Live Load Distribution in Multi-Cell Box-Girder Bridges
and its Comparison with Current AASHTO LRFD Bridge Design Specifications
byRob Y.H. Chai, Eddy Shin-Tai Song & Karl M. Romstad
Department of Civil & Environmental Engineering University of California, Davis
Susan E. HidaCalifornia 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
Parameter Mean Std. DeviationSpan length 89.5 ft 20.1 ft
Depth 4.94 ft 0.95 ftNumber of cells 5.9 3.7
Width (curb-to-curb) 46.6 ft 24.6 ft
• Reference – NCHRP 12-26/1
• Caltrans Memo-To-Designers 15-2 (May 1989)
Box-girder Type Girder spacing-to-depth ratio
Reinforced concrete 1.5Prestressed concrete 2.0
Load Cases For Comparison Between Grillage and Finite Element Models
0.4L
L LCL
0.4L
889.8 kN889.8 kN
0.5L 0.5L
L LCL
889.8 kN 889.8 kN
L LCL
889.8 kN
889.8 kN
0.4L
L LCL
889.8 kN 889.8 kN
0.1L 0.1L
1
5
34
2
Girder
1
5
34
2
Girder
1
5
34
2
Girder
1
5
34
2
Girder
0.6L
L LCL
1334.7 kN
1
5
34
2
Girder
0.4L
Load Case 1
Load Case 2
Load Case 3
Load Case 4
Load Case 5
Grillage model per Hambly (1991)
Analysis toolSAP2000
Results from Grillage and Finite Element Models
0 20 40 60 80 100 120 140 160 180 200 (ft)15001000500
0-500
-1000-1500
Mom
ent
(kip
-ft)
GrillageF.E.M
0 5 10 15 20 25 30 35 40 45 50 55 60 (m)
200010000-1000-2000
(kN-
m)
Girder 2
0 20 40 60 80 100 120 140 160 180 200 (ft)-200-150-100-50
050
100150200
Shea
r For
ce
(k
ip)
GrillageF.E.M
0 5 10 15 20 25 30 35 40 45 50 55 60 (m)
-800-4000400800
(kN)
Girder 3
0 20 40 60 80 100 120 140 160 180 200 (ft)2500200015001000500
0-500
-1000
Mom
ent
(kip
-ft)
0 5 10 15 20 25 30 35 40 45 50 55 60 (m)
3000200010000-1000
(kN-
m)
GrillageF.E.M
Girder 4
Case 2, Girder #2
Case 4, Girder #4
Case 5, Girder #3
AASHTO HL-93 Design Vehicular Loads
33% dynamic load allowance applied to design truck and design tandem
Design truck with lane load Design tandem with lane load
PresenterPresentation NotesHL 93: Heavy load truck developed in-1993 By knowing the width of lane, we can position lanes next to each other on the bridge deck and see how many lanes the bridge can fit......However, of course, it is not necessary to put all of lane on the bridge deck
Dual Truck and Dual Tandem Load
33% dynamic load allowance applied to dual truck and dual tandem
Dual Truck Load
Dual Tandem Load
PresenterPresentation NotesHL 93: Heavy load truck developed in-1993 By knowing the width of lane, we can position lanes next to each other on the bridge deck and see how many lanes the bridge can fit......However, of course, it is not necessary to put all of lane on the bridge deck
Live Load Distribution Factor – Definition
Beam-line modelMmax = M1 Vmax = V1
Mmax = M2 Vmax = V2
Live Load Distribution Factor g = M2M1
or V2V1
Definition applies to both interior and exterior girders
Distribution to girder:
QConBridgeSAP2000
Grillage Model
PresenterPresentation NotesDistribution factor shows the portion of load goes to that girder.
Definition of Acceptance Ratio
mg(M) = m x MgrillageMbeamline
mg(V) = m x VgrillageVbeamline
Acceptance Ratio =mg(from analyses)mg(LRFD formula)
Longitudinal
PresenterPresentation NotesThe plane grillage method involves modeling the bridge slab as a skeletal structure made up of a mesh of beams lying in a plane. Each grillage member presents a portion of the slab.
Non-Constant Deck Width Bridge – Two Spans
0.379
1.14
1.52
1.52
2.27
1.52 1.52
2.27
9.09
2.27 2.27
0.152
0.196
9.09
2.27
1.14
2.27
1.52
0.152
0.196
1.52
2.272.27
11.36
2.27
0.152
0.196
Section A-A
Section B-B
Section C-C & Section D-D
1.14
[email protected] 1.14
1.52
1.52
1.141.14
All dimensions are in meters
Two-Span Continuous
(1:16)6.25% flare
A
9.09
A
30.3
B B
6.06
30.3
C C11.36
Distribution Factor and Acceptance Ratio for Non-Constant Deck Width Bridges
Sheet1
Single Lane Loaded, m=1.2Two Lanes Loaded, m=1
Positive MomentNegative MomentShear ForcePositive MomentNegative MomentShear Force
Refined Analysis, mganalysis0.330.370.610.480.500.73
LRFD Formula, mgformula0.460.410.640.620.570.76
Acceptance Ratio, RA0.720.900.950.770.880.96
(a) Interior Girders
Single Lane Loaded, m=1.2Two Lanes Loaded, m=1
Positive MomentNegative MomentShear ForcePositive MomentNegative MomentShear Force
Refined Analysis, mganalysis0.260.330.510.370.430.52
LRFD Formula, mgformula0.50.50.830.50.50.67
Acceptance Ratio, RA0.520.660.610.740.860.78
(b) Exterior Girders
Single Lane Loaded, m=1.2Two Lanes Loaded, m=1
Positive MomentNegative MomentShear ForcePositive MomentNegative MomentShear Force
Straight Bridge, mganalysis0.350.380.640.50.510.63
LRFD Formula, mgformula0.410.410.640.570.570.76
Acceptance Ratio, RA0.850.931.000.880.890.83
(a) Interior Girders
Single Lane Loaded, m=1.2Two Lanes Loaded, m=1
Positive MomentNegative MomentShear ForcePositive MomentNegative MomentShear Force
Straight Bridge, mganalysis0.270.330.480.380.410.48
LRFD Formula, mgformula0.50.50.830.50.50.67
Acceptance Ratio, RA0.540.660.580.760.830.72
(b) Exterior Girders
Sheet2
Single Design Lane Load, m=1.2Two Design Lane Load, m=1
