Giải thích hệ số PBN - Objective

BridgeTech, Inc. Simplified Live Load Distribution Formula NCHRP 12-62 Research Team Jay A. Puckett, Ph.D., P.E. Dennis Mertz, Ph.D., P.E. X. Sharon Huo, Ph.D., P.E. Mark Jablin, P.E. Michael Patrick, Graduate Student Matthew Peavy, P.E. NCHRP Manager: David Beal, P.E. BridgeTech, Inc. Objective  The objective of this project is to develop new recommended LRFD live-load distribution-factor design equations for shear and moment that are simpler to apply and have a wider range of applicability than those in the current LRFD. The need for refined methods of analysis should be minimized. BridgeTech, Inc. The Problem BridgeTech, Inc. Basics Behavior Stiff Deck relative to Girders – better distribution, more uniform All analysis and numerical approaches attempt to quantify this behavior Somewhere between Equal (Rigid body) and Lever Rule BridgeTech, Inc. Accuracy Simplicity BridgeTech, Inc. Accuracy Simplicity BridgeTech, Inc. Literature Review Current Specifications & Simplified Approach Modeling Techniques Field Testing Parametric Effects Bridge Type Nonlinear effects BridgeTech, Inc. PI Bias for a Simple Method • Analytically based approach • Canadian Specification Orthotropic Plate Theory space BridgeTech, Inc. NBI 1990 - most recent NBI Total Inventory Number Skewed 14275 66263 30.0% 43.8% 1464 3075 3.1% 63.4% 1811 3546 3.8% 62.0% 360 3677 0.8% 65.3% 629 11340 1.3% 40.3% 5329 9514 11.2% 53.6% 933 1396 2.0% 49.0% 40 82 0.1% 9.2% 208 300 0.4% 35.3% 208 300 0.4% 35.3% 14168 26691 29.8% 50.1% 1571 4213 3.3% 15.8% 6799 20728 14.3% 37.1% 47587 353845 150825 100.0% 42.6% Precast Solid, Voided, or Cellular Concrete Boxes with Shear Keys and with or without Transverse Posttensioning Open Steel or Precast Concrete Boxes Cast-in-Place Concrete Multicell Boxes Cast-in-Place Concrete Tee Beam Precast Solid, Voided, or Cellular Concrete Boxes with Shear Keys Steel Beam Cast in place concrete slab, precast concrete Closed Steel or Precast Concrete Boxes Cast in place concrete slab Cast-in-place concrete or plank, glued/spiked panels or stressed wood Precast Concrete Channel Sections with Shear Keys Precast Concrete Double Tee Section with Shear Keys and with or without Transverse Posttensioning Precast Concrete I or Bulb- Tee Sections Precast Concrete Tee Section with Shear Keys and with or without Transverse Reinforcement Integral Concrete Integral Concrete Cast-in-place concrete overlay Integral Concrete Cast-in-place concrete, precast concrete Cast-in-place concrete slab, precast concrete slab Monolithic Concrete Monolithic Concrete Cast-in-place concrete overlay j slab on girders slab on girders slab on girders monolithic slab and girders monolithic slab and girders slab on girders i h g slab on girders slab on girders slab on girders slab on girders Supporting Components Type of Deck AASHTO Letter (see Table 4.6.2.2.1-1) 2848 a d c b f e Number of Bridges Analytical Group Type 28106 17766 5718 5633 151398 Q 4847 slab on girders 53285 Slabs Not Applicable Not Applicable Slabs 26629 l k slab on girdersWood Beams Total: 55869 895 851 851 NBI Database BridgeTech, Inc. Summary Table (NBI Data) Type 1990-present Total Inventory Steel Beam 30.0% 42.8% Concrete I 29.8% 15.1% Precast Concrete Boxes with Shear Keys 11.2% 5.0% Slabs 14.3% 15.8% 85.3% 78.7% Bridge Percentages by Type [...]... 13b, K-16 0.9656 1.0657 -0 .0713 0.9674 14a, N-117 0.9384 0.0669 0.94 0.07 14b, K-15 0.9485 1 Lane 0.9209 0.1355 0.9198 15a, N-93 1.0859 -0 .1471 1.09 -0 .15 15b, K-12 0.9198 2 or More Lanes Exterior 1.1041 -0 .0553 0.9343 16a, N-85 0.9057 0.0501 0.91 0.05 16b, K-11 0.9343 1.6396 -0 .2679 0.8894 17a, N-61 0.6099 0.1634 0.61 0.16 17b, K-8 0.8894 1.0440 0.1098 0.8757 18a, N-51 n/a n/a 1.15 n/a 18b, K-7 0.8757... bv 0.81 0.09 0.94 0.07 1.09 -0 .15 0.91 0.05 0.79 0.09 0.94 0.05 1.24 -0 .22 1.21 -0 .17 0.85 0.04 0.90 0.04 1.27 -0 .22 1.04 -0 .06 0.63 0.14 0.79 0.12 0.85 Use Article 4.6.2.2.3 -0 .01 1.02 -0 .10 i j h e d f g b, c c BridgeTech, Inc Structural Factor (Moment) Multiple Lanes Loaded Two or more loaded lanes Structure Type Steel I-Beam Precast Concrete I-Beam Precast Concrete Bulb-Tee Beam Precast Concrete... 