Simplified Full-Depth Precast Concrete Deck Panel Systems (2018) / Chapter Skim
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From page 24... ...
24 This chapter presents the results of the analytical and experimental programs conducted to validate the full-depth precast concrete panel system proposed in Chapter 2 and to offer guidelines for its design. The affected sections in the AASHTO LRFD Bridge Design Specifications and proposed revisions to these sections are also presented.
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Research Findings 25 girder lines. The point supports allowed rotation in all directions, while restraining displacement in all directions.
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Case Girder Spacing (ft) Spacing Between Joints (ft)
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Research Findings 27 given by Table A4.1 of the AASHTO LRFD Bridge Design Specifications, where one-way slab behavior is considered.
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28 Simplified Full-Depth Precast Concrete Deck Panel Systems Design Aid Description Figure 3.2 Transverse bending moment caused by rear axle of an HL93 truck (including multiple presence factor and dynamic allowance) Figure 3.3 Longitudinal bending moment caused by rear axle of an HL93 truck solid-thickness slab Figure 3.4 Reaction caused by rear axle of an HL93 truck (including multiple presence factor and dynamic allowance)
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Research Findings 29 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 2 3 4 5 6 7 8 M om en t ( ki pft /ft ) Transverse Negative Moment (24 x 24 in.
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30 Simplified Full-Depth Precast Concrete Deck Panel Systems 0.0 10.0 20.0 30.0 40.0 50.0 60.0 2 3 4 5 6 7 8 Re ac tio n (k ip s) Connector Spacing (ft)
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Research Findings 31 0.0 0.5 1.0 1.5 2.0 2 3 4 5 6 7 8 M om en t ( ki pft /ft ) Connector Spacing (ft)
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32 Simplified Full-Depth Precast Concrete Deck Panel Systems 3.1.3 Design Requirement 2: Two-Way Shear at the Discrete Joints Since the deck slab is supported by discrete joints, two-way (punching) shear of the slab should be checked around the joint.
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Research Findings 33 Factored two-way shear: Vu ( )
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34 Simplified Full-Depth Precast Concrete Deck Panel Systems 1.34, 5.0 3.0 2.0 in., (at level of reinforcement assuming 45-degree distribution)
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Research Findings 35 at its own centroid. Geometrical properties of the top chord are determined based on the slab thickness and effective flange width.
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36 Simplified Full-Depth Precast Concrete Deck Panel Systems In addition, the Vierendeel Model was used to study the effect of varying the following parameters on the design requirements: • Span length = 80 ft to 216 ft, • Span-to-girder depth ratio = 15 to 35, • Girder spacing = 6 ft to 12 ft, • Girder material = concrete girders (6 ksi and 12 ksi) and steel girders, • Spacing between shear connectors = 2 ft to 8 ft, • Size of the bearing area at shear connections = 12 in.
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Research Findings 37 3.1.7 Design Requirement 5: One-Way Shear in the Slab The Vierendeel Model was loaded with the following combination of factored loads: DC Loads: Slab weight = (area of the slab ft2)
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38 Simplified Full-Depth Precast Concrete Deck Panel Systems 3.1.8 Design Requirement 6: Flexural Stresses of Composite Member Service I Limit State was used to determine the load effects. The following procedure was used to obtain the flexural stresses from the Vierendeel Model.
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Research Findings 39 Comparison between the Vierendeel and simplified models revealed that the Vierendeel Model showed a 5% to 7% increase in the deflection, compared to the Simple Beam Model when: (1) a thicker deck or haunch was used, (2)
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40 Simplified Full-Depth Precast Concrete Deck Panel Systems 3.1.12 Design Requirement 10: Distribution Factors DFM and shear are key components for design of a bridge superstructure. Article 4.6.2.2 of the AASHTO LRFD Bridge Design Specifications provides a group of tables that are used to determine these factors for interior and exterior beams of slab–beam bridges.
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Research Findings 41 where DFMj = live load distribution factor for moment of girder j, Mj = live load bending moment of girder j (determined from Step 1) , M i n iΣ =1 = sum of live load moment for all girders, and m = LRFD multiple presence factor = 1.2 for one lane loaded, 1.0 for two lanes loaded, and 0.85 for three lanes loaded.
