Analysis of Full Depth Precast Concrete Bridge Deck Panels

Transcription

1 Analysis of Full Depth Precast Concrete Bridge Deck Panels Mohsen A. lssa, Ph.D., P.E. Associate Professor of Civil Engineering Department of Civil and Materials Engineering University of illinois at Chicago Chicago, Illinois Alfred A. Yousif Graduate Research Assistant Department of Civil and Materials Engineering University of Illinois at Chicago Chicago, Illinois Mahmoud A. lssa, Ph.D. Research Associate Department of Civi l and Materials Engineering University of Illinois at Chicago Chicago, illinois lraj I. Kaspar, P.E. Engineer of Bridge Design illinois Department of Transportation Bureau of Bridges and Structures Springfield, Illinois Salah Y. Khayyat, P.E. Bridge Standard and Specifications Engineer illinois Department of Transportation Bureau of Bridges and Structures Springfield, Illinois Several researchers have reported on the use of full depth precast concrete bridge deck panels for the replacement and rehabilitation of deteriorated bridge decks. They presented the advantages of the system and generally recommended viable alternatives to many aspects of the system. However, a critical aspect of the system in terms of design is the consideration of the longitudinal post-tensioning. This paper presents the analysis of selected simply supported and continuous bridges using finite element modeling of the structural system. The objective of this analytical study was to determine the amount of posttensioning needed in the longitudinal direction to secure the tightness of the adjacent transverse joints and to keep them in compression. Results of the study indicate that the minimum prestress level is 200 psi (1.4 MPa) for simply supported bridges, while a prestress level of 450 psi (3. 1 MPa) is needed over the interior supports for continuous bridges. 74 PCI JOURNAL

2 The overall objective of this rehabilitation study was to evaluate the durability, performance, and cost effectiveness of full depth precast concrete bridge decks in order to formulate an optimum bridge deck system for the Illinois Department of Transportation and nationwide. These panels can be installed on steel stringers as well as precast, prestressed concrete girders. This optimum design can help in further establishing the effectiveness of precast and prestressed concrete components in the design and construction of the nation' s bridges and highway systems. The investigation of cracking, stiffness degradation, and deterioration problems is vital in determining what part of the system is inappropriate and needs to be replaced or modified. A major advantage in using a precast system is the minimal interference with traffic resulting from a reduction in construction time. In most cases, traffic is maintained in both directions during the rehabilitation process by either employing a two-phase construction plan or weekend and/or night closures of the replacement bridge. The authors have previously presented a comprehensive literature review and field investigation on full depth precast/prestressed bridge deck panels for bridge rehabilitation. ' These publications described the application and performance of these systems in two-stage replacement projects and new construction of bridge decks. All components of the bridge deck system were investigated in the field and the most appropriate features of the system were selected and recommended as a result of the initial study. The most effective joint configuration (female-to-female type) was determined as a result of the survey and inspection. Very few states use longitudinal post-tensioning for tightening deck joints; hence, debonding of the transverse joint was evident, which prompted the finite element analysis presented in this paper. The previous investigation also provided an indication of the most effective materials used in this type of construction. Finite element modeling was performed on several bridges to verify the con- January-February 1998 elusions drawn from the previous work presented in those earlier papers. The main objective of the present analytical study was to determine the amount of longitudinal post-tensioning needed to secure the tightness of the transverse joints and to keep these joints in compression. The structural performance of the entire system is of much importance. The analysis phase of the study facilitates the investigation of the joints between adjacent precast panels as well as the connection between the slab and its supporting system (shear pockets). It is essential to determine the performance of these joints under load and the materials included within, such as grout, shear stud connectors and other components. CONSTRUCTION PROCEDURES The first phase of construction for replacing a deteriorated bridge deck using this system is to close half of the bridge and maintain the other half for normal two-way traffic to accommodate motorists. The existing slabs are saw cut to approximately 1 /2 in. (12.7 mm) from the edge of the top flanges of the beams. The top flanges of the beams are then cleaned prior to the placement of the precast panels. A minimum haunch of 1 in. (25 mm) is provided to account for any dimensional misalignment or expansion. The precast panels are then set in proper sequence on the supporting system. As each panel is placed, it is adjusted with the use of leveling screws to precisely align the slab units Parapet Fig. 1. Typical tra nsverse section of bridge model. adjacent to one another. A set of posttensioning tendons are then run through the sheath ducts from the live end to the dead end. After the ducts at the joints are properly connected and secured, the transverse joints between the precast panels are grouted using polymer grout to achieve a minimum strength of 4500 psi (31 MPa) in one hour. Strength and material requirements are dependent on the practice of the state department of transportation. Details pertaining to these construction procedures are given in Refs. 3 and 4. Headed shear studs are then welded to the top flanges of the steel. Mild steel reinforcement is placed in the closure pours at both ends of the span where cast-in-place concrete is required. One hour after the grouting of the shear keys (transverse joints), the slab units are posttensioned longitudinally to secure the tightness in the joints. After post-tensioning, the sheath ducts are grouted. The shear connector pockets and girder haunches are then grouted with -a non-shrink grout. High early strength concrete is then placed in the closure pours. FINITE ELEMENT MODELING The finite element method is an effective tool in terms of predicting the behavior of structures such as bridges and their components.'- 6 Several bridges were modeled in order to determine the optimum amount of posttensioning required to keep the transverse joints in compression and to 75

