service live load. The calculated moments in Table 10.2.2 and Table 10.2.3 represent the loadings per lane. The first bridge model in Table 10.2.2 is a two-span bridge with a span of 176 ft and one of 84 ft.

364 Table 10.2.2: Moment over piers in bridge models with DBT65 Bridge System DBT 65 Span (ft) Moment (kip-ft) First Second Third Design (-) Fatigue (-) Design (+) Fatigue (+) Two-Span 176 84 -4780 -1385 Three Span 176 176 176 -4523 -1091 689 268 Table 10.2.3: Moment over piers in bridge models with BT72 Bridge System BT 72 Span (ft) Moment (kip-ft) First Second Third Design (-) Fatigue (-) Design (+) Fatigue (+) Two-Span 105 70 -2067 -679 Three Span 105 105 105 -2333 -603 346 147 In order to determine the distribution factor for a typical interior girder by the simplified distribution factor formulas (AASHTO LRFD 4.6.2.2), the following conditions must be met: 1. Number of beams, Nb ≥ 4 2. Width of deck is constant 3. Beams are parallel and approximately of the same stiffness 4. Roadway part of overhang ≤ 3 ft 5. Curvature < Limit of AASHTO 4.6.1.2.4 6. For precast concrete T-section with shear keys and with or without transverse post-tensioning, the bridge type is (j) 7. For precast concrete I or Bulb-Tee section, the bridge type is (k) The BT72 and DBT65 were classified by type and the distribution factors were determined accordingly. Bridge Type (K) or Type (J) if sufficiently connected to act as a unit: BT72 For one design lane loaded, 1.0 3 3.04.0 ) 12 ()() 14 (06.0 s g Lt K L SSDFM += (10.2.1) For two or more design lanes loaded,

365 1.0 3 2.06.0 ) 12 ()() 5.9 (075.0 s g Lt K L SSDFM += (10.2.2) where: DFM = distribution factor for moment for interior beam S = beams spacing, ft L = beam span, ft ts = depth of deck, in. Kg = longitudinal stiffness parameter, in.4, = n (I+Aeg 2) n = modular ratio between beam and deck materials 32.1 3605 4769 )( )( === deckE beamE c c A = cross-sectional area of the beam, in.2 I = moment of inertia of the beam, in.4 eg = distance between the centers of gravity of the beam and deck, in. The parameters were determined as follows for the BT72: S = 12 ft L = 70 ft ts = 6 in. Kg=n (I+Aeg 2) = (1.3229) (545894+767x38.42) = 2218347 in.4 For one design lane loaded, 772.0) 67012 2218347 () 70 12 () 14 12 (06.0 1.0 3 3.04.0 = ×× +=DFM For two or more design lanes loaded, 114.1) 67012 2218347 () 70 12 () 5.9 12 (075.0 1.0 3 2.06.0 = ×× +=DFM Thus, for the case of where two or more design lanes loaded control, DFM=1.114 lanes/beam.

366 The maximum moment in the transverse joint over the interior piers with girder section BT72 due to the HL- 93 service live load was determined as: negative design load: M=-(0.9)(1.114)(2333)=-2339 kip-ft/beam negative fatigue load: M=-(0.9)(1.114)(679)=-681 kip-ft/beam positive design load: M=(1.114)(346)=385 kip-ft/beam positive fatigue load: M=(1.114)(147)=164 kip-ft/beam Bridge Type (J) if connected only enough to prevent relative vertical displacement at the interface: DBT65 Regardless of number of loaded lanes, DFM = S/D (10.2.3) where: D= 11.5-NL + 1.4NL (1-0.2C) 2 where C ≤ 5 D=11.5-NL where C > 5 C=K (W/L) ≤K J IK )1( µ+= DFM = distribution factor for moment for interior beam S = beams spacing, ft D = width of distribution per lane ft NL= number of design lanes as specified in Article 3.6.1.1.1 C = stiffness parameter K = constant for different types of construction W = edge to edge width of bridge, ft L = beam span, ft µ = Poisson’s ratio I = moment of inertia of the beam, in.4 J = St. Venant’s torsional inertia, in.4 For thin-walled open beam, J=(1/3) (Σbt3)

367 The parameters were determined as follows for the DBT65: S = 8 ft W = 40 ft NL= 3 L = 84 ft to 176 ft µ = 0.18 I = 835069 in.4 J = 190789 in.4 16.5 190789 835069)18.01( = ×+ =K C=5.16(40/176) = 1.173<K D=11.5-3+1.4x 3x (1-0.2x1.173)2=10.96 DFM=8/10.96=0.73 The maximum moment in the transverse joint over the interior piers with girder section DBT65 due to the HL-93 service live load was determined by: negative design load: M= -(0.9) (0.73) (4780)=-3140 kip-ft/beam negative fatigue load: M=-(0.9)(0.73)(1385)=-910 kip-ft/beam positive design load: M=(0.73)(689)=503 kip-ft/beam positive fatigue load: M=(0.73)(268)=196 kip-ft/beam In summary, the maximum moments in the transverse joint over the interior piers with girder section DBT65 were larger than the maximum moments in the girder section BT72 due to the HL-93 service live load. For girder section DBT65, the negative design moment was -3140 kip-ft/beam; the negative fatigue moment was -910 kip-ft/beam; the positive design moment was 503 kip-ft/beam; and the positive fatigue moment was 196 kip-ft/beam. Assuming uncracked sections, the resulting extreme fiber stresses at the top of the girder over the interior piers in the transverse joint associated with the maximum moments were -1.06 ksi, -0.31 ksi, 0.17 ksi, and 0.07 ksi under the negative design load, negative fatigue load, positive design load, and positive fatigue