653 Parametric Bridges N/A 74 Conc T-Beam Steel I-Beam Prestressed I-Beam Prestressed Conc Box R/C Box Slab Multi-Box Conc Spread Box Steel Spread Box Precast Conc Spread Box Precast Conc Bulb-Tee Precast Conc I-Beam CIP Conc T-Beam CIP Conc Multicell Steel I-Beam Steel Open Box 71 163 94 112 121 127 66 35 20 4 4 3 3 4 4 2 Slab on RC, Prest., and Steel Girders 653 1-7 18.00 243.00 2.33 18.00 0.00 8.00... Structure Type Steel I-Beam Precast Concrete I-Beam Precast Concrete Bulb-Tee Beam Precast Concrete Double Tee with Shear Keys with or without PostTensioning Precast Concrete Tee Section with Shear Keys and with or without Transverse Post-Tensioning Precast Concrete Channel with Shear Keys Cast-in-Place Concrete Tee Beam Cast-in-Place Concrete Multicell Box Beam Adjacent Box Beam with Cast-inPlace Concrete... Section Type a k k Moment One Loaded Lane Exterior Interior am bm am bm 0.61 0.16 1.20 -0 .37 0.65 0.15 1.40 -0 .41 0.41 -0 .03 1.51 -0 .69 i j h e d f g b, c c 0.50 0.06 0.77 Use Article 4.6.2.2.3 -0 .17 BridgeTech, Inc Calibration Coefficients (Moment) Structure Type Steel I-Beam Precast Concrete I-Beam Precast Concrete Bulb-Tee Beam Precast Concrete Double Tee with Shear Keys with or without PostTensioning... Post-Tensioning Precast Concrete Channel with Shear Keys Cast-in-Place Concrete Tee Beam Cast-in-Place Concrete Multicell Box Beam Adjacent Box Beam with Cast-inPlace Concrete Overlay Adjacent Box Beam with Integral Concrete Precast Concrete Spread Box Beam Open Steel Box Beam AASHTO LRFD Cross Section Type a k k Moment One Loaded Lane Exterior Interior am bm am bm 0.61 0.16 1.20 -0 .37 0.65 0.15 1.40 -0 .41... 20.75 n/a 35.2 147 6.58 10.67 n/a 14.2 68 n/a n/a n/a 21 112.7 n/a n/a n/a 29.3 136.5 6.42 11.75 n/a 58 281.7 8.67 24 1-6 44.38 81.49 5.67 13.75 2-6 115.49 159.00 8.33 10.29 3-5 67.42 74.33 9.00 10.58 4-5 66.00 88.50 8.17 12.58 2-3 98.75 140.00 9.00 10.33 2-4 140.00 182.00 9.33 11.50 1-3 170.67 252.00 9.00 9.38 Slab Thickness (in) min max 5 11 4.42 12 5 9 n/a n/a n/a n/a 9.8 36 0 11 6 8.5 5 9.5 7.75... 1.40 -0 .41 0.41 -0 .03 1.51 -0 .69 i j h e d f g b, c c 0.50 0.06 0.77 Use Article 4.6.2.2.3 -0 .17 BridgeTech, Inc Calibration Coefficients (Shear) Shear Structure Type Steel I-Beam Precast Concrete I-Beam Precast Concrete Bulb-Tee Beam Precast Concrete Double Tee with Shear Keys with or without PostTensioning Precast Concrete Tee Section with Shear Keys and with or without Transverse Post-Tensioning Precast... 0.16 17b, K-8 0.8894 1.0440 0.1098 0.8757 18a, N-51 n/a n/a 1.15 n/a 18b, K-7 0.8757 0.8346 0.3076 0.4497 19a, N-29 1.1982 -0 .3686 1.20 -0 .37 19b, K-4 0.4508 1.0112 0.0658 0.9216 20a, N-19 n/a n/a 1.15 n/a 20b, K-3 0.9216 1 Lane Calibrated 2 or More Lanes Lever Interior Exterior Moment I-Girders (a, h, i, j, k) Slope Interior Calibrated Lever 1 Lane Henry's Method 2 or More Lanes Calibrated Lever 1... with Shear Keys with or without PostTensioning Precast Concrete Tee Section with Shear Keys and with or without Transverse Post-Tensioning Precast Concrete Channel with Shear Keys Cast-in-Place Concrete Tee Beam Cast-in-Place Concrete Multicell Box Beam Adjacent Box Beam with Cast-inPlace Concrete Overlay Adjacent Box Beam with Integral Concrete Precast Concrete Spread Box Beam Open Steel Box Beam AASHTO . Concrete Cast-in-place concrete, precast concrete Cast-in-place concrete slab, precast concrete slab Monolithic Concrete Monolithic Concrete Cast-in-place concrete. Posttensioning Open Steel or Precast Concrete Boxes Cast-in-Place Concrete Multicell Boxes Cast-in-Place Concrete Tee Beam Precast Solid, Voided, or Cellular