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APPENDIX J – RECOMMENDED SIMPLIFIED METHOD VS. RIGOROUS ANALYSIS

J-1

Introduction

This appendix contains comparisons of distribution factors computed by the

recommended simplified method to distribution factors computed using the grillage

techniques outlined in Appendix F. The results are presented as plots of the simplified

method distribution factor on the Y axis and the rigorous distribution factor on the X axis.

No multiple presence or analysis factors have been included in these calculations. The

location reference is based on 10ths of the span lengths. For example, location 104

indicates a point 40 percent along the length of span number one. Similarly, location 100

indicates zero percent along span number one.

The plots are then repeated for the alternate distribution factor method for

moments. This method was developed to address the large variability in the primary

simplified method for one loaded lane for moment. These should be viewed with a focus

on the one lane loaded case.

J-2

Results

Slab On Steel I Girders

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 0.9669x + 0.064R2 = 0.862

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Figure J-1. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-3

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.8869x + 0.0645R2 = 0.9001

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Figure J-2. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9959x - 0.0032R2 = 0.8718

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Figure J-3. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-4

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0047x - 0.0037R2 = 0.3355

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Figure J-4. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.5127x + 0.4117R2 = 0.6799

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Figure J-5. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-5

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.4879x + 0.3299R2 = 0.4254

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Figure J-6. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9977x - 0.0006R2 = 0.6297

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Figure J-7. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-6

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0074x - 0.0026R2 = 0.8727

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Figure J-8. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00y = 0.9817x - 0.0043R2 = 0.9519

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Figure J-9. Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00

J-7

Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00y = 1.0166x - 0.029R2 = 0.9327

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Figure J-10. Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.001x + 0.0047R2 = 0.9

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Figure J-11. Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00

J-8

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 1.0045x + 0.005R2 = 0.8934

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Figure J-12. Shear in the Interior Girder, 1 Lane Loaded, Location 100.00

Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00y = 1.0032x - 0.0086R2 = 0.981

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Figure J-13. Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00

J-9

Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00y = 1.0043x - 0.0151R2 = 0.9814

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Figure J-14. Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 1.0012x + 0.0007R2 = 0.9683

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Figure J-15. Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00

J-10

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 0.9962x + 0.0012R2 = 0.9446

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Figure J-16. Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00

J-11

Slab on Prestressed I and Prestressed Bulb Tee Girders

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.1096x - 0.023R2 = 0.9455

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Figure J-17. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-12

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.0532x - 0.0227R2 = 0.9182

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Figure J-18. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x + 0.0023R2 = 0.9268

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Figure J-19. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-13

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0004x + 0.001R2 = 0.6213

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Figure J-20. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.7534x + 0.2433R2 = 0.6417

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Figure J-21. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-14

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.7449x + 0.178R2 = 0.7768

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Figure J-22. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0006x - 0.0032R2 = 0.6586

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Figure J-23. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-15

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0017x + 0.0039R2 = 0.9152

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Figure J-24. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00y = 0.9491x + 0.0345R2 = 0.9275

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Figure J-25. Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00

J-16

Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00y = 0.9515x + 0.0247R2 = 0.8987

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Figure J-26. Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0013x + 0.0042R2 = 0.887

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Figure J-27. Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00

J-17

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 0.9992x + 0.0021R2 = 0.9146

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Figure J-28. Shear in the Interior Girder, 1 Lane Loaded, Location 100.00

Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00y = 1.0027x + 0.0032R2 = 0.9904

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Figure J-29. Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00

J-18

Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00y = 0.9951x + 0.0025R2 = 0.985

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Figure J-30. Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 0.995x + 0.0014R2 = 0.9834

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Figure J-31. Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00

J-19

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 0.9973x - 0.0044R2 = 0.9889

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Figure J-32. Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00

J-20

Cast-In-Place Concrete Tee Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.1779x - 0.1031R2 = 0.9449

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Figure J-33. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-21

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.8458x + 0.0756R2 = 0.9838

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Figure J-34. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 1.0011x - 0.0016R2 = 0.9546

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Figure J-35. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-22

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0004x - 0.0015R2 = 0.7347

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Figure J-36. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.8785x + 0.1306R2 = 0.666

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Figure J-37. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-23

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 1.0183x + 0.0194R2 = 0.8899

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Figure J-38. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9986x + 0.0035R2 = 0.9767

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Figure J-39. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-24

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0001x + 0.0042R2 = 0.9133

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Figure J-40. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00y = 1.0817x - 0.039R2 = 0.9706

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Figure J-41. Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00

J-25

Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00y = 1.2527x - 0.1851R2 = 0.9384