3 prevent any leakage. However, for the purpose of this paper, the finite element analysis results presented consist of modeling two selected bridges from the previous findings. The two bridge types were the simply supported and three-span continuous bridge types. The finite element package, ALGOR,' was used to perform the analysis on these bridges. Details of the models as well as the results obtained from each analysis are described below. The Young's moduli of elasticity for the reinforcing steel, normal concrete and polymer concrete were 30 x 10 6, 4.03 x 10 6 and 5.1 x 10 6 psi (206.7, 27.8 and 35.1 GPa), respectively. The Poisson's ratios for the steel and concrete were 0.3 and 0.18, respectively, while the coefficients of thermal expansion were 6.5 x 10 6 per F (2.2 x!q-4 per 0 C) for the steel and 5.5 x 10 6 per F (1.9 X lq- 4 per 0 C) for the concrete. The applied AASHTO truck loading was HS Ten different component models were prepared and combined to simulate the bridge geometry and materials. The ten models consisted of: 1. Beams and diaphragms 2. Precast panels 3. Grout material for pockets 4. Transverse joints 5. Closure pours 6. Parapets 7. Shear connecting studs 8. Mild steel reinforcement for precast panels 9. Mild steel reinforcement for closure pours 10. Post-tensioning tendons Modeling Types of elements - Several types of elements are available in the finite element package ALGOR.' These types of elements can be selected to correspond to the types of structural components as well as the types of stresses desired. Four types of elements were used to perform the finite element analysis for the two selected bridges. The following is a brief description of these elements: Beam Elements: Two-noded elements in three-dimensional space with a maximum of six degrees of freedom defined per node, three translations and three rotations. 76 Fig. 2. Isometric view of simply supported bridge model. Brick Elements: Six-noded or eightnoded elements in three-dimensional space with only three translational degrees of freedom per node. Plate Elements: Four-noded elements in three-dimensional space with five degrees of freedom defined, three translations and two rotations, which produce out-of-plane bending. The rotation normal to the plane of the plate is not defined. Truss Elements: Two-noded elements in three-dimensional space with a maximum of three translational degrees of freedom defined. Beams and diaphragms - Fournoded plate elements were used to model the supporting steel stringers (flanges and web) and diaphragms. Fig. 1 shows a cross section of a bridge model showing the steel stringers and diaphragms. Precast panels - Six-noded and eight-noded brick elements were used to model the precast concrete panels. Fig. 2 shows an isometric view of a bridge model with the precast panels. Four layers of brick elements were considered to allow pl acement of the top and bottom mild steel reinforcement as well as the post-tensioning tendons. The concrete compressive strength used for the precast panels was 5000 psi (34.5 MPa). Shear connecting pockets - Eight-noded brick elements were used to model the grout material for the pockets. Fig. 2 shows an isometric view of a bridge model with the pockets. The concrete compressive strength used for the pockets was 5000 psi (34.5 MPa). The strength of the grout material used depends on the practice of the state DOT. Transverse joints - Eight-noded brick elements were used to model the grout material for the transverse joints. Fig. 3 shows a close-up view of an isometric section of the joint. The concrete compressive strength used for the transverse joints between adjacent precast panels was 8000 p si (55. 1 MPa). Other materials that meet the desired strength criteria can be used depending on the state DOT practice. Closure pours - Eight-noded brick elements were used to model the concrete closure pour at the end. Fig. 2 shows an isometric view of a bridge model with the closure pour. The concrete compressive strength used for the closure pours was 5000 psi (34.5 MPa). PCI JOURNAL