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42 Simplified Full-Depth Precast Concrete Deck Panel Systems Example 1 of Highway Structures Design Handbook (American Iron and Steel Institute 1999) , with some minor changes.
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Research Findings 43 of the span. This stage is typically checked, regardless of whether a continuous or discrete joint system is used.
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44 Simplified Full-Depth Precast Concrete Deck Panel Systems FLB: Article 6.10.8.2.2 of the AASHTO LRFD Bridge Design Specifications states that the compression flange is considered compact if: b t E F b t t b fc fc yc fc fc fc fc ( ) ≤ ≤ ≥ 2 0.38 LRFD Equation 6.10.8.2.2-3 and LRFD Equation 6.10.8.2.2-4 2 0.38 29,000 50 0.055 where bfc = full width of the compression flange (in.)
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Research Findings 45 Timoshenko has shown that the bending moment that is required to cause lateral bending can be expressed as follows: (1) M L EI GKbuckling b y t= Π where Lb = unbraced length of the compression flange Lb (6 ft, in this case)
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46 Simplified Full-Depth Precast Concrete Deck Panel Systems obtained from the push-off specimens and the predicted capacity. An advanced commercial finite element package was used in the analysis (ABAQUS 6.13 package)
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Research Findings 47 • Ratio of the second stress invariant on the tensile meridian to that on the compressive meridian at initial yield, Kc: Kc< = − φ + φ <0.5 3 sin 3 sin 1.0 • Flow potential eccentricity e: A default value of 0.1 was used. • Ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress: A default value of 1.16 was used.
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48 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.11. Overall view of the finite element mesh of CD3 on a steel girder.
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Research Findings 49 However, the common method of deck panel post-tensioning has created challenges. The common method requires that multistrand ducts be placed in the precast panels.
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50 Simplified Full-Depth Precast Concrete Deck Panel Systems Table 3.15 shows that this ratio is dependent on the girder stiffness and girder spacing. However, the smallest ratio in this table is 80%, which means that at the most only 20% of post-tensioning effect is lost to the girder because of the composite action.
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Research Findings 51 effective prestress; and (b) it is not necessary to fill the transverse joint with more than the conventional concrete used for the deck material.
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52 Simplified Full-Depth Precast Concrete Deck Panel Systems specimens, as designed for this testing program, inherently have overturning forces that tend to have an opposite effect on the compression induced by the deck weight and additional loads in a composite beam test. Thus, results of push-off specimens are shown here to be on the low side, which is consistent with testing done in previous projects.
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Research Findings 53 Figure 3.14 and Figure 3.15 show the dimensions of the three push-off specimens. The first specimen, shown in Figure 3.14, was made using a concrete block that was lightly reinforced.
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54 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.15. Details of the second and third push-off test specimens.
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Research Findings 55 Figure 3.16 shows the compressive strength versus age for the UHPC mix used in each of the three push-off specimens. This figure indicates consistency of the UHPC performance.
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56 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.18. Setup showing the tee-section beams used in testing the second and third specimens (LVDT = linear variable differential transformer)
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Research Findings 57 Specimen UHPC C1: In this test, the load was applied incrementally at an approximate rate of 5 kips/s. The UHPC compressive strength at the time of testing (4 days old)
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58 Simplified Full-Depth Precast Concrete Deck Panel Systems bottom portion includes the damaged concrete block with significant cracking. This behavior indicated that the use of lightly reinforced concrete block was inadequate, and the specimen anchorage system to the floor needs to be revised to reduce the bending moment resulting from load eccentricity.
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Research Findings 59 Specimen UHPC C3: In this test, the load was also applied incrementally at an approximate rate of 5 kips/s. The compressive strength of UHPC at the time of testing (4 days old)
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60 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.28 shows the load-displacement plots of the three push-off specimens, as well as the one obtained from finite element analysis. The figure indicates the accuracy of the Finite Element Model in representing the behavior of the tested specimen and, therefore, its reliability.