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Figure J-42. Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 0.9996x + 0.0014R2 = 0.8368

0

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Rigorous Distribution Factor

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Figure J-43. Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00

J-26

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 0.9982x + 0.0012R2 = 0.9168

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Figure J-44. Shear in the Interior Girder, 1 Lane Loaded, Location 100.00

Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00y = 0.7812x + 0.1339R2 = 0.8751

0

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Figure J-45. Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00

J-27

Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00y = 0.8251x + 0.1069R2 = 0.9113

0

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Rigorous Distribution Factor

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Figure J-46. Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 1.002x + 0.0031R2 = 0.953

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Figure J-47. Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00

J-28

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 0.9995x + 0.0035R2 = 0.9309

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Rigorous Distribution Factor

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Figure J-48. Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00

J-29

Concrete Spread Box Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.432x - 0.3942R2 = 0.9054

0

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(Cal

ibra

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Onl

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Figure J-49. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-30

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.0667x - 0.0904R2 = 0.8164

0

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(Cal

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Onl

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Figure J-50. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x - 0.004R2 = 0.9092

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(Cal

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Figure J-51. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-31

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0058x + 0.002R2 = 0.6774

0

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(Cal

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Figure J-52. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 1.0443x - 0.0287R2 = 0.9699

0

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(Cal

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Figure J-53. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-32

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 1.2632x - 0.1978R2 = 0.9739

0

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(Cal

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Figure J-54. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9978x + 0.002R2 = 0.6756

0

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(Cal

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Figure J-55. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-33

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 0.9942x + 0.002R2 = 0.5625

0

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(Cal

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Figure J-56. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00y = 0.7748x + 0.1173R2 = 0.9827

0

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Rigorous Distribution Factor

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(Cal

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Figure J-57. Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00

J-34

Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00y = 0.8533x + 0.0843R2 = 0.9854

0

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

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(Cal

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Onl

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Figure J-58. Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 0.9977x + 0.003R2 = 0.9566

0

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(Cal

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Figure J-59. Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00

J-35

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 0.9965x + 0.0023R2 = 0.9235

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(Cal

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Figure J-60. Shear in the Interior Girder, 1 Lane Loaded, Location 100.00

Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00y = 0.8752x + 0.0313R2 = 0.9875

0

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Rigorous Distribution Factor

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(Cal

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Figure J-61. Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00

J-36

Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00y = 0.9014x + 0.031R2 = 0.9859

0

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(Cal

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Figure J-62. Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 0.9971x - 0.0015R2 = 0.9807

0

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(Cal

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Figure J-63. Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00

J-37

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 0.9975x + 0.0038R2 = 0.9452

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Figure J-64. Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00

J-38

Cast-In-Place Concrete Box Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 0.81x + 0.0514R2 = 0.4949

0

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-65. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-39

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.8566x - 0.0241R2 = 0.6494

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-66. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9975x - 0.002R2 = 0.4313

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-67. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-40

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0002x - 0.0028R2 = 0.2318

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-68. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.6368x + 0.1152R2 = 0.4314

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-69. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-41

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.7894x + 0.0223R2 = 0.7423

0

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(Cal

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fdsgs

Figure J-70. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9967x + 0.0012R2 = 0.5843

0

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-71. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-42

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 0.9937x - 0.0016R2 = 0.2739

0

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Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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fdsgs

Figure J-72. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00y = 1.0947x - 0.1032R2 = 0.8734

0

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Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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fdsgs

Figure J-73. Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00

J-43

Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00y = 1.091x - 0.0867R2 = 0.8558

0

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-74. Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0033x - 0.0002R2 = 0.7972

0

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-75. Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00

J-44

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 1.0023x + 0.0008R2 = 0.8017

0

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Rigorous Distribution Factor

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(Cal

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fdsgs

Figure J-76. Shear in the Interior Girder, 1 Lane Loaded, Location 100.00

Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00y = 0.9384x + 0.0136R2 = 0.991

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Rigorous Distribution Factor

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Dis

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(Cal

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fdsgs

Figure J-77. Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00

J-45

Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00y = 0.9711x + 0.003R2 = 0.9892

0

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(Cal

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fdsgs

Figure J-78. Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 0.9982x + 0.0007R2 = 0.9764

0

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Rigorous Distribution Factor

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fdsgs

Figure J-79. Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00

J-46

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 0.996x - 0.0026R2 = 0.8782

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Rigorous Distribution Factor

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fdsgs

Figure J-80. Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00

J-47

Adjacent Concrete Box Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 0.7171x + 0.1012R2 = 0.7315

0

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Figure J-81. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-48

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.7318x + 0.0383R2 = 0.9846

0

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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(Cal