4 Fig. 3. Isometric view of typical transverse joint section. Parapets - Eight-noded brick elements were used to model the concrete parapets. Fig. 2 shows an isometric view of a bridge model with the parapets. The concrete compressive strength used for the parapets was 5000 psi (34.5 MPa). Reinforcement for precast panels - Truss elements were used to model the mild steel reinforcement for the precast panels. Fig. 4 shows an isometric view of a typical steel layout for a bridge model with the mild steel for the precast deck. Reinforcement for closure pours - Truss elements were used to model the mild steel reinforcement for the closure pour at the end. Fig. 4 shows an isometric view of a typical steel layout for a bridge model with the mild steel for the closure pour. Shear connecting studs - Beam elements were used to model the shear connecting studs in order to obtain their actual behavior, i.e., to obtain both shear and moment. Fig. 5 shows a close-up view of the section showing the location of the studs on the steel stringers. Post-tensioning tendons - Truss elements were used to model the posttensioning tendons. The post-tensioning was imposed using the concept of temperature change on the truss elements. The concrete tributary area was calculated based on the full width of the panel in order to obtain the required strain, while the coefficient of temperature for the steel was taken as 6.5 X 10 6 per F (2.2 X 10 4 per 0 C). As a result, the temperature change,!j.t, was determined by dividing the Mild steel reinforcement for closure pour Shear studs Top flange Web Beam Bottom flange Fig. 4. Typica l stee l layout for bridge model. Fig. 5. Section with stee l stringer and shea r studs. January-February

5 calculated strain with the coefficient of temperature. Care was taken to ensure that the effective applied stress in the tendons after all losses did not exceed the effective prestress, i.e., 0.6fr,u Fig. 4 shows an isometric view of a typical steel layout of a bridge model with the longitudinal post-tensioning tendons. DESCRIPTION OF BRIDGE MODELS The following section provides a detailed description of the two selected bridges with respect to modeling techniques and material properties. The discussion also provides the number of elements used in each model based on the description of the previously mentioned elements. Culpeper Bridge This bridge is simply supported, 54.5 ft (16.6 m) in length and 30 ft (9.1 m) wide. The existing steel rolled beams were 6.25 ft (1.9 m) center to center. This structure is maintained by the Virginia Department of Transportation. The two exterior beams, spaced 3 ft (0.91 m) from the end, are W33x125 while the interior beams are W33x 132. The joints between adjacent panels are the female-to-female type. The connection system between the slab and the beams consists of 4 in. (102 mm), 7 /s in. (22 mm) diameter shear studs. Every structural aspect of the bridge was incorporated into the model, including the diaphragms and parapets. Fig. 2 shows an isometric view of the simply supported bridge model. In all bridges considered, symmetry was imposed in the transverse direction to reduce the number of elements and nodes for the finite element solution. This procedure provided a faster and more efficient means of performing the analysis. However, symmetry in the longitudinal direction depends on several parameters such as materials, geometry, and, most significantly, the type of applied loading. In some cases, symmetry in the longitudinal direction was considered because the loading was symmetrically located on the structure. However, when the loading was not symmetric, predetermined 78 Table 1. Element and node details for simply supported bridge. Model Number of elements Number of nodes Beams and diaphragms Precast panels Grout for pockets Transverse joints Closure pour Parapet Shear connecting studs Reinfo rcement for precast panels Reinforcement for closure pour Post-tensioning moments and shears were superimposed on the centerline of the bridge to accurately simulate the actual loading. The bridge was analyzed using a structural analysis program, PCBRIDGE, 8 in order to obtain the necessary moments and shears at the bridge centerline. As a result, only a quarter of the bridge structure was considered in the analysis. The moments and shears were distributed along the centerline of the bridge in accordance with the equivalent moment of inertia for the steel and concrete. The simply supported model consisted of ten models with a total of 9312 elements and 8351 nodes. Table 1 presents the number of ele- --- Fi g. 6. Isometric view of three-span continuous bridge model ments and nodes for each of the ten combined models. Five separate analyses were made to account for dead loads, live loads, and three different levels of post-tensioning. The analysis accounting for the live loads included two separate load cases, i.e., strategically locating the trucks in order to obtain the maximum shear and maximum positive moment for the simply supported bridges. The structural program PCBRIDGE 8 was used to obtain truck locations prior to superimposing the loading on the model structure. Three different post-tensioning prestress levels were implemented, namely, 200, 300 and 400 psi (1.38, 2.07 and 2.76 MPa), in PCI JOURNAL -