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Research Findings 61 0 50 100 150 200 250 300 350 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Lo ad (k ip ) Horizontal Displacement (in.)
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(a) Von Mises stresses in the deck and girder (b)
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Figure 3.32. Elevation (top)
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64 Simplified Full-Depth Precast Concrete Deck Panel Systems (a) 6-ft-long precast panel (b)
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Research Findings 65 UHPC placed. Each transverse joint was overfilled with UHPC using ¾-in.
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66 Simplified Full-Depth Precast Concrete Deck Panel Systems Table 3.20 lists the cracking moment, cracking deflection, ultimate moment, and ultimate vertical shear predicted according to AASHTO LRFD Bridge Design Specifications for both fully composite and noncomposite sections. The corresponding midspan point load for each case is also listed.
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Research Findings 67 Figure 3.36 shows the average compressive strength of UHPC with age. This figure indicates that compressive strength reached 18.3 ksi after 28 days, which is significantly lower than that of the push-off specimens.
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1 2 43 North Side South Side 1 2 3 4 North Side South Side Figure 3.37. Flexure test setup and location of LVDTs and strain gauges.
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Research Findings 69 South Side Figure 3.38. Applied concrete strain gauge at two sections of the specimen.
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70 Simplified Full-Depth Precast Concrete Deck Panel Systems North Side South Side Midspan Figure 3.41. Shear cracks at 200 kips at midspan.
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Research Findings 71 50 100 150 200 250 300 350 400 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Lo ad (k ip ) Displacement (in.)
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North Side South Side Midspan 1 2 3 4 Figure 3.45. Setup of the first vertical shear test.
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Research Findings 73 North Side Midspan Figure 3.48. Test 3: Second Vertical Shear Test setup.
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74 Simplified Full-Depth Precast Concrete Deck Panel Systems connections remained intact with no signs of cracking or separation from the girder. The load– deflection relationship for this test is very similar to that for Test 2.
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Figure 3.51. Details of the push-off specimen.
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Figure 3.52. Predicted capacity of the connection.
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Research Findings 77 Design Specifications was used here based on previous research work by Issa et al.
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78 Simplified Full-Depth Precast Concrete Deck Panel Systems concrete deck panels, while the steel girder was restrained against horizontal movement using a horizontal steel frame. To avoid specimen rotation caused by eccentricity between the hydraulic jack and the horizontal frame, vertical steel frames were built around both ends of the precast deck.
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Research Findings 79 the tension force generated in these bars. Two LVDTs were installed -- one LVDT at each side of the specimen -- to measure the relative horizontal displacement between the panels and the top surface of the steel beam.
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80 Simplified Full-Depth Precast Concrete Deck Panel Systems (a) Steel bearing plate was bent (b)
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Research Findings 81 Push-Off, Steel Girder, Sp.
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82 Simplified Full-Depth Precast Concrete Deck Panel Systems uniformly across the width of the panel. The research team loaded the specimen up to 295 kips, which was the yield capacity of the Dywidag bars tying the specimen to the strong wall.
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Research Findings 83 the first row, carried more load than the corner studs. The maximum reported stud stress at the panel–haunch interface was about 27 ksi.
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84 Simplified Full-Depth Precast Concrete Deck Panel Systems (a)
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Research Findings 85 Figure 3.65. Axial tensile stress in the studs at the panel–haunch interface.
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86 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.68 and Figure 3.69 show the Von Mises stresses in the steel studs at the panel–haunch interface and the base of the studs, respectively. These figures show that the maximum tensile stress in the studs was at the base, and it was about 33 ksi in the center stud of the first row.
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Research Findings 87 respectively. Height of the studs was 8 in.
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Research Findings 89 Ductal JS1000 mix was produced by Lafarge North America. The mix is the same as has been used for the push testing and for the concrete girder-to-deck panel testing.
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(a) Locations of the strain gauges on the steel studs and horizontal LVDTs (b)
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Figure 3.74. Instrument installed on the large-scale beam.
