Page 1
E-1
NCHRP Project 12-71 Design Specifications and Commentary for Horizontally Curved Concrete Box-Girder
Highway Bridges
Appendix E Detailed Global Analysis Results
This Appendix contains the graphical results generated from the finite element global bridge analysis. The three bridge loading scenarios are “self weight”, “live load total” and “post tension total”. The plots are arranged in the following order:
1 Bridge Model Scattergrams – Spine vs. Grillage
2 Bridge Model Ratio Plots – Spine vs. Grillage
3 Bridge Model Ratio Plots - Straight to Curve (spine and grillage)
4 Effect of Diaphragms – Grillage Analysis
5 Effect of Diaphragms – Ratio Plots
6 Effect of Hinges – Grillage Analysis
7 Effect of Hinges – Ratio Plots
8 Effect of Skews
Page 3
E-3
9 Figure E.1.1: Single Cell, Pre-Cast, 6’x18’ Column: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.007 -0.005 -0.003 -0.001 0.001
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-70000 -50000 -30000 -10000 10000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-3500 -3000 -2500 -2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
100
200
300
400
500
600
0 100 200 300 400 500 600
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 4
E-4
Figure E.1.2: Single Cell, Pre-Cast, 6'x6' Column: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-80000
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
50
100
150
200
250
300
350
400
0 100 200 300 400
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 5
E-5
Figure E.1.3: Single Cell, Precast, 6'x18' Column: Live Load Total
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.08 -0.06 -0.04 -0.02 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.0012
-0.001
-0.0008
-0.0006
-0.0004
-0.0002
0-0.0012 -0.0007 -0.0002
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-120
-100
-80
-60
-40
-20
0-100.21 -100.01 -99.8099
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-12000
-10000
-8000
-6000
-4000
-2000
0
-12000 -10000 -8000 -6000 -4000 -2000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-700
-600
-500
-400
-300
-200
-100
0
-700 -600 -500 -400 -300 -200 -100 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-6000
-5000
-4000
-3000
-2000
-1000
0-6000 -5000 -4000 -3000 -2000 -1000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 6
E-6
Figure E.1.4: Single Cell, Pre-Cast, 6x6 Column: Live Load Total
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-80000
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
50
100
150
200
250
300
350
400
0 100 200 300 400
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 7
E-7
Figure E.1.5: Single Cell, Pre-Cast, 6'x18' Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.003
-0.002
-0.001
0
0.001
0.002
0.003-0.003 -0.002 -0.001 0 0.001 0.002 0.003
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
12000 200 400 600 800 1000 1200
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
0 10000 20000 30000 40000 50000 60000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-2500
-2000
-1500
-1000
-500
0
-2500 -2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000
14000-2000 3000 8000 13000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
9600
9650
9700
9750
9800
9850
9900
9950
10000
10050
9600 9700 9800 9900 10000
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 8
E-8
Figure E.1.6: Single Cell, Pre-Cast, 6x6 Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003-0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
12000 200 400 600 800 1000 1200
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
0 10000 20000 30000 40000 50000 60000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
-2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000-2000 3000 8000 13000 18000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
9600
9650
9700
9750
9800
9850
9900
9950
10000
10050
9600 9700 9800 9900 10000
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 9
E-9
Figure E.1.7: Single Cell, Cast In Place, 6’x18’ Column: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Mid-span Def lections
-0.008
-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.008 -0.006 -0.004 -0.002 -1E-17
Sing
le G
irde
r Mod
el
2 Girder Grillage
Mid-span Rotations
-2500
-2000
-1500
-1000
-500
0-2500 -2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Abutment Shear
-80000
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-25000
-20000
-15000
-10000
-5000
0
-25000 -20000 -15000 -10000 -5000 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Transverse Moment
0
100
200
300
400
500
6000 100 200 300 400 500 600