6 Table 2. Element and node details for three-span bridge. Model Beams Precast panels Grout for pockets Transverse joints - - Closure pour Parapet Shear connecting studs Rei nforcement for precast panels Reinforcement for closure pour Post-tensioning order to distinguish the effect of posttensioning on the transverse joint and to satisfy the main objective of the study, i.e., to establish the necessary effective prestress level for keeping the joint in compression. Weiland River Bridge The 18-span Weiland River Bridge, carrying two southbound lanes near the City of Niagara Falls, was selected for redecking. This structure is maintained by the Ontario Ministry of Transportation. The structure was noncomposite prior to the rehabilitation. For comparison purposes, four of the five units were rehabilitated using cast-in-place concrete decks and only Number of elements Number of nodes ,244 14, one unit of three spans at the south end with precast concrete decks. These three spans were 48 ft (14.6 m) long each and 43.5 ft (13.3 m) wide, while the panel depth was 8.85 in. (225 mm). The deck supporting system consisted of four lines of steel girders with sizes of 33WF125 for the exterior girders and 33WF150 for the interior girders. The full depth precast panels measured 43.5 x 7.9 ft (13.26 x 2.42 m). Eight to twelve 7 /s in. (22 mm) diameter shear studs were placed in each pocket, depending on location. Nonprestressed steel was used as reinforcement for the panels. The steel sizes were #5 at 10 in. (15 at 250 mm) longitudinally and #5 at 9 in. (15 at 230 mm) transversely, with a 13.4 in. (340 mm) spacing at the openings for stud connectors. The tendons consisted of 11 [four 0.6 in. (16 mm) diameter strands] tendons in the panels near the ends to 20 [four 0.6 in. (16 mm) diameter strands] tendons over the piers and center span. The strands had a strength of 58.4 kips (260 kn). All the structural elements of the bridge were modeled as discussed for the previous simply supported bridge. Fig. 6 shows an isometric view of the three-span continuous bridge model; Fig. 7 shows a close-up view of a typical precast panel. Symmetry was once again imposed in both transverse and longitudinal directions in order to reduce the number of elements and nodes for the finite element solution. This was accomplished by considering only one and a half spans of the bridge. The three-span continuous model consisted of ten models and a total of 22,812 elements and 19,528 nodes. Table 2 lists the number of elements and nodes for each of the ten combined models. As before, the loading was not symmetric. As a result, the moments and shears were predetermined and superimposed on the centerline of the bridge to accurately simulate the actual loading. However, because this structure was continuous, the maximum negative moment was also considered. Fig. 8 shows the location of the AASHTO truck loading to produce the maximum negative moment. The remaining portion of the axles was superimposed as boundary conditions to impose longitudinal symmetry. The analyses were similar to those of the previous bridge; however, additional analysis was necessary to account for the maximum negative moment condition. Otherwise, all other modeling procedures were similar. Fig. 7. Typical precast panel. January-February 1998 DISCUSSION OF RESULTS The main purpose of the results obtained from the finite element analysis was to determine the stresses in the transverse joints and precast panels.under service loading conditions, and to determine the ideal level of post- 79