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Figure J-82. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9933x - 0.0026R2 = 0.9528

0

0.2

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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(Cal

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Figure J-83. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-49

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 0.9973x - 0.0003R2 = 0.4194

0

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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(Cal

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Figure J-84. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.7041x + 0.0894R2 = 0.7595

0

0.2

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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peci

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Dis

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(Cal

ibra

tion

Onl

y)

Figure J-85. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-50

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.6926x + 0.0456R2 = 0.9498

0

0.2

0.4

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0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

y)

Figure J-86. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9943x - 0.005R2 = 0.9233

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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LR

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peci

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Dis

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(Cal

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Onl

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Figure J-87. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-51

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0171x - 0.0036R2 = 0.7059

0

0.2

0.4

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0.8

1

1.2

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-88. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00y = 1.0486x - 0.0678R2 = 0.9743

0

0.2

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0.8

1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-89. Shear in the Interior Girder, 4 Lanes Loaded, Location 100.00

J-52

Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00y = 0.9822x - 0.0042R2 = 0.9643

0

0.2

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0.8

1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-90. Shear in the Interior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0017x - 0.0009R2 = 0.965

0

0.2

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1

1.2

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-91. Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00

J-53

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 1.0033x - 0.0019R2 = 0.9342

0

0.2

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-92. Shear in the Interior Girder, 1 Lane Loaded, Location 100.00

Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00y = 0.988x - 0.0183R2 = 0.998

0

0.2

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1

1.2

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-93. Shear in the Exterior Girder, 4 Lanes Loaded, Location 100.00

J-54

Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00y = 0.9772x - 0.0037R2 = 0.9959

0

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-94. Shear in the Exterior Girder, 3 Lanes Loaded, Location 100.00

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 1.0034x - 0.0049R2 = 0.9898

0

0.2

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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(Cal

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Onl

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Figure J-95. Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00

J-55

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 1.0011x + 0.003R2 = 0.9898

0

0.2

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4Rigorous Distribution Factor

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Dis

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(Cal

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Onl

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Figure J-96. Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00

J-56

Results – Alternate Method for Moment

Slab On Steel I Girders

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 0.9669x + 0.064R2 = 0.862

0

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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FD S

peci

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Dis

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For

Mom

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Cal

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Figure J-97. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-57

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.8869x + 0.0645R2 = 0.9001

0

0.2

0.4

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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FD S

peci

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For

Mom

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Cal

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Onl

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Figure J-98. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9959x - 0.0032R2 = 0.8718

0

0.2

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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e LR

FD S

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For

Mom

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Cal

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Onl

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Figure J-99. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-58

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 0.9991x + 0.003R2 = 0.6518

0

0.2

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1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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e LR

FD S

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Dis

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For

Mom

ent (

Cal

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Onl

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Figure J-100. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.9606x - 0.0461R2 = 0.9455

0

0.2

0.4

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0.8

1

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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e LR

FD S

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For

Mom

ent (

Cal

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Onl

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Figure J-101. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-59

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.9916x - 0.0646R2 = 0.9346

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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e LR

FD S

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For

Mom

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Cal

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Onl

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Figure J-102. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9954x + 0.0012R2 = 0.8566

0

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0.6

0.8

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1.2

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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FD S

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For

Mom

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Cal

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Figure J-103. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-60

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0074x - 0.0026R2 = 0.8727

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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e LR

FD S

peci

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Dis

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For

Mom

ent (

Cal

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Onl

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Figure J-104. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

J-61

Slab on Prestressed I and Prestressed Bulb Tee Girders

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.1096x - 0.023R2 = 0.9455

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

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e LR

FD S

peci

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Dis

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For

Mom

ent (

Cal

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Onl

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Figure J-105. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-62

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.0532x - 0.0227R2 = 0.9182

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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For

Mom

ent (

Cal

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Onl

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Figure J-106. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x + 0.0023R2 = 0.9268

0

0.2

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0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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utio

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For

Mom

ent (

Cal

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Onl

y)

Figure J-107. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-63

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 0.9882x - 0.0059R2 = 0.8786

0

0.2

0.4

0.6

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1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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For

Mom

ent (

Cal

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Onl

y)

Figure J-108. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.9814x + 0.0197R2 = 0.9581

0

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1

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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utio

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ctor

For

Mom

ent (

Cal

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Onl

y)

Figure J-109. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-64

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.9823x + 0.0019R2 = 0.9507

0

0.2

0.4

0.6

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

trib

utio

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For

Mom

ent (

Cal

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Onl

y)