Positive MomentNegative MomentShear ForcePositive MomentNegative MomentShear Force
Non-Prismatic Bridge0.720.900.950.770.880.96
Straight Bridge0.850.931.000.880.890.83
(a) Interior girders
Single Design Lane Load, m=1.2Two Design Lane Load, m=1
Positive MomentNegative MomentShear ForcePositive MomentNegative MomentShear Force
Non-Prismatic Bridge0.520.660.610.740.860.78
Straight Bridge0.540.660.580.760.830.72
(b) Exterior girders
Sheet3
Plan Aspect Ratio & Cell Width-to-Depth Ratio
Cell width-to-depth ratio (S/D): 1.25, 1.83 and 2.25 Plan aspect ratio (L/W): 0.9 ~ 3.3
Distribution Factor for Interior Girder Moment (2 Lanes Loaded)
3.2752.483
2.3922.118
1.8851.761
1.5551.482
1.3651.14
1.1140.926
S/D:
1.25
S/D:
1.83
S/D:
2.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mg
L/W
S/D
3.2752.483
2.3922.118
1.8851.761
1.5551.482
1.3651.14
1.1140.926
S/D
:1.2
5
S/D
:1.8
3
S/D
:2.2
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mg
L/W
S/D
LRFD formula Analyses
Table
Distribution Factor (mg) from analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Sheet1
2.4830.3360.5070.62400.6710.6710.6660
1.7610.350.5210.63800.7150.7090.6980
1.3650.2770.3950.4660.4220.6550.6330.6120.501
1.1140.3020.430.4930.5450.6990.6780.6550.564
2.1180.2570.3550.4110.4330.6490.620.5930.5
1.4820.2880.4050.4530.5710.6940.6690.6410.574
1.140.2560.3460.3960.4660.6510.6230.590.513
0.9260.2830.3970.4420.5460.6920.6660.6370.568
2.4830.2480.3580.41400.4580.450.3930
1.7610.2680.380.43100.5430.5410.4850
1.3650.2130.2960.330.3020.450.4440.3990.306
1.1140.2370.3270.3590.3640.520.5190.470.367
2.1180.20.2740.3010.30.4480.4420.40.312
1.4820.2280.3310.3390.3760.5190.5170.4690.372
1.140.2030.2760.2980.3210.4640.4650.4240.331
0.9260.2260.3080.3330.370.5190.5170.470.374
Int,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 1 Lane
0.298
0.336
0.233
0.35
0.207
0.277
0.194
0.302
0.257
0.288
0.256
0.283
Int,M,L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Int.Girder, Moment, 2 lanes
0.438
0.507
0.332
0.521
0.287
0.395
0.264
0.43
0.355
0.405
0.346
0.397
Int,M,L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 3Lanes
0
0.624
0.406
0.638
0.33
0.466
0.294
0.493
0.411
0.453
0.396
0.442
Int,M,L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, M, More Than 3 Lanes
0
0
0
0
0.316
0.422
0.321
0.545
0.433
0.571
0.466
0.546
Ext,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 1 Lane
0.25
0.248
0.203
0.268
0.183
0.213
0.172
0.237
0.2
0.228
0.203
0.226
Ext, M, L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext. Girder, Moment, 2 Lanes
0.375
0.358
0.294
0.38
0.259
0.296
0.241
0.327
0.274
0.331
0.276
0.308
Ext, M, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 3 Lanes
0
0.414
0.339
0.431
0.292
0.33
0.267
0.359
0.301
0.339
0.298
0.333
Ext, M, L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, More Than 3 Lanes
0
0
0
0
0.268
0.302
0.273
0.364
0.3
0.376
0.321
0.37
Int, V, L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 1 Lane
0.54
0.671
0.521
0.715
0.497
0.655
0.507
0.699
0.649
0.694
0.651
0.692
Int, V, L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 2 Lanes
0.543
0.671
0.509
0.709
0.482
0.633
0.485
0.678
0.62
0.669
0.623
0.666
Int, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 3 Lanes
0
0.666
0.528
0.698
0.456
0.612
0.449
0.655
0.593
0.641
0.59
0.637
Int, V, L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, More Than 3 Lanes
0
0
0
0
0.379
0.501
0.388
0.564
0.5
0.574
0.513
0.568
Ext, V, L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 1Lane
0.372
0.458
0.359
0.543
0.346
0.45
0.352
0.52
0.448
0.519
0.464
0.519
Ext, V, L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 2 Lanes
0.365
0.45
0.366
0.541
0.36
0.444
0.364
0.519
0.442
0.517
0.465
0.517
Ext, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
S/D:1.25
S/D:1.83
s/D:2.25
L/W
mg
S/D
Ext. Girder, Shear Force, 3 Lanes
0
0.393
0.317
0.485
0.326
0.399
0.333
0.47
0.4
0.469
0.424
0.47
Ext, V, L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, L4
0
0
0
0
0.25
0.306
0.255
0.367
0.312
0.372
0.331
0.374
do
Int-girder Moment
3.2750.2980.43800
2.4830.3360.5070.6240
2.3920.2330.3320.4060
2.1180.350.5210.6380
1.8850.2070.2870.330.316
1.7610.2770.3950.4660.422
1.5550.1940.2640.2940.321
1.4820.3020.430.4930.545
1.3650.2570.3550.4110.433
1.140.2880.4050.4530.571
1.1140.2560.3460.3960.466
0.9260.2830.3970.4420.546
Ext-girder Moment
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
Int-girder Shear
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
Ext-girder Shear
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
wprk
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Draw
2.4830.3360.5070.62400.6710.6710.6660
2.1180.350.5210.63800.7150.7090.6980
1.7610.2770.3950.4660.4220.6550.6330.6120.501
1.4820.3020.430.4930.5450.6990.6780.6550.564
1.3650.2570.3550.4110.4330.6490.620.5930.5
1.140.2880.4050.4530.5710.6940.6690.6410.574
1.1140.2560.3460.3960.4660.6510.6230.590.513
0.9260.2830.3970.4420.5460.6920.6660.6370.568
2.4830.2480.3580.41400.4580.450.3930
2.1180.2680.380.43100.5430.5410.4850