368 load, respectively. The negative design stress (-1.06 ksi) under the design load (-3140 kip-ft) was greater than the modulus of rupture of concrete. Thus, the transverse joint was reanalyzed assuming cracked section properties. Based on the cracked section analysis, the stresses of the U-bar in girder DBT65 were determined to be 35.6 ksi and 10.3 ksi under the negative design load (-3140 kip-ft) and negative fatigue load (-910kip-ft), respectively. 10.3. Conclusions For the longitudinal joints, a total of seven bridge models with different girder geometries were developed and subjected to the HL-93 live load in the parametric study. The purpose of the study was to provide a database of maximum forces in the longitudinal joints for determination of loadings for the static and fatigue tests described in Chapters 12 and 13 to determine the serviceability, static load strengths, and fatigue characteristics for the selected longitudinal/transverse joints. The following parameters were considered: different loading locations, effect of bridge width, design truck and lane loading versus design tandem and lane loading, girder geometry (depth, spacing and span), bridge skew, single-lane loading versus multi-lane loading, and impact of cracking of the joints. Based on the parametric study discussed above, the following findings are summarized below: 1. The position of lane load had little effect on the maximum forces in the joint. Typically, the lane load which was fully applied along the bridge length direction produced the largest moment in the joint while the lane load terminated at the center of rear truck wheel produced the largest shear in the joint. 2. While the influence of truck load position in the longitudinal direction on the maximum moment and shear in the joint was not significant, truck loads with heavy wheels located near midspan produced the largest maximum moment and shear. 3. The truck and lane load combination produced larger maximum forces than the tandem and lane load combination in both the long and short span bridges. This occurred because the practical span range of the DBT girders was much longer than the truck length which made the truck and lane load dominate the loading. 4. Increasing the bridge width decreased the maximum negative moment in the joints while it had a negligible effect on the maximum positive moment and maximum shear. 5. The effect of girder span on the maximum forces in the joints was not significant. However, the maximum forces were influenced significantly by the spacing and depth of the girder. Girders with larger spacings and shallower depths produced larger moments and shears. 6. The bridge skew had an influence on the maximum moment in the joints while it had no influence on the shear. However, the effect of skew on the maximum moment depended on the loading positions related to the joint of interest. 7. Single-lane loading was observed to dominate the loading compared to multi-lane loading. Both moment and shear under single-lane loadings were larger than those under multi-lane loading in the two joints investigated.

369 8. The maximum forces in the joints decreased after the joint cracking. However, the impact of cracking had more effect on moment than on shear. 9. Before cracking, the maximum positive moment was 7.92 kip-ft/ft; the maximum negative moment was -2.15 kip-ft/ft; the maximum shear was 6.09 kip/ft. After cracking, the maximum positive moment was 4.55 kip-ft/ft; the maximum negative moment was -1.40 kip-ft/ft; the maximum shear was 5.34 kip/ft, based on the estimated 84% reduction in stiffness from the theoretical calculations associated with WB-1 to account for the effects of joint cracking. The maximum forces before and after cracking were subsequently used to determine the static loading demand for the test specimens described in Chapters 12 and 13 to investigate serviceability (including crack control), static load strengths, and fatigue characteristics for the selected longitudinal/transverse joint. 10. The maximum positive moment, negative moment and shear in the longitudinal joint under fatigue live load HL-93 was determined to be 1.99 kip-ft/ft, -0.35 kip-ft/ft and 2.34 kip/ft respectively. These forces were subsequently used to determine the fatigue loading demand for the test specimens described in Chapters 12 and 13. To determine the controlling load case for a transverse joint, the transverse joint should be positioned over an interior support in a continuous span bridge system. In this case, if the deck was compositely connected to the girder, the deck would have to resist large tensile forces that would be produced by the negative moment developed there. Conservatively it was assumed that all the tension force created by the negative moment would be resisted by the deck. The decked bulb-T girder section (DBT65) and the bulb-T girder section (BT72) were chosen for the study of the maximum loads including the design loading and the fatigue loading in the transverse joints. The following findings are summarized below: 1. The maximum moments in the transverse joint over the interior piers with girder section DBT65 were larger than the maximum moments in the girder section BT72 due to the HL-93 service live load. For girder section DBT65, the negative design moment was -3140 kip-ft/beam; the negative fatigue moment was -910 kip-ft/beam; the positive design moment was 503 kip-ft/beam; and the positive fatigue moment was 196 kip-ft/beam. 2. Assuming uncracked sections, the resulting extreme fiber stresses at the top of the girder in the transverse joint associated with the maximum moments were -1.06 ksi, -0.31 ksi, 0.17 ksi, and 0.07 ksi under the negative design load, negative fatigue load, positive design load, and positive fatigue load, respectively. The negative design stress (-1.06 ksi) under the design load (-3140 kip-ft) was greater than the modulus of rupture of concrete. Thus, the transverse joint was reanalyzed assuming cracked section properties. Based on the cracked section analysis, the stresses of the U- bar in girder DBT65 were determined to be 35.6 ksi and 10.3 ksi under the negative design load (- 3140 kip-ft) and negative fatigue load (-910kip-ft), respectively.