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-3
-2.5
-2
-1.5
-1
-0.5
0
-3 -2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 10
E-10
Figure E.1.8: Single Cell, Cast In Place, 6'x6' Column: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.008
-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.008 -0.006 -0.004 -0.002 -1E-17
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-2500
-2000
-1500
-1000
-500
0-2500 -2000 -1500 -1000 -500 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-80000
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-25000
-20000
-15000
-10000
-5000
0-25000 -20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
50
100
150
200
250
300
350
400
450
0 100 200 300 400
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-3
-2.5
-2
-1.5
-1
-0.5
0-3 -2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 11
E-11
Figure E.1.9: Single Cell, Cast In Place, 6'x18' Column: Live Load Total
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.08 -0.06 -0.04 -0.02 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.0008
-0.0007
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0-0.0008 -0.0006 -0.0004 -0.0002 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-101
-100.8
-100.6
-100.4
-100.2
-100
-99.8
-99.6
-99.4
-99.2
-99-101 -100.5 -100 -99.5 -99
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-12000
-10000
-8000
-6000
-4000
-2000
0
-12000 -10000 -8000 -6000 -4000 -2000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-700
-600
-500
-400
-300
-200
-100
0
-700 -600 -500 -400 -300 -200 -100 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-6000
-5000
-4000
-3000
-2000
-1000
0-6000 -5000 -4000 -3000 -2000 -1000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 12
E-12
Figure E.1.10: Single Cell, Cast In Place, 6'x6' Column: Live Load Total
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.08 -0.06 -0.04 -0.02 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.0008
-0.0007
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0-0.0008 -0.0006 -0.0004 -0.0002 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-120
-100
-80
-60
-40
-20
0-120 -100 -80 -60 -40 -20 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-12000
-10000
-8000
-6000
-4000
-2000
0
-12000 -10000 -8000 -6000 -4000 -2000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-800
-700
-600
-500
-400
-300
-200
-100
0
-800 -600 -400 -200 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-4000 -3000 -2000 -1000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
10
20
30
40
50
60
70
80
0 20 40 60 80
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 13
E-13
Figure E.1.11: Single Cell, Cast In Place, 6'x18' Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002-0.004 -0.002 0 0.002
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
12000 200 400 600 800 1000 1200
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
0 10000 20000 30000 40000 50000 60000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-2500
-2000
-1500
-1000
-500
0
-2500 -2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000-2000 3000 8000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
9600
9650
9700
9750
9800
9850
9900
9950
10000
10050
10100
9600 9700 9800 9900 10000 10100
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 14
E-14
Figure E.1.12: Single Cell, Cast In Place, 6'x6' Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sing
le G
irder
Mod
el
2 Girder Grillage
Mid-span Def lections
-0.005
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002-0.005 -0.003 -0.001 0.001
Sing
le G
irder
Mod
el
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
12000 200 400 600 800 1000 1200
Sing
le G
irder
Mod
el
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
0 10000 20000 30000 40000 50000 60000
Sing
le G
irder
Mod
el
2 Girder Grillage
Midspan Moment
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Sing
le G
irder
Mod
el
2 Girder Grillage
Midspan Torsion
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 5000 10000 15000
Sing
le G
irder
Mod
el
2 Girder Grillage
Midspan Transverse Moment
9700
9750
9800
9850
9900
9950
10000
10050
101009700 9750 9800 9850 9900 9950 10000 10050
Sing
le G
irder
Mod
el
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 15
E-15
Figure E.1.13: Two Cell, Cast In Place, 6'x18' Column: Self Weight
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0-0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-1400
-1200
-1000
-800
-600
-400
-200