1.7610.2130.2960.330.3020.450.4440.3990.306
1.4820.2370.3270.3590.3640.520.5190.470.367
1.3650.20.2740.3010.30.4480.4420.40.312
1.140.2280.3310.3390.3760.5190.5170.4690.372
1.1140.2030.2760.2980.3210.4640.4650.4240.331
0.9260.2260.3080.3330.370.5190.5170.470.374
analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Table-analysis
Distribution Factor (mg) from Analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Table-formula
Distribution Factor (mg) from LRFD Formula
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.3518750.43001.253.2750.5353140.586400
2.3920.29320.38080.380802.3920.53530.58640.58640
1.8850.25760.34930.34930.34931.8850.53530.58640.58640.5864
1.5550.25760.34930.34930.34931.5550.53530.58640.58640.5864
1.832.4830.42930.63080.630801.832.4830.67360.82780.82780
1.7610.35770.55860.55860.55861.7610.67360.82780.82780.8278
1.3650.31420.51240.51240.51241.3650.67360.82780.82780.8278
1.1140.31420.51240.51240.51241.1140.67360.82780.82780.8278
2.252.1180.48460.77420.774202.252.1180.76170.99540.99540
1.4820.40370.68550.68550.68551.4820.76170.99540.99540.9954
1.140.35470.62880.62880.62881.140.76170.99540.99540.9954
0.9260.35470.62880.62880.62880.9260.76170.99540.99540.9954
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.422930.4229001.253.2750.62980.49200
2.3920.42180.42180.421802.3920.62980.49370.49370
1.8850.42110.42110.42110.42111.8850.62980.49440.49440.4944
1.5550.42060.42070.42070.42071.5550.62980.4950.4950.495
1.832.4830.52190.52190.521901.832.4830.80670.65770.65770
1.7610.5210.5210.5210.5211.7610.80670.65940.65940.6594
1.3650.52060.52060.52060.52061.3650.80670.66040.66040.6604
1.1140.52030.52030.52030.52031.1140.80670.66080.66080.6608
2.252.1180.55840.55840.558402.252.1180.88930.83140.83140
1.4820.55760.55760.55760.55761.4820.88930.83330.83330.8333
1.140.55710.55710.55710.55711.140.88930.83420.83420.8342
0.9260.55680.55680.55680.55680.9260.88930.83490.83490.8349
Int,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 1 Lane
0.351875
0.4293
0.2932
0.4846
0.2576
0.3577
0.2576
0.4037
0.3142
0.3547
0.3142
0.3547
Int,M,L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7742
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Int.Girder, Moment, 2 lanes
0.43
0.6308
0.3808
0.3493
0.5586
0.3493
0.5124
0.5124
Int,M,L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7742
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 3Lanes
0
0.6308
0.3808
0.3493
0.5586
0.3493
0.5124
0.5124
Int,M,L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, M, More Than 3 Lanes
0
0
0
0.3493
0.5586
0.3493
0.5124
0.5124
Ext,M,L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 1 Lane
0.42293
0.5219
0.4218
0.4211
0.521
0.4206
0.5206
0.5203
Ext, M, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext. Girder, Moment, 2 Lanes
0.4229
0.5219
0.4218
0.4211
0.521
0.4207
0.5206
0.5203
Ext, M, L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 3 Lanes
0
0.5219
0.4218
0.4211
0.521
0.4207
0.5206
0.5203
Ext, M, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, More Than 3 Lanes
0
0
0
0.4211
0.521
0.4207
0.5206
0.5203
Int, V, L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7617
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.7617
1.3651.365
1.141.140.7617
1.1141.114
0.9260.9260.7617
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 1 Lane
0.535314
0.6736
0.5353
0.5353
0.6736
0.5353
0.6736
0.6736
Int, V, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.9954
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.9954
1.3651.365
1.141.140.9954
1.1141.114
0.9260.9260.9954
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 2 Lanes
0.5864
0.8278
0.5864
0.5864
0.8278
0.5864
0.8278
0.8278
Int, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 3 Lanes
0
0.8278
0.5864
0.9954
0.5864
0.8278
0.5864
0.9954
0.8278
0.9954
0.8278
0.9954
Int, V, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.9954
1.3651.365
1.141.140.9954
1.1141.114
0.9260.9260.9954
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, More Than 3 Lanes
0
0
0
0.5864
0.8278
0.5864
0.8278
0.8278
Ext, V, L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8893
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8893
1.3651.365
1.141.140.8893
1.1141.114
0.9260.9260.8893
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 1Lane
0.6298
0.8067
0.6298
0.6298
0.8067
0.6298
0.8067
0.8067
Ext, V, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8314
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 2 Lanes
0.492
0.6577
0.4937
0.4944
0.6594
0.495
0.6604
0.6608
Ext, V, L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8314
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext. Girder, Shear Force, 3 Lanes
0
0.6577
0.4937
0.4944
0.6594
0.495
0.6604
0.6608
Ext, V, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, L4
0
0
0
0.4944
0.6594
0.495
0.6604
0.6608
plot-analysis
Int-girder Moment
3.2750.2980.43800
2.4830.3360.5070.6240
2.3920.2330.3320.4060
2.1180.350.5210.6380
1.8850.2070.2870.330.316
1.7610.2770.3950.4660.422
1.5550.1940.2640.2940.321