7 Portion ofhs-20 truck Moments & shear simulating live load truck loading Fig. 8. Layout of AASHTO truck loading. tensioning to keep the joints in compression. Therefore, analysis of the results was concentrated on these transverse joints. The areas of consideration for the joints were at the locations where tension stresses were significant. As expected, tension was more pronounced at the bottom of the transverse joints in the simply supported bridges. The joints in the continuous bridges would behave similarly at midspan. However, as expected, the behavior of the joints would be reversed at the supports, i.e., there is more tension at the top of the joint. Culpeper Bridge Initially, the transverse joints were inspected in regard to the normal stress distribution along the bridge. Fig. 9 presents a three-dimensional plot showing the stress variations in both directions in the plane of the slab deck. This figure considers only the stresses in the transverse joints, i.e., only one panel between two points longitudinally and all nodes trans- 80 Fig. 9. Simply supported bridge. Variation of stresses in transverse joints. PCI JOURNAL

8 Distance Along Half Bridge Length (mm) ~ ~~~~~~~~~~rn~r.n~~~~~~~ : : 7~ ,... j ! LL - LL psi post-tensioning ---. LL psi post-tensioning --- LL psi post-tensioning ~ 200 2~ 300 3~ Distance Along Half Bridge Length (in.) Fig. 10. Simply supported bridge. Stresses along bridge length ~ ~ ;;;- ~ 0 d' 0 -~ a 'il 'i3 s " 'Sb 3.s 5 D "' ] 0 z versely. The stresses along the transverse joint vary within ±50 psi (±345 kpa), while the fluctuations would be reduced if the data were collected away from the stress concentrations due to the AASHTO truck loading. Fig. 10 shows the normal stresses along the length of the slab deck at a typical location away from the stress concentrations. The results obtained from individual analyses corresponding to live load due to maximum shear, live load due to maximum moment, and various post-tensioning levels were superimposed to compare the stresses in the bridge deck. Because the panels rested on the supporting system prior to post-tensioning, the effect of dead load was neglected in superimposing the loads. The finite element analysis already accounted for impact during the initial analyses. Inspection of the results revealed that the deck is only in tension at locations where the magnitude is almost negligible, i.e., approximately 100 psi (0.689 MPa) (see Fig. 10). Fig. 11. Typical stress distribution at top surface of bridge deck. January-February

9 Fig. 12. Stresses at top su rface of three-span bridge. However, a minimum 200 psi (1.38 MPa) prestress level is necessary to secure the tightness of the transverse joints and to account for all the residual stresses in the concrete including the effect of creep and shrinkage. Fig. 11 shows typical stress distribution output for the top surface of the bridge deck Distance Along Half Bridge Length (nun) Weiland River Bridge The results obtained for this threespan continuous bridge revealed a different behavior because negative moments are introduced into the structure as a result of the continuous nature of the structure. As expected, the critical location for achieving compression in the transverse joints is at the central supports. The stress distributions were obtained along a line spanning the bridge half length in the location of the applied AASHTO truck loading. These stresses were obtained at the top and bottom surfaces of the bridge deck (see Fig. 12). 0 --LL LL psi post-tensioning --- LL psi post-tensioning -- LL psi post-tensioning --- LL psi post-tensioning BOO 1 ()()() Distance Along Half Bridge Length (in.) Fig. 13. Th ree-span bridge. Stresses in top layer of bridge deck. 82 PCI JOURNAL