0-1400 -1200 -1000 -800 -600 -400 -200 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-70000 -60000 -50000 -40000 -30000 -20000 -10000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-5000 -4000 -3000 -2000 -1000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Torsion
-25000
-20000
-15000
-10000
-5000
0-25000 -20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
100
200
300
400
500
600
0 100 200 300 400 500 600
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 16
E-16
Figure E.1.14: Two Cell, Cast In Place, 7'x7'Column: Self Weight
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0-0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-1400
-1200
-1000
-800
-600
-400
-200
0-1400 -1200 -1000 -800 -600 -400 -200 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0
-70000 -60000 -50000 -40000 -30000 -20000 -10000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-25000
-20000
-15000
-10000
-5000
0-25000 -20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
100
200
300
400
500
600
0 100 200 300 400 500 600
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 17
E-17
Figure E.1.15: Two Cell, Cast In Place, 6'x18' Column: Live Load Total
-0.1
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.1 -0.08 -0.06 -0.04 -0.02 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.001
-0.0008
-0.0006
-0.0004
-0.0002
0-0.001 -0.0008 -0.0006 -0.0004 -0.0002 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
-160
-140
-120
-100
-80
-60
-40
-20
0-160 -110 -60 -10
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-1200
-1000
-800
-600
-400
-200
0
-1200 -1000 -800 -600 -400 -200 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0-8000 -6000 -4000 -2000 0
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 18
E-18
Figure E.1.16: Two Cell, Cast In Place, 7'x7'Column: Live Load Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sin
gle
Gir
der M
odel
2 Girder Grillage
Mid-span Def lections
-0.003
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015-0.003 -0.002 -0.001 0 0.001
Sin
gle
Gir
der M
odel
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
1200
1400
0 500 1000 1500
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
600000 10000 20000 30000 40000 50000 60000
Sin
gle
Gir
der M
odel
2 Girder Grillage
Midspan Moment
-2500
-2000
-1500
-1000
-500
0-2500 -2000 -1500 -1000 -500 0
Sin
gle
Gir
der M
odel
2 Girder Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
-2000 3000 8000 13000 18000
Sin
gle
Gir
der M
odel
2 Girder Grillage
Midspan Transverse Moment
11500
11600
11700
11800
11900
12000
1210011500 11600 11700 11800 11900 12000 12100
Sin
gle
Gir
der M
odel
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 19
E-19
Figure E.1.17: Two Cell, Cast In Place, 6'x18' Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.350 0.1 0.2 0.3 0.4
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.003
-0.0025
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015-0.003 -0.002 -0.001 0 0.001 0.002
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
1200
14000 500 1000
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
600000 10000 20000 30000 40000 50000 60000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-2500
-2000
-1500
-1000
-500
0
-2500 -2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000-2000 3000 8000 13000 18000
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Transverse Moment
11500
11600
11700
11800
11900
12000
1210011500 11600 11700 11800 11900 12000 12100
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 20
E-20
Figure E.1.18: Two Cell, Cast In Place, 7'x7'Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Def lections
-0.003
-0.002
-0.001
0
0.001
0.002-0.003 -0.002 -0.001 0 0.001 0.002
Sin
gle
Gird
er M
odel
2 Girder Grillage
Mid-span Rotations
0
200
400
600
800
1000
1200
14000 500 1000
Sin
gle
Gir
der M
odel
2 Girder Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
0 10000 20000 30000 40000 50000 60000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Moment
-2000
-1500
-1000
-500
0
-2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Torsion
-5000
0
5000
10000
15000
20000
25000-5000 0 5000 10000 15000 20000 25000
Sing
le G
irde
r Mod
el
2 Girder Grillage
Midspan Transverse Moment
11500
11550
11600
11650
11700
11750
11800
11850
11900
11950
12000
12050
11500 11600 11700 11800 11900 12000
Sin
gle
Gird
er M
odel
2 Girder Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 21
E-21
Figure E.1.19: Five Cell, Cast In Place, 6'x18' Column: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
Grillage
Mid-span Def lections
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.006 -0.004 -0.002 0
Sing
le G
irde
r Mod
el
Grillage