1.4820.3020.430.4930.545
1.3650.2570.3550.4110.433
1.140.2880.4050.4530.571
1.1140.2560.3460.3960.466
0.9260.2830.3970.4420.546
Ext-girder Moment
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
Int-girder Shear
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
Ext-girder Shear
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Plot-formula
Int-girder Moment
3.2750.3518750.4300
2.4830.42930.63080.63080
2.3920.29320.38080.38080
2.1180.48460.77420.77420
1.8850.25760.34930.34930.3493
1.7610.35770.55860.55860.5586
1.5550.25760.34930.34930.3493
1.4820.40370.68550.68550.6855
1.3650.31420.51240.51240.5124
1.140.35470.62880.62880.6288
1.1140.31420.51240.51240.5124
0.9260.35470.62880.62880.6288
Ext-girder Moment
3.2750.422930.422900
2.4830.52190.52190.52190
2.3920.42180.42180.42180
2.1180.55840.55840.55840
1.8850.42110.42110.42110.4211
1.7610.5210.5210.5210.521
1.5550.42060.42070.42070.4207
1.4820.55760.55760.55760.5576
1.3650.52060.52060.52060.5206
1.140.55710.55710.55710.5571
1.1140.52030.52030.52030.5203
0.9260.55680.55680.55680.5568
Int-girder Shear
3.2750.5353140.586400
2.4830.67360.82780.82780
2.3920.53530.58640.58640
2.1180.76170.99540.99540
1.8850.53530.58640.58640.5864
1.7610.67360.82780.82780.8278
1.5550.53530.58640.58640.5864
1.4820.76170.99540.99540.9954
1.3650.67360.82780.82780.8278
1.140.76170.99540.99540.9954
1.1140.67360.82780.82780.8278
0.9260.76170.99540.99540.9954
Ext-girder Shear
3.2750.62980.49200
2.4830.80670.65770.65770
2.3920.62980.49370.49370
2.1180.88930.83140.83140
1.8850.62980.49440.49440.4944
1.7610.80670.65940.65940.6594
1.5550.62980.4950.4950.495
1.4820.88930.83330.83330.8333
1.3650.80670.66040.66040.6604
1.140.88930.83420.83420.8342
1.1140.80670.66080.66080.6608
0.9260.88930.83490.83490.8349
work
3.2750.3518750.4300
2.4830.42930.63080.63080
2.3920.29320.38080.38080
2.1180.48460.77420.77420
1.8850.25760.34930.34930.3493
1.7610.35770.55860.55860.5586
1.5550.25760.34930.34930.3493
1.4820.40370.68550.68550.6855
1.3650.31420.51240.51240.5124
1.140.35470.62880.62880.6288
1.1140.31420.51240.51240.5124
0.9260.35470.62880.62880.6288
3.2750.422930.422900
2.4830.52190.52190.52190
2.3920.42180.42180.42180
2.1180.55840.55840.55840
1.8850.42110.42110.42110.4211
1.7610.5210.5210.5210.521
1.5550.42060.42070.42070.4207
1.4820.55760.55760.55760.5576
1.3650.52060.52060.52060.5206
1.140.55710.55710.55710.5571
1.1140.52030.52030.52030.5203
0.9260.55680.55680.55680.5568
3.2750.5353140.586400
2.4830.67360.82780.82780
2.3920.53530.58640.58640
2.1180.76170.99540.99540
1.8850.53530.58640.58640.5864
1.7610.67360.82780.82780.8278
1.5550.53530.58640.58640.5864
1.4820.76170.99540.99540.9954
1.3650.67360.82780.82780.8278
1.140.76170.99540.99540.9954
1.1140.67360.82780.82780.8278
0.9260.76170.99540.99540.9954
3.2750.62980.49200
2.4830.80670.65770.65770
2.3920.62980.49370.49370
2.1180.88930.83140.83140
1.8850.62980.49440.49440.4944
1.7610.80670.65940.65940.6594
1.5550.62980.4950.4950.495
1.4820.88930.83330.83330.8333
1.3650.80670.66040.66040.6604
1.140.88930.83420.83420.8342
1.1140.80670.66080.66080.6608
0.9260.88930.83490.83490.8349
wprk
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Distribution Factor for Exterior Girder Moment (3 Lanes Loaded)
3.2752.483
2.3922.118
1.8851.761
1.5551.482
1.3651.14
1.1140.926
1.25 1.832.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mg
L/W
S/D
3.2752.483
2.3922.118
1.8851.761
1.5551.482
1.3651.14
1.1140.926
1.25 1.832.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mg
L/W
S/D
LRFD formula Analyses
analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Table-analysis
Distribution Factor (mg) from Analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Table-formula
Distribution Factor (mg) from LRFD Formula
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.3518750.43001.253.2750.5353140.586400
2.3920.29320.38080.380802.3920.53530.58640.58640
1.8850.25760.34930.34930.34931.8850.53530.58640.58640.5864
1.5550.25760.34930.34930.34931.5550.53530.58640.58640.5864
1.832.4830.42930.63080.630801.832.4830.67360.82780.82780
1.7610.35770.55860.55860.55861.7610.67360.82780.82780.8278
1.3650.31420.51240.51240.51241.3650.67360.82780.82780.8278
1.1140.31420.51240.51240.51241.1140.67360.82780.82780.8278
2.252.1180.48460.77420.774202.252.1180.76170.99540.99540
1.4820.40370.68550.68550.68551.4820.76170.99540.99540.9954
1.140.35470.62880.62880.62881.140.76170.99540.99540.9954
0.9260.35470.62880.62880.62880.9260.76170.99540.99540.9954
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.422930.4229001.253.2750.62980.49200
2.3920.42180.42180.421802.3920.62980.49370.49370
1.8850.42110.42110.42110.42111.8850.62980.49440.49440.4944
1.5550.42060.42070.42070.42071.5550.62980.4950.4950.495
1.832.4830.52190.52190.521901.832.4830.80670.65770.65770
1.7610.5210.5210.5210.5211.7610.80670.65940.65940.6594
1.3650.52060.52060.52060.52061.3650.80670.66040.66040.6604
1.1140.52030.52030.52030.52031.1140.80670.66080.66080.6608
2.252.1180.55840.55840.558402.252.1180.88930.83140.83140