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92 Simplified Full-Depth Precast Concrete Deck Panel Systems Modes of failure: Three modes of failure were investigated: (1) flexural failure based on the plastic flexural capacity of the composite beam, (2)
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Research Findings 93 Therefore, if the fatigue test is conducted for 1,900,000 cycles (according to ASTM D6275-98) at the magnified load level, it is equivalent to = (1.900 × 106)
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94 Simplified Full-Depth Precast Concrete Deck Panel Systems East Side West Side Midspan Midspan Midspan Figure 3.76. Deck cracks developed at 800,000 running cycles at midspan.
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Research Findings 95 East SideWest Side Midspan String Pot D5 String Pot D4 String Pot D3 String Pot D2 String Pot D1 Figure 3.77. Fracture fatigue crack developed in the steel beam.
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96 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.78. Preparation of the crack before welding.
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Research Findings 97 Figure 3.80. The steel beam after welding the web plates and the bottom steel bars.
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98 Simplified Full-Depth Precast Concrete Deck Panel Systems Number of Cycles (millions) (fatigue design load)
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Research Findings 99 Number of Cycles (millions) (fatigue design load)
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West Side Midspan A B C D Figure 3.86. Flexural stresses of the composite beam (81 kips)
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Research Findings 101 Figure 3.87 shows a comparison between the deflection obtained by analysis (using the Euler–Bernoulli Beam Theory, along with the full composite section properties) and the fatigue test.
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102 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.88. Setup of the strength test.
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Research Findings 103 (a) Joint B (south side)
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104 Simplified Full-Depth Precast Concrete Deck Panel Systems the setup. No cracks were observed on the top surface of the deck except the crack that appeared at Joint B at 322 kips.
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Research Findings 105 Elastic Beam Analysis with 100% EI, 80% EI, and 75% EI, where EI is the stiffness of the composite beam. The comparison between the measured and predicted deflection shows that an 80% reduction of the stiffness should be used in the beam model to accurately predict the short-term deflection.
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106 Simplified Full-Depth Precast Concrete Deck Panel Systems Load Versus Relative Vertical Displacement Figure 3.93. Relative vertical displacement between the deck and the steel beam.
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Research Findings 107 Bridge Design Specifications if a group effect factor of 0.72 is applied. Thus, the modified formula is 0.5 0.72Q A f E A Fn sc c c sc u= ′ ≤ where Qn = nominal shear resistance of the stud shear connectors in the cluster (kips)
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108 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure 3.95. Details of the precast deck (transverse section)
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Research Findings 109 3.3.1.2 Loads Deck weight (DC) : Deck weight between girders: Volume= 9 12 6 12 9 2 12 4 12 3.5 = 69,984 12,096 = 57,888 in.
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110 Simplified Full-Depth Precast Concrete Deck Panel Systems Mservice I = 1.11 + 0.30 + 6.0 = 7.41 k-ft/ft = 44.46 k-ft/6-ft long panel Mservice III = 1.11 + 0.30 + 0.8 × 6.0 = 6.21 k-ft/ft = 37.26 k-ft/6-ft long panel Mstrength I = 1.25 × 1.11 + 1.5 × 0.30 + 1.75 × 6.0 = 12.34 k-ft/ft = 74.03 k-ft/6-ft long panel Geometrical properties of the panel in positive moment zone between girder lines: Variable-thickness panel (Figure 3.96)
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Research Findings 111 Centroid of the six strands is at 3.92 in. from the top fiber of the panel.
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112 Simplified Full-Depth Precast Concrete Deck Panel Systems (b) Long-term prestress losses: Using Section 5.9.3.3 of the AASHTO LRFD Bridge Design Specifications, time-dependent losses can be estimated as follows: 10.0 12.0 LRFD Equation 5.9.3.3-1f f A A fpLT pi ps g h st h st pR ( )
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From page 113... ...