Mid-span Rotations
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000-4000 -3000 -2000 -1000 0 1000
Sin
gle
Gird
er M
odel
Grillage
Abutment Shear
-120000
-100000
-80000
-60000
-40000
-20000
0
-120000 -100000 -80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0-7000 -6000 -5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-50000
-45000
-40000
-35000
-30000
-25000
-20000
-15000
-10000
-5000
0-50000 -40000 -30000 -20000 -10000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Transverse Moment
0
100
200
300
400
500
600
700
800
900
1000
0 200 400 600 800 1000
Sing
le G
irde
r Mod
el
Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0
-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 22
E-22
Figure E.1.20: Five Cell, Cast In Place, 8'x8' Column: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
Grillage
Mid-span Def lections
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.006 -0.004 -0.002 0
Sing
le G
irde
r Mod
el
Grillage
Mid-span Rotations
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000-4000 -3000 -2000 -1000 0 1000
Sin
gle
Gird
er M
odel
Grillage
Abutment Shear
-120000
-100000
-80000
-60000
-40000
-20000
0
-120000 -100000 -80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0-7000 -6000 -5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-50000
-45000
-40000
-35000
-30000
-25000
-20000
-15000
-10000
-5000
0-50000 -40000 -30000 -20000 -10000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Transverse Moment
0
100
200
300
400
500
600
700
800
0 200 400 600 800
Sing
le G
irde
r Mod
el
Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0
-2.5 -2 -1.5 -1 -0.5 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 23
E-23
Figure E.1.21: Five Cell, Cast In Place, 6'x18' Column: Live Load Total
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.08 -0.06 -0.04 -0.02 0
Sin
gle
Gird
er M
odel
Grillage
Mid-span Def lections
-0.0008
-0.0007
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0-0.0008 -0.0006 -0.0004 -0.0002 0
Sing
le G
irde
r Mod
el
Grillage
Mid-span Rotations
-200
-150
-100
-50
0
50-200 -150 -100 -50 0 50
Sin
gle
Gird
er M
odel
Grillage
Abutment Shear
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-10000
-9000
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0-10000 -8000 -6000 -4000 -2000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Transverse Moment
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200
Sing
le G
irde
r Mod
el
Grillage
Midspan Axial Force
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 24
E-24
Figure E.1.22: Five Cell, Cast In Place, 8'x8' Column: Live Load Total
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.08 -0.06 -0.04 -0.02 0
Sin
gle
Gird
er M
odel
Grillage
Mid-span Def lections
-0.0008
-0.0007
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0-0.0008 -0.0006 -0.0004 -0.0002 0
Sing
le G
irde
r Mod
el
Grillage
Mid-span Rotations
-200
-150
-100
-50
0
50-200 -150 -100 -50 0 50
Sin
gle
Gird
er M
odel
Grillage
Abutment Shear
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0
-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-1200
-1000
-800
-600
-400
-200
0-1200 -1000 -800 -600 -400 -200 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0-8000 -6000 -4000 -2000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Transverse Moment
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200
Sing
le G
irde
r Mod
el
Grillage
Midspan Axial Force
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
-0.5 -0.4 -0.3 -0.2 -0.1 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 25
E-25
Figure E.1.23: Five Cell, Cast In Place, 6'x18' Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sin
gle
Gird
er M
odel
Grillage
Mid-span Def lections
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002-0.002 -0.001 0 0.001 0.002
Sing
le G
irde
r Mod
el
Grillage
Mid-span Rotations
0
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000
Sin
gle
Gird
er M
odel
Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 20000 40000 60000 80000 100000
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000-2000 3000 8000 13000
Sin
gle
Gird
er M
odel
Grillage
Midspan Transverse Moment
0
5000
10000
15000
20000
25000
30000
0 5000 10000 15000 20000 25000 30000
Sing
le G
irde
r Mod
el
Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irde
r Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 26
E-26
Figure E.1.24: Five Cell, Cast In Place, 8'x8' Column: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Sing
le G
irde
r Mod
el
Grillage
Mid-span Def lections
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002-0.004 -0.002 0 0.002