10 'i s ~:r g ~ i5! a-200 eo..s!-400 rl) Oi ~ Distance Along Half Bridge Length (mm) ~LL~~~~~~~~~~~~~~~~~~~ Distance Along Half Bridge Length (in.) Fig. 14. Three-span bridge. Stresses in bottom layer of bridge deck Fig. 15. Stress distribution in typical transverse joint under AASHTO truck loading. January-February 1998 The stresses were then plotted as a function of the longitudinal distance to obtain the stress levels in the concrete bridge deck at the top and bottom surfaces, as shown in Figs. 13 and 14, respectively. The critical stresses were located at the top surface of the deck in the vicinity of the central supports. Inspection of the graphs reveals that the 400 psi (2.76 MPa) post-tensioning stress was not adequate to eliminate tension in the joint near the central support of this particular bridge. Several continuous bridges were modeled in order to obtain the required prestress level. As a result, additional analysis was necessary using a prestress level of 600 psi (4.13 MPa) to achieve the desired goals (see Fig. 13). The curve denoting the 600 psi (4.13 MPa) effective prestress level appears short of the zero tension plateau. However, because the effect of post-tensioning is linear with respect to a specific point on the bridge, the necessary minimum post-tensioning stress level can be interpolated at 450 psi (3.1 MPa). This stress would be utilized in the vicinity of the central supports. The effect of post-tensioning can clearly be seen in Figs. 15 and 16. Fig. 15 shows the stress distribution in a typical transverse joint due to AASHTO truck loading only, while Fig. 16 corresponds to the stresses in the same section of the joint due to a 400 psi (2.76 MPa) post-tensioning stress. The stress distribution can clearly be seen across the depth of the joint (see Figs 15 and 16). In the meantime, the remaining regions spanning the bridge require only the minimum post-tensioning stress level of 200 psi (1.38 MPa), as in the simply supported case. The maximum direct effective prestress level that can be applied to the concrete bridge deck is approximately 800 psi (5.51 MPa) for these panels. Therefore, this stress cannot be exceeded. The short kinks that are distributed in the curves signify the locations of the transverse joints between the precast panels. The magnitude of the compression stresses in the joints is more than those in the deck panels because the material used to model these joints is more stiff, i.e., 83

11 its strength is almost double that of the precast panels. The AASHTO truck loading imposed on the structure yielded stress concentrations at the point of application. As a result, another perspective view was considered along the bridge to reduce the effect of the stress concentrations from the wheel loads. Fig. 17 shows the post-tensioning stress levels along a line located near the centerline of the bridge. Hence, the curve is observed to be free of fluctuations due to stress concentrations, except for the kinks denoting the locations of the transverse joints. However, the conclusions drawn from Figs. 13 and 14 regarding the necessary post-tensioning levels were confirmed. Additional analyses were carried out on other bridges including a four-span bridge, which indicated that the stress distribution follows the same trend as the three-span bridge as shown in Fig. 13. APPLICATION EXAMPLES The Illinois Department of Transportation has implemented the design recommendations and construction procedures provided by this study, as well as previous studies, in at least five bridge deck replacement projects throughout the state. These projects include a bridge rehabilitation over I-74 in Knox County and another over Interstate I-57 in Williamson and Champaign Counties. These application bridges implemented all aspects of design and construction including the female-tofemale type transverse joints, shear connectjon blockouts and studs, as well as all material-related features of the system. The following is a general description of two selected bridges. Structure No This structure is a four-span bridge over I-57 in Williamson County. Twostage construction was implemented during the rehabilitation of the structure, as shown in Fig. 18. The two end spans are 40.5 ft ( m) long while the middle spans are 83.2 ft (25.35 m) wide. The panel depth is 84 Fig. 16. Stress distribution for typical transverse joint subjected to 400 psi (2.76 MPa) post-tensioning Distance Along Half Bridge Length (mm) ~ ;;,e. ~:r t,- ~f ~f ~ ~ i i5 01 c 01 c "' B 'lib "' B 'lib c.s R "' -;; "' ~ z -+-LL ~ -- LL psi post-tensioning -800._ LL psi post-tensioning._ LL psi post-tensioning LL psi post-tensioning Distance Along Half Bridge Length (in.) Fig Three-span bridge. Stresses in top layer of bridge deck. -;;;- ~ ~ PCI JOURNAL