1.4820.55760.55760.55760.55761.4820.88930.83330.83330.8333
1.140.55710.55710.55710.55711.140.88930.83420.83420.8342
0.9260.55680.55680.55680.55680.9260.88930.83490.83490.8349
Int,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 1 Lane
0.351875
0.4293
0.2932
0.4846
0.2576
0.3577
0.2576
0.4037
0.3142
0.3547
0.3142
0.3547
Int,M,L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7742
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Int.Girder, Moment, 2 lanes
0.43
0.6308
0.3808
0.3493
0.5586
0.3493
0.5124
0.5124
Int,M,L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7742
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 3Lanes
0
0.6308
0.3808
0.3493
0.5586
0.3493
0.5124
0.5124
Int,M,L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, M, More Than 3 Lanes
0
0
0
0.3493
0.5586
0.3493
0.5124
0.5124
Ext,M,L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 1 Lane
0.42293
0.5219
0.4218
0.4211
0.521
0.4206
0.5206
0.5203
Ext, M, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext. Girder, Moment, 2 Lanes
0.4229
0.5219
0.4218
0.4211
0.521
0.4207
0.5206
0.5203
Ext, M, L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 3 Lanes
0
0.5219
0.4218
0.4211
0.521
0.4207
0.5206
0.5203
Ext, M, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, More Than 3 Lanes
0
0
0
0.4211
0.521
0.4207
0.5206
0.5203
Int, V, L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7617
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.7617
1.3651.365
1.141.140.7617
1.1141.114
0.9260.9260.7617
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 1 Lane
0.535314
0.6736
0.5353
0.5353
0.6736
0.5353
0.6736
0.6736
Int, V, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.9954
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.9954
1.3651.365
1.141.140.9954
1.1141.114
0.9260.9260.9954
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 2 Lanes
0.5864
0.8278
0.5864
0.5864
0.8278
0.5864
0.8278
0.8278
Int, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 3 Lanes
0
0.8278
0.5864
0.9954
0.5864
0.8278
0.5864
0.9954
0.8278
0.9954
0.8278
0.9954
Int, V, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.9954
1.3651.365
1.141.140.9954
1.1141.114
0.9260.9260.9954
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, More Than 3 Lanes
0
0
0
0.5864
0.8278
0.5864
0.8278
0.8278
Ext, V, L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8893
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8893
1.3651.365
1.141.140.8893
1.1141.114
0.9260.9260.8893
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 1Lane
0.6298
0.8067
0.6298
0.6298
0.8067
0.6298
0.8067
0.8067
Ext, V, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8314
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 2 Lanes
0.492
0.6577
0.4937
0.4944
0.6594
0.495
0.6604
0.6608
Ext, V, L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8314
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext. Girder, Shear Force, 3 Lanes
0
0.6577
0.4937
0.4944
0.6594
0.495
0.6604
0.6608
Ext, V, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, L4
0
0
0
0.4944
0.6594
0.495
0.6604
0.6608
plot-analysis
Int-girder Moment
3.2750.2980.43800
2.4830.3360.5070.6240
2.3920.2330.3320.4060
2.1180.350.5210.6380
1.8850.2070.2870.330.316
1.7610.2770.3950.4660.422
1.5550.1940.2640.2940.321
1.4820.3020.430.4930.545
1.3650.2570.3550.4110.433
1.140.2880.4050.4530.571
1.1140.2560.3460.3960.466
0.9260.2830.3970.4420.546
Ext-girder Moment
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
Int-girder Shear
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
Ext-girder Shear
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Plot-formula
Int-girder Moment
3.2750.3518750.4300
2.4830.42930.63080.63080
2.3920.29320.38080.38080
2.1180.48460.77420.77420
1.8850.25760.34930.34930.3493
1.7610.35770.55860.55860.5586
1.5550.25760.34930.34930.3493
1.4820.40370.68550.68550.6855
1.3650.31420.51240.51240.5124
1.140.35470.62880.62880.6288
1.1140.31420.51240.51240.5124
0.9260.35470.62880.62880.6288
Ext-girder Moment
3.2750.422930.422900
2.4830.52190.52190.52190
2.3920.42180.42180.42180
2.1180.55840.55840.55840
1.8850.42110.42110.42110.4211
1.7610.5210.5210.5210.521
1.5550.42060.42070.42070.4207
1.4820.55760.55760.55760.5576
1.3650.52060.52060.52060.5206
1.140.55710.55710.55710.5571
1.1140.52030.52030.52030.5203
0.9260.55680.55680.55680.5568
Int-girder Shear
3.2750.5353140.586400
2.4830.67360.82780.82780
2.3920.53530.58640.58640
2.1180.76170.99540.99540
1.8850.53530.58640.58640.5864
1.7610.67360.82780.82780.8278
1.5550.53530.58640.58640.5864
1.4820.76170.99540.99540.9954
1.3650.67360.82780.82780.8278
1.140.76170.99540.99540.9954
1.1140.67360.82780.82780.8278
0.9260.76170.99540.99540.9954
Ext-girder Shear
3.2750.62980.49200
2.4830.80670.65770.65770
2.3920.62980.49370.49370
2.1180.88930.83140.83140
1.8850.62980.49440.49440.4944
1.7610.80670.65940.65940.6594
1.5550.62980.4950.4950.495
1.4820.88930.83330.83330.8333
1.3650.80670.66040.66040.6604
1.140.88930.83420.83420.8342
1.1140.80670.66080.66080.6608
0.9260.88930.83490.83490.8349
work