Research Findings 113 165.916 444 165.916 0.62 3.3 2066 5.40 12 3.3 2066 0.374 0.164 0.104 0.314 ksi 2.7 ksi Compression stress limit due to effective prestress, permanent loads, and transient loads 0.6 0.6 6.0 3.6 ksi 0.70 0.20 6.2 7.10 k-ft/ft = 42.60 k-ft/6-ft-long panel 165.916 444 165.916 0.62 3.3 2066 42.60 12 3.3 2066 0.374 0.164 0.817 1.027 ksi 3.6 ksi f P A P e y I M y I f M f P A P e y I M y I top pe g pe p top service top c service III top pe g pe p top service top ( )
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114 Simplified Full-Depth Precast Concrete Deck Panel Systems Compression stress limit due to sum of effective prestress and permanent loads 0.45 0.45 6.0 2.7 ksi 1.11 0.30 1.41 k-ft/ft = 8.46 k-ft/6-ft-long panel 165.916 612 165.916 0.33 4.25 3684.8 4.77 12 4.25 3684.8 0.271 0.063 0.066 0.274 ksi 2.7 ksi f M f P A P e y I M y I c service I bottom pe g pe p bottom service bottom( )
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Research Findings 115 Strength Limit State at the negative moment area: Mstrength I = 1.25 × 1.11 + 1.5 × 0.30 + 1.75 × 6.0 = 12.34 k-ft/ft = 74.03 k-ft/6-ft-long panel Cross section: 8.5-in. solid section Using Strain Compatibility analysis: Depth of the equivalent compression block = 0.625 in.
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116 Simplified Full-Depth Precast Concrete Deck Panel Systems Mservice I = 0.75 + 0.20 + 4.2 = 5.15 k-ft/ft = 46.35 k-ft/9-ft Mservice III = 0.75 + 0.20 + 0.8 × 4.2 = 4.31 k-ft/ft = 38.79 k-ft/9-ft Mstrength I = 1.25 × 0.75 + 1.5 × 0.20 + 1.75 × 4.2 = 8.59 k-ft/ft = 77.29 k-ft/9-ft Geometrical properties of the panel in positive moment zone (Figure 3.95, shaded area) : Height = 8.5 in., Area = 618 in.2, Inertia = 2782.5 in.4, ytop = 3.125 in., ybottom = 5.375 in.
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From page 117... ...
Research Findings 117 368.1 618 368.1 1.125 2782.5 0.56 12 1.125 2782.5 0.760 ksi 2 2 f P A Pe I M e I cgp i g i p g deck p g ( )
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From page 118... ...
118 Simplified Full-Depth Precast Concrete Deck Panel Systems (d) Long-term losses: Using Section 5.9.5.3 of the AASHTO LRFD Bridge Design Specifications, the time-dependent losses can be estimated as follows: 10.0 12.0 LRFD Equation 5.9.3.3-1f f A A fpLT pi ps g h st h st pR ( )
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From page 119... ...
Research Findings 119 0.56 0.15 5.95 6.66 k-ft/ft = 59.94 k-ft/9-ft 307.812 618 307.812 1.125 3.125 2782.5 59.94 12 3.125 2782.5 0.498 0.389 0.808 0.917 ksi 3.6 ksi M f P A P e y I M y I service I top pe g pe p top service top( )
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120 Simplified Full-Depth Precast Concrete Deck Panel Systems Using Strain Compatibility analysis: Depth of the equivalent compression block = 0.855 in. Depth of the neutral axis = 0.855/0.75 = 1.14 in.
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Research Findings 121 βc = 1.0 dv = 6 in.
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122 Simplified Full-Depth Precast Concrete Deck Panel Systems A1 = 12 × 12 = 144 in.2 m = 1.0(to simplify the calculations)
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Research Findings 123 where Vhi = horizontal factored shear force per unit length of the beam (kips/in.) Vu = factored shear force at specified section due to superimposed loads after the deck is cast (kips)
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124 Simplified Full-Depth Precast Concrete Deck Panel Systems 3.3.3 Longitudinal Design of Deck–Girder System with Steel Girders 3.3.3.1 Parametric Study The parametric study included a wide range of bridges with the following criteria: Number of spans = 1 and 2 Span length = 100 ft, 125 ft, and 150 ft Girder spacing = 6 ft, 9 ft, and 12 ft Span-to-depth ratio = 21.1 to 27.4 Shear connector groups: Spacing = up to 6 ft Number of studs = nine studs/group Size of studs = 7/8 in., 1 in., and 1¼ in. Minimum spacing between individual studs longitudinally and transversely = 4 times the stud diameter Fatigue capacity: AASHTO LRFD Bridge Design Specifications Strength: 75% of the strength determined by Article 6.10.10.4.3 of the AASHTO LRFD Bridge Design Specifications.