12 7.67 in. (195 mm) while the bridge width is 38.7 ft (11.8 m). The deck supporting system consists of six lines of steel girders with sizes of W33 or W36. The full depth precast panels were of a length of x 18.2 ft (2.24 x 5.55 m). The shear connection blackouts were x 5.1 in. (400 x 130 mm) at 22 in. (560 mm) distances, center to center. Non-prestressed steel was used as reinforcement for the panels. The eight lines of tendons used consist of four 1 iz in. (12.7 mm) diameter, 270 ksi (1860 MPa) strands (see Fig. 19). Hence, two lines of posttensioning are provided between every two beams. 6.2 m!>;ii Co~tc..-:..,;:,. c~!; in place Clo~~;e Pour Fig. 18. Two-stage construction for bridge over 1-57 in Williamson County. Number indicates the alternating sequence of stressing Structure No This structure is a four-span bridge over I-74 in Knox County. Twostage construction was also implemented during the rehabilitation of this structure. The two end spans are 43.3 ft (13.2 m) long while the middle spans are 67.6 ft (20.6 m) wide. The panel depth is 7.67 in. (195 mm) while the bridge width is 33.1 ft (10.1 m). The deck supporting system consists of six lines of W30x 118 steel girders. The full depth precast panels are of a length of 7.35 x 18.2 ft (2.24 x 5.55 m). The shear connection blackouts are x 5.1 in. (400 x 130 mm). Non-prestressed steel is used as reinforcement for the panels. The tendons consist of four 1 iz in. (12.7 mm) diameter, 270 ksi (1860 MPa) strands (see Fig. 19). CONCLUSIONS Based on the finite element analysis for several selected bridges, including the two bridges presented in this paper, the following conclusions can be drawn relative to the amount of post-tensioning required to keep the transverse joints in compression: 1. A minimum post-tensioning stress level of 200 psi (1.38 MPa) is needed longitudinally to secure the tightness of the transverse joints for simply supported bridges. 2. A post-tensioning stress level of approximately 450 psi (3.1 MPa) is re- January-February 1998 Fig. 19. Post-tensioning tendons. quired to keep the transverse joint at the interior support (negative moment region) in compression for continuous bridges. 3. A minimum stress level of approximately 200 psi (1.38 MPa) is needed at midspan (positive moment region) for continuous bridges. 1. Issa, M. A., Yousif, A. A., Issa, M. A., Kaspar, I. I., and Khayyat, S. Y., "Field Performance of Full Depth Precast Panels in Bridge Deck Reconstruction," PCI JOURNAL, V. 40, No. 3, May-June 1995, pp Issa, M. A., Idriss, A. T., Kaspar, I. I., and Khayyat, S. Y., "Full Depth Precast and Precast, Prestressed Concrete Bridge Deck Panels," PCI JOURNAL, V. 40, No. 1, January-February 1995, pp Issa, M. A., Yousif, A. A., and Issa, M. A., "Construction Procedures for Rapid Replacement of Bridge Decks," Concrete International, V. 17, No. 2, February 1995, pp Issa, M. A., Yousif, A. A., and Issa, M. A., "Structural Behavior of Full Depth End plates REFERENCES Post-tensioning tendons 4. As a result of this study, the Illinois Department of Transportation has implemented these design recommendations and construction procedures on several bridges, including bridges over I-74 in Knox County and bridges over Interstate I-57 in Williamson and Champaign Counties. Precast Prestressed Concrete Bridge Deck Replacement," Final Report submitted to Illinois Department of Transportation, Springfield, IL, October Saadeghvaziri, M. A., "Finite Element Analysis of Highway Bridge Subjected to Moving Loads," Computer and Structures, V. 49, No. 5, September-October 1993, pp Marzouk, H. M., and Chen, Z., "Finite Element Analysis of High-Strength Concrete Slabs," ACI Structural Journal, V. 90, No. 5, September-October 1993, pp ALGOR Linear Stress and Vibration Analysis Processor Reference Manual, ALGOR, Inc., Pittsburgh, PA, PCBRIDGE, PCLinks, Inc., Gold River, CA,