3.2750.3518750.4300
2.4830.42930.63080.63080
2.3920.29320.38080.38080
2.1180.48460.77420.77420
1.8850.25760.34930.34930.3493
1.7610.35770.55860.55860.5586
1.5550.25760.34930.34930.3493
1.4820.40370.68550.68550.6855
1.3650.31420.51240.51240.5124
1.140.35470.62880.62880.6288
1.1140.31420.51240.51240.5124
0.9260.35470.62880.62880.6288
3.2750.422930.422900
2.4830.52190.52190.52190
2.3920.42180.42180.42180
2.1180.55840.55840.55840
1.8850.42110.42110.42110.4211
1.7610.5210.5210.5210.521
1.5550.42060.42070.42070.4207
1.4820.55760.55760.55760.5576
1.3650.52060.52060.52060.5206
1.140.55710.55710.55710.5571
1.1140.52030.52030.52030.5203
0.9260.55680.55680.55680.5568
3.2750.5353140.586400
2.4830.67360.82780.82780
2.3920.53530.58640.58640
2.1180.76170.99540.99540
1.8850.53530.58640.58640.5864
1.7610.67360.82780.82780.8278
1.5550.53530.58640.58640.5864
1.4820.76170.99540.99540.9954
1.3650.67360.82780.82780.8278
1.140.76170.99540.99540.9954
1.1140.67360.82780.82780.8278
0.9260.76170.99540.99540.9954
3.2750.62980.49200
2.4830.80670.65770.65770
2.3920.62980.49370.49370
2.1180.88930.83140.83140
1.8850.62980.49440.49440.4944
1.7610.80670.65940.65940.6594
1.5550.62980.4950.4950.495
1.4820.88930.83330.83330.8333
1.3650.80670.66040.66040.6604
1.140.88930.83420.83420.8342
1.1140.80670.66080.66080.6608
0.9260.88930.83490.83490.8349
wprk
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Table
Distribution Factor (mg) from analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Sheet1
2.4830.3360.5070.62400.6710.6710.6660
1.7610.350.5210.63800.7150.7090.6980
1.3650.2770.3950.4660.4220.6550.6330.6120.501
1.1140.3020.430.4930.5450.6990.6780.6550.564
2.1180.2570.3550.4110.4330.6490.620.5930.5
1.4820.2880.4050.4530.5710.6940.6690.6410.574
1.140.2560.3460.3960.4660.6510.6230.590.513
0.9260.2830.3970.4420.5460.6920.6660.6370.568
2.4830.2480.3580.41400.4580.450.3930
1.7610.2680.380.43100.5430.5410.4850
1.3650.2130.2960.330.3020.450.4440.3990.306
1.1140.2370.3270.3590.3640.520.5190.470.367
2.1180.20.2740.3010.30.4480.4420.40.312
1.4820.2280.3310.3390.3760.5190.5170.4690.372
1.140.2030.2760.2980.3210.4640.4650.4240.331
0.9260.2260.3080.3330.370.5190.5170.470.374
Int,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 1 Lane
0.298
0.336
0.233
0.35
0.207
0.277
0.194
0.302
0.257
0.288
0.256
0.283
Int,M,L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Int.Girder, Moment, 2 lanes
0.438
0.507
0.332
0.521
0.287
0.395
0.264
0.43
0.355
0.405
0.346
0.397
Int,M,L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 3Lanes
0
0.624
0.406
0.638
0.33
0.466
0.294
0.493
0.411
0.453
0.396
0.442
Int,M,L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, M, More Than 3 Lanes
0
0
0
0
0.316
0.422
0.321
0.545
0.433
0.571
0.466
0.546
Ext,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 1 Lane
0.25
0.248
0.203
0.268
0.183
0.213
0.172
0.237
0.2
0.228
0.203
0.226
Ext, M, L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext. Girder, Moment, 2 Lanes
0.375
0.358
0.294
0.38
0.259
0.296
0.241
0.327
0.274
0.331
0.276
0.308
Ext, M, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 3 Lanes
0
0.414
0.339
0.431
0.292
0.33
0.267
0.359
0.301
0.339
0.298
0.333
Ext, M, L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, More Than 3 Lanes
0
0
0
0
0.268
0.302
0.273
0.364
0.3
0.376
0.321
0.37
Int, V, L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 1 Lane
0.54
0.671
0.521
0.715
0.497
0.655
0.507
0.699
0.649
0.694
0.651
0.692
Int, V, L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 2 Lanes
0.543
0.671
0.509
0.709
0.482
0.633
0.485
0.678
0.62
0.669
0.623
0.666
Int, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 3 Lanes
0
0.666
0.528
0.698
0.456
0.612
0.449
0.655
0.593
0.641
0.59
0.637
Int, V, L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, More Than 3 Lanes
0
0
0
0
0.379
0.501
0.388
0.564
0.5
0.574
0.513
0.568
Ext, V, L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 1Lane
0.372
0.458
0.359
0.543
0.346
0.45
0.352
0.52
0.448
0.519
0.464
0.519
Ext, V, L2
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 2 Lanes
0.365
0.45
0.366
0.541
0.36
0.444
0.364
0.519
0.442
0.517
0.465
0.517
Ext, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
S/D:1.25
S/D:1.83
s/D:2.25
L/W
mg
S/D
Ext. Girder, Shear Force, 3 Lanes
0
0.393
0.317
0.485
0.326
0.399
0.333
0.47
0.4
0.469
0.424
0.47
Ext, V, L4
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, L4
0
0
0
0
0.25
0.306
0.255
0.367
0.312
0.372
0.331
0.374
do
Int-girder Moment
3.2750.2980.43800
2.4830.3360.5070.6240
2.3920.2330.3320.4060
2.1180.350.5210.6380
1.8850.2070.2870.330.316
1.7610.2770.3950.4660.422
1.5550.1940.2640.2940.321
1.4820.3020.430.4930.545
1.3650.2570.3550.4110.433
1.140.2880.4050.4530.571
1.1140.2560.3460.3960.466
0.9260.2830.3970.4420.546
Ext-girder Moment
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
Int-girder Shear
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
Ext-girder Shear
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
wprk
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Draw