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From page 125... ...
Case No. Title N um be r o f S pa ns Sp an L en gt h G ird er S pa ci ng To ta l D ep th Sp an -to -D ep th R at io Pr ov id ed S pa ci ng B et w ee n C lu st er s of 7 /8 -in .
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126 Simplified Full-Depth Precast Concrete Deck Panel Systems Bridge criteria Span length: Two equal spans = 150 ft each Number of girder lines = 9 Girder spacing = 6 ft Deck overhang = 2 ft Bridge roadway width: 52 ft, no pedestrian traffic Skew = 0° Slab thickness ts = 8.5 in. Haunch thickness = 3.25 in.
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From page 127... ...
Research Findings 127 Width of the top flange bft = width of the bottom flange bfb = 16 in. Thickness of the bottom flange tfb = 0.875 in.
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From page 128... ...
128 Simplified Full-Depth Precast Concrete Deck Panel Systems The depth from the top of the top flange to the bottom of the deck does not exceed 2.375 in. Therefore, the stud shear connectors penetrate more than 2 in.
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From page 129... ...
Research Findings 129 P F Dt F b t F b t 3087.5 kip LRFD Equation 6.10.10.4.2-32p yw w yt ft ft yc fc fc ( ) = + + = where Fyw is the yield strength of the web (ksi)
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From page 130... ...
130 Simplified Full-Depth Precast Concrete Deck Panel Systems Number of required studs = 4712.9/53.3 = 88.4 studs (over 86.79 ft) Number of provided clusters over 86.79 ft at 6 ft = 86.79/6 = 14 clusters Number of provided studs = 14 clusters (9 studs per cluster)
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Research Findings 131 ( )
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132 Simplified Full-Depth Precast Concrete Deck Panel Systems 2. It is possible to have panels that are as long as 12 ft, generally considered the maximum allowed for shipping without a special permit in most of the United States.
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Research Findings 133 longitudinal deck continuity. The recommended details are given and are consistent with FHWA recommendations.
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134 Simplified Full-Depth Precast Concrete Deck Panel Systems flange is the lesser of the cluster spacing or the cross-frame spacing. No changes are proposed for FLB or LTB provisions.
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Research Findings 135 3.5.3 Item 3: Modify Section 5.7.4 This item is related to changing the maximum spacing of shear connectors for concrete girders. 5.7.4 -- Interface Shear Transfer -- Shear Friction 5.7.4.1 -- General Interface shear transfer shall be considered across a given plane at: • An existing or potential crack, • An interface between dissimilar materials, • An interface between two concretes cast at different times, or • The interface between different elements of the cross section.
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From page 136... ...
136 Simplified Full-Depth Precast Concrete Deck Panel Systems Figure C5.7.4.3-1 Special connection system developed by Badie et al.
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Research Findings 137 Figure C5.7.4.5-1 -- Free Body Diagrams Vh = = = Cu2 – C1 (C5.7.4.5-5)
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138 Simplified Full-Depth Precast Concrete Deck Panel Systems 3.5.4 Item 4: Add a New Reference to Section 5.15 Badie, S
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Research Findings 139 = distance between brace points (ft) n = number of shear connectors in a cross section p = pitch of shear connectors along the longitudinal axis (in.)
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From page 140... ...
140 Simplified Full-Depth Precast Concrete Deck Panel Systems 3.5.6 Item 6: Modify Section 6.10.10.4.3 This item is related to changing the nominal shear resistance of steel studs. 6.10.10.4.3 -- Nominal Shear Resistance The nominal shear resistance of one stud shear connector embedded in a concrete deck shall be taken as 0.5n sc c c g sc uQ A f E R A F (6.10.10.4.3-1)
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From page 141... ...
Research Findings 141 3.5.9 Item 9: Add New Reference to Section 9.10 Badie, S
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