Live Load Distribution in Multi-Cell Box-Girder Bridges and its Comparison with Current AASHTO LRFD Bridge Design Specifications by Rob Y.H. Chai, Eddy Shin-Tai Song & Karl M. Romstad Department of Civil & Environmental Engineering University of California, Davis & Susan E. Hida California Department of Transportation AASHTO LRFD Live Load Distribution Factors Range of Applicability of Live Load Distribution Factors  Bridges of constant deck width  Number of girders greater than or equal to 4  Parallel girders with approximately equal spacing  Span length must exceed 2.5 times the deck width  Plan curvature of less than 12 degrees in any one span These requirements are very restrictive for the inventory of box-girder bridges in California. Structures outside of these limits require refined 3D models, which are not a part of the routine design Objectives of Study  Conduct a detailed study of the limits imposed by the 1998 AASHTO LRFD Specifications  Investigate whether these limits can be broadened to include typical box-girder bridges in California  Emphasis is placed on these three parameters: • Non-prismatic cross-sections • Plan aspect ratio (length/width) less than 2.5 • Plan curvature > 12 degrees in any one span Selection of Bridge Parameters • Reference – NCHRP 12-26/1 Parameter Mean Std. Deviation Span length 89.5 ft 20.1 ft Depth 4.94 ft 0.95 ft Number of cells 5.9 3.7 Width (curb-to-curb) 46.6 ft 24.6 ft • Caltrans Memo-To-Designers 15-2 (May 1989) Box-girder Type Girder spacing-to-depth ratio Reinforced concrete 1.5 Prestressed concrete 2.0 Load Cases For Comparison Between Grillage and Finite Element Models 0.5L 0.5L Girder 1 2 Load Case 1 3 889.8 kN 889.8 kN 4 5 L L Grillage model per CL 0.4L 0.4L Girder Hambly (1991) 1 2 889.8 kN Load Case 2 3 889.8 kN 4 5 L L CL Analysis tool 0.6L Girder 1 SAP2000 2 Load Case 3 3 1334.7 kN 4 5 L L CL 0.4L 0.4L Girder 1 2 889.8 kN Load Case 4 3 4 889.8 kN 5 L L CL 0.1L 0.1L Girder 1 2 Load Case 5 3 889.8 kN 889.8 kN 4 5 L L CL Results from Grillage and Finite Element Models 0 5 10 15 20 25 30 35 40 45 50 55 60(m) -1500 -2000 entt)-1-500000 Girder 2 -1000m) mp-f 0 0 N- o 500 Grillage Mki 1000 k 1000 F.E.M ( ( 1500 2000 0 20 40 60 80 100 120 140 160 180 200 (ft) Case 2, Girder #2 0 5 10 15 20 25 30 35 40 45 50 55 60(m) -1000 -1000 nt -500 Girder 4 ) e) 0 0 m t mp-f1500000 1000 N- Moki1500 Grillage 2000 k (2000 F.E.M 3000 ( 2500 0 20 40 60 80 100 120 140 160 180 200 (ft) Case 4, Girder #4 0 5 10 15 20 25 30 35 40 45 50 55 60(m) e c 200 800 r 150 Girder 3 o 100 400 Fp) 50 N) 0 0 arki-50 k e (-100 Grillage -400 ( h -150 F.E.M -800 S -200 (ft) 0 20 40 60 80 100 120 140 160 180 200 Case 5, Girder #3 AASHTO HL-93 Design Vehicular Loads Design truck with lane load Design tandem with lane load 33% dynamic load allowance applied to design truck and design tandem Dual Truck and Dual Tandem Load Dual Truck Load Dual Tandem Load 33% dynamic load allowance applied to dual truck and dual tandem Live Load Distribution Factor – Definition QConBridge SAP2000 Beam-line model Grillage Model M = M max 1 M = M max 2 Distribution to girder: V = V max 1 V = V max 2 M V 2 2 Live Load Distribution Factor g = or M V 1 1 Definition applies to both interior and exterior girders