Figure J-110. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0025x - 0.0014R2 = 0.945

0

0.2

0.4

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1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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utio

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For

Mom

ent (

Cal

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Onl

y)

Figure J-111. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-65

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0017x + 0.0039R2 = 0.9152

0

0.2

0.4

0.6

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1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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Dis

trib

utio

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For

Mom

ent (

Cal

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Onl

y)

Figure J-112. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

J-66

Cast-In-Place Concrete Tee Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.284x - 0.2908R2 = 0.5959

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

ficat

ion

Dis

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utio

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ctor

For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-113. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-67

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.4459x - 0.3087R2 = 0.6699

0

0.2

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0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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utio

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ctor

For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-114. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 1.0408x - 0.0122R2 = 0.6405

0

0.2

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0.8

1

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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Dis

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utio

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For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-115. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-68

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0627x - 0.0173R2 = 0.6387

0

0.2

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0.8

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

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Alte

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e LR

FD S

peci

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Dis

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utio

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ctor

For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-116. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.5835x + 0.2319R2 = 0.5679

0

0.2

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1

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

ficat

ion

Dis

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utio

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ctor

For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-117. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-69

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.725x + 0.1552R2 = 0.7428

0

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0.8

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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Dis

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utio

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ctor

For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-118. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9953x + 0.0015R2 = 0.9454

0

0.2

0.4

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0.8

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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Dis

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utio

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ctor

For

Mom

ent,

Cal

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Onl

y

Figure J-119. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-70

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0001x + 0.0042R2 = 0.9133

0

0.2

0.4

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1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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ion

Dis

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utio

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ctor

For

Mom

ent,

Cal

ibra

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Onl

y

Figure J-120. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

J-71

Concrete Spread Box Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.432x - 0.3942R2 = 0.9054

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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Dis

trib

utio

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ctor

For

Mom

ent (

Cal

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tion

Onl

y)

Figure J-121. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-72

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.0667x - 0.0904R2 = 0.8164

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

rnat

e LR

FD S

peci

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ion

Dis

trib

utio

n Fa

ctor

For

Mom

ent (

Cal

ibra

tion

Onl

y)

Figure J-122. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x - 0.004R2 = 0.9092

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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Dis

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utio

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ctor

For

Mom

ent (

Cal

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Onl

y)

Figure J-123. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-73

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 0.9978x + 0.0005R2 = 0.6475

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Prop

osed

Alte

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e LR

FD S

peci

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ion

Dis

trib

utio

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ctor

For

Mom

ent (

Cal

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Onl

y)

Figure J-124. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.7142x + 0.0488R2 = 0.9414

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Figure J-125. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-74

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.8243x + 0.0114R2 = 0.9217

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Figure J-126. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0012x - 0.0032R2 = 0.8327

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Figure J-127. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-75

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 0.9999x + 0.0043R2 = 0.6184

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Figure J-128. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

J-76

Cast-In-Place Concrete Box Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 0.5036x + 0.0851R2 = 0.7048

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Figure J-129. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-77

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.6751x + 0.0403R2 = 0.7714

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Figure J-130. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 1.0001x + 0.0003R2 = 0.8361

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Figure J-131. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-78

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 0.9981x - 0.0047R2 = 0.8136

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Figure J-132. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.5573x + 0.0473R2 = 0.5171

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Figure J-133. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-79

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.7394x + 0.0148R2 = 0.5624

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Figure J-134. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0021x + 0.0046R2 = 0.5944

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Figure J-135. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-80

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 0.9995x + 0.0018R2 = 0.5565

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Figure J-136. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

J-81

Adjacent Concrete Box Beams

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 0.7171x + 0.1012R2 = 0.7315

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Mom

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Figure J-137. Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00

J-82

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 0.7318x + 0.0383R2 = 0.9846

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Mom

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Figure J-138. Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9933x - 0.0026R2 = 0.9528

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Figure J-139. Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00

J-83

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0035x - 0.0044R2 = 0.9086

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Figure J-140. Moment in the Interior Girder, 1 Lane Loaded, Location 104.00

Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00y = 0.7041x + 0.0894R2 = 0.7595

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Figure J-141. Moment in the Exterior Girder, 4 Lanes Loaded, Location 104.00

J-84

Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00y = 0.6926x + 0.0456R2 = 0.9498

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Mom

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Figure J-142. Moment in the Exterior Girder, 3 Lanes Loaded, Location 104.00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.9943x - 0.005R2 = 0.9233

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Mom

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Figure J-143. Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00

J-85

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0011x - 0.0023R2 = 0.7406

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Figure J-144. Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00

J-86

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