2.4830.3360.5070.62400.6710.6710.6660
2.1180.350.5210.63800.7150.7090.6980
1.7610.2770.3950.4660.4220.6550.6330.6120.501
1.4820.3020.430.4930.5450.6990.6780.6550.564
1.3650.2570.3550.4110.4330.6490.620.5930.5
1.140.2880.4050.4530.5710.6940.6690.6410.574
1.1140.2560.3460.3960.4660.6510.6230.590.513
0.9260.2830.3970.4420.5460.6920.6660.6370.568
2.4830.2480.3580.41400.4580.450.3930
2.1180.2680.380.43100.5430.5410.4850
1.7610.2130.2960.330.3020.450.4440.3990.306
1.4820.2370.3270.3590.3640.520.5190.470.367
1.3650.20.2740.3010.30.4480.4420.40.312
1.140.2280.3310.3390.3760.5190.5170.4690.372
1.1140.2030.2760.2980.3210.4640.4650.4240.331
0.9260.2260.3080.3330.370.5190.5170.470.374
Distribution Factor for Exterior Girder Shear Force (More Than 3 Lanes Loaded)
3.2752.483
2.3922.118
1.8851.761
1.5551.482
1.3651.14
1.1140.926
1.25 1.832.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mg
L/W
S/D
3.2752.483
2.3922.118
1.8851.761
1.5551.482
1.3651.14
1.1140.926
1.25 1.832.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
mg
L/W
S/D
LRFD formula Analyses
analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Table-analysis
Distribution Factor (mg) from Analysis
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.2980.438001.253.2750.540.54300
2.3920.2330.3320.40602.3920.5210.5090.5280
1.8850.2070.2870.330.3161.8850.4970.4820.4560.379
1.5550.1940.2640.2940.3211.5550.5070.4850.4490.388
1.832.4830.3360.5070.62401.832.4830.6710.6710.6660
1.7610.2770.3950.4660.4221.7610.6550.6330.6120.501
1.3650.2570.3550.4110.4331.3650.6490.620.5930.5
1.1140.2560.3460.3960.4661.1140.6510.6230.590.513
2.252.1180.350.5210.63802.252.1180.7150.7090.6980
1.4820.3020.430.4930.5451.4820.6990.6780.6550.564
1.140.2880.4050.4530.5711.140.6940.6690.6410.574
0.9260.2830.3970.4420.5460.9260.6920.6660.6370.568
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.250.375001.253.2750.3720.36500
2.3920.2030.2940.33902.3920.3590.3660.3170
1.8850.1830.2590.2920.2681.8850.3460.360.3260.25
1.5550.1720.2410.2670.2731.5550.3520.3640.3330.255
1.832.4830.2480.3580.41401.832.4830.4580.450.3930
1.7610.2130.2960.330.3021.7610.450.4440.3990.306
1.3650.20.2740.3010.31.3650.4480.4420.40.312
1.1140.2030.2760.2980.3211.1140.4640.4650.4240.331
2.252.1180.2680.380.43102.252.1180.5430.5410.4850
1.4820.2370.3270.3590.3641.4820.520.5190.470.367
1.140.2280.3310.3390.3761.140.5190.5170.4690.372
0.9260.2260.3080.3330.370.9260.5190.5170.470.374
Table-formula
Distribution Factor (mg) from LRFD Formula
Int. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.3518750.43001.253.2750.5353140.586400
2.3920.29320.38080.380802.3920.53530.58640.58640
1.8850.25760.34930.34930.34931.8850.53530.58640.58640.5864
1.5550.25760.34930.34930.34931.5550.53530.58640.58640.5864
1.832.4830.42930.63080.630801.832.4830.67360.82780.82780
1.7610.35770.55860.55860.55861.7610.67360.82780.82780.8278
1.3650.31420.51240.51240.51241.3650.67360.82780.82780.8278
1.1140.31420.51240.51240.51241.1140.67360.82780.82780.8278
2.252.1180.48460.77420.774202.252.1180.76170.99540.99540
1.4820.40370.68550.68550.68551.4820.76170.99540.99540.9954
1.140.35470.62880.62880.62881.140.76170.99540.99540.9954
0.9260.35470.62880.62880.62880.9260.76170.99540.99540.9954
Ext. Girder
MomentShear
Cell S/dLength/Width1Lane2Lane3Lane4LaneCell S/dLength/Width1Lane2Lane3Lane4Lane
1.253.2750.422930.4229001.253.2750.62980.49200
2.3920.42180.42180.421802.3920.62980.49370.49370
1.8850.42110.42110.42110.42111.8850.62980.49440.49440.4944
1.5550.42060.42070.42070.42071.5550.62980.4950.4950.495
1.832.4830.52190.52190.521901.832.4830.80670.65770.65770
1.7610.5210.5210.5210.5211.7610.80670.65940.65940.6594
1.3650.52060.52060.52060.52061.3650.80670.66040.66040.6604
1.1140.52030.52030.52030.52031.1140.80670.66080.66080.6608
2.252.1180.55840.55840.558402.252.1180.88930.83140.83140
1.4820.55760.55760.55760.55761.4820.88930.83330.83330.8333
1.140.55710.55710.55710.55711.140.88930.83420.83420.8342
0.9260.55680.55680.55680.55680.9260.88930.83490.83490.8349
Int,M,L1
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 1 Lane
0.351875
0.4293
0.2932
0.4846
0.2576
0.3577
0.2576
0.4037
0.3142
0.3547
0.3142
0.3547
Int,M,L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7742
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Int.Girder, Moment, 2 lanes
0.43
0.6308
0.3808
0.3493
0.5586
0.3493
0.5124
0.5124
Int,M,L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7742
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Moment, 3Lanes
0
0.6308
0.3808
0.3493
0.5586
0.3493
0.5124
0.5124
Int,M,L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.6855
1.3651.365
1.141.140.6288
1.1141.114
0.9260.9260.6288
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, M, More Than 3 Lanes
0
0
0
0.3493
0.5586
0.3493
0.5124
0.5124
Ext,M,L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 1 Lane
0.42293
0.5219
0.4218
0.4211
0.521
0.4206
0.5206
0.5203
Ext, M, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext. Girder, Moment, 2 Lanes
0.4229
0.5219
0.4218
0.4211
0.521
0.4207
0.5206
0.5203
Ext, M, L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.5584
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, 3 Lanes
0
0.5219
0.4218
0.4211
0.521
0.4207
0.5206
0.5203
Ext, M, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.5576
1.3651.365
1.141.140.5571
1.1141.114
0.9260.9260.5568
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Moment, More Than 3 Lanes
0
0
0
0.4211
0.521
0.4207
0.5206
0.5203
Int, V, L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.7617
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.7617
1.3651.365
1.141.140.7617
1.1141.114
0.9260.9260.7617
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 1 Lane
0.535314
0.6736
0.5353
0.5353
0.6736
0.5353
0.6736
0.6736
Int, V, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.9954
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.9954
1.3651.365
1.141.140.9954
1.1141.114
0.9260.9260.9954
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 2 Lanes
0.5864
0.8278
0.5864
0.5864
0.8278
0.5864
0.8278
0.8278
Int, V, L3
3.2753.2753.275
2.4832.4832.483
2.3922.3922.392
2.1182.1182.118
1.8851.8851.885
1.7611.7611.761
1.5551.5551.555
1.4821.4821.482
1.3651.3651.365
1.141.141.14
1.1141.1141.114
0.9260.9260.926
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, 3 Lanes
0
0.8278
0.5864
0.9954
0.5864
0.8278
0.5864
0.9954
0.8278
0.9954
0.8278
0.9954
Int, V, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.9954
1.3651.365
1.141.140.9954
1.1141.114
0.9260.9260.9954
1.25
1.83
2.25
L/W
mg
S/D
Int.Girder, Shear Force, More Than 3 Lanes
0
0
0
0.5864
0.8278
0.5864
0.8278
0.8278
Ext, V, L1
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8893
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8893
1.3651.365
1.141.140.8893
1.1141.114
0.9260.9260.8893
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 1Lane
0.6298
0.8067
0.6298
0.6298
0.8067
0.6298
0.8067
0.8067
Ext, V, L2
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8314
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, 2 Lanes
0.492
0.6577
0.4937
0.4944
0.6594
0.495
0.6604
0.6608
Ext, V, L3
3.2753.275
2.4832.483
2.3922.392
2.1182.1180.8314
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
S/D:1.25
S/D:1.83
S/D:2.25
L/W
mg
S/D
Ext. Girder, Shear Force, 3 Lanes
0
0.6577
0.4937
0.4944
0.6594
0.495
0.6604
0.6608
Ext, V, L4
3.2753.275
2.4832.483
2.3922.392
2.1182.1180
1.8851.885
1.7611.761
1.5551.555
1.4821.4820.8333
1.3651.365
1.141.140.8342
1.1141.114
0.9260.9260.8349
1.25
1.83
2.25
L/W
mg
S/D
Ext.Girder, Shear Force, L4
0
0
0
0.4944
0.6594
0.495
0.6604
0.6608
plot-analysis
Int-girder Moment
3.2750.2980.43800
2.4830.3360.5070.6240
2.3920.2330.3320.4060
2.1180.350.5210.6380
1.8850.2070.2870.330.316
1.7610.2770.3950.4660.422
1.5550.1940.2640.2940.321
1.4820.3020.430.4930.545
1.3650.2570.3550.4110.433
1.140.2880.4050.4530.571
1.1140.2560.3460.3960.466
0.9260.2830.3970.4420.546
Ext-girder Moment
3.2750.250.37500
2.4830.2480.3580.4140
2.3920.2030.2940.3390
2.1180.2680.380.4310
1.8850.1830.2590.2920.268
1.7610.2130.2960.330.302
1.5550.1720.2410.2670.273
1.4820.2370.3270.3590.364
1.3650.20.2740.3010.3
1.140.2280.3310.3390.376
1.1140.2030.2760.2980.321
0.9260.2260.3080.3330.37
Int-girder Shear
3.2750.540.54300
2.4830.6710.6710.6660
2.3920.5210.5090.5280
2.1180.7150.7090.6980
1.8850.4970.4820.4560.379
1.7610.6550.6330.6120.501
1.5550.5070.4850.4490.388
1.4820.6990.6780.6550.564
1.3650.6490.620.5930.5
1.140.6940.6690.6410.574
1.1140.6510.6230.590.513
0.9260.6920.6660.6370.568
Ext-girder Shear
3.2750.3720.36500
2.4830.4580.450.3930
2.3920.3590.3660.3170
2.1180.5430.5410.4850
1.8850.3460.360.3260.25
1.7610.450.4440.3990.306
1.5550.3520.3640.3330.255
1.4820.520.5190.470.367
1.3650.4480.4420.40.312
1.140.5190.5170.4690.372
1.1140.4640.4650.4240.331
0.9260.5190.5170.470.374
Plot-formula
Int-girder Moment
3.2750.3518750.4300
2.4830.42930.63080.63080
2.3920.29320.38080.38080
2.1180.48460.77420.77420
1.8850.25760.34930.34930.3493
1.7610.35770.55860.55860.5586
1.5550.25760.34930.34930.3493
1.4820.40370.68550.68550.6855
1.3650.31420.51240.51240.5124
1.140.35470.62880.62880.6288
1.1140.31420.51240.51240.5124
0.9260.35470.62880.62880.6288
Ext-girder Moment
3.2750.422930.422900
2.4830.52190.52190.52190
2.3920.42180.42180.42180
2.1180.55840.55840.55840
1.8850.42110.42110.42110.4211
1.7610.5210.5210.5210.521
1.5550.42060.42070.42070.4207
1.4820.55760.55760.55760.5576
1.3650.52060.52060.52060.5206
1.140.55710.55710.55710.5571
1.1140.52030.52030.52030.5203
0.9260.55680.55680.55680.5568
Int-girder Shear
3.2750.5353140.586400
2.4830.67360.82780.82780
2.3920.53530.58640.58640
2.1180.76170.99540.99540
1.8850.53530.58640.58640.5864
1.7610.67360.82780.82780.8278
1.5550.53530.58640.58640.5864
1.4820.76170.99540.99540.9954
1.3650.67360.82780.82780.8278
1.140.76170.99540.99540.9954
1.1140.67360.82780.82780.8278
0.9260.76170.99540.99540.9954
Ext-girder Shear
3.2750.62980.49200
2.4830.80670.65770.65770
2.3920.62980.49370.49370
2.1180.88930.83140.83140
1.8850.62980.49440.49440.4944
1.761