Sin
gle
Gird
er M
odel
Grillage
Mid-span Rotations
0
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000
Sing
le G
irde
r Mod
el
Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1000000 20000 40000 60000 80000 100000
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-10000
0
10000
20000
30000
40000
50000
60000-10000 0 10000 20000 30000 40000 50000 60000
Sing
le G
irde
r Mod
el
Grillage
Midspan Transverse Moment
0
5000
10000
15000
20000
25000
30000
0 5000 10000 15000 20000 25000 30000
Sing
le G
irde
r Mod
el
Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irde
r Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 27
E-27
Figure E.2.1: Single Cell, Precast, 6'x18' Column: Self Weight
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.9550.96
0.9650.97
0.9750.98
0.9850.99
0.9951
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.2: Single Cell, Pre-Cast, 6'x6' Column: Self Weight
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.970.980.99
11.011.021.031.041.051.061.071.08
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 28
E-28
Figure E.2.3: Single Cell, Precast, 6'x18' Column: Live Load Total
0.9
0.92
0.94
0.96
0.98
1
1.02
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.960.965
0.970.975
0.980.985
0.990.995
11.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.4: Single Cell, Pre-Cast, 6x6 Column: Live Load Total
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 29
E-29
Figure E.2.5: Single Cell, Pre-Cast, 6'x18' Column: Post Tension Total
0.96
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.981
1.021.041.061.081.1
1.121.141.16
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.6: Single Cell, Pre-Cast, 6x6 Column: Post Tension Total
0.96
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 30
E-30
Figure E.2.7: Single Cell, Cast In Place, 6x18 Column: Self Weight
0.920.930.940.950.960.970.980.99
11.011.021.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.8: Single Cell, Cast In Place, 6'x6' Column: Self Weight
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.9550.96
0.9650.97
0.9750.98
0.9850.99
0.9951
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.960.970.980.99
11.011.021.031.041.051.061.07
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 31
E-31
Figure E.2.9: Single Cell, Cast In Place, 6’x18’ Column: Live Load Total
0.9
0.92
0.94
0.96
0.98
1
1.02
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.95
0.96
0.97
0.98
0.99
1
1.01
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.10: Single Cell, Cast In Place, 6'x6' Column: Live Load Total
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0.9650.97
0.9750.98
0.9850.99
0.9951
1.0051.01
1.015
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 32
E-32
Figure E.2.11: Single Cell, Cast In Place, 6'x18' Column: Post Tension Total
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.981
1.021.041.061.081.1
1.121.141.16
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.12: Single Cell, Cast In Place, 6'x6' Column: Post Tension Total
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 33
E-33
Figure E.2.13: Two Cell, Cast In Place, 6'x18' Column: Self Weight
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.90.905
0.910.915
0.920.925
0.930.935
0.940.945
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
1.02
1.04
1.06
1.08
1.1
1.12
1.14
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.97
0.98
0.99
1
1.01
1.02
1.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.14: Two Cell, Cast In Place, 7'x7'Column: Self Weight
0.850.860.870.880.890.9
0.910.920.930.940.95
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.90.905
0.910.915
0.920.925
0.930.935
0.940.945
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 34
E-34
Figure E.2.15: Two Cell, Cast In Place, 6'x18' Column: Live Load Total
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
1.041.061.081.1
1.121.141.161.181.2
1.221.24
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.16: Two Cell, Cast In Place, 7'x7'Column: Live Load Total
0.830.840.850.860.870.880.890.9
0.910.920.930.94
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
1.041.061.081.1
1.121.141.161.181.2
1.221.24
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0.980.985
0.990.995
11.005
1.011.015
1.021.025
1.031.035
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 35
E-35
Figure E.2.17: Two Cell, Cast In Place, 6'x18' Column: Post Tension Total
0.880.890.9
0.910.920.930.940.950.960.970.98
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.940.960.98
11.021.041.061.081.1
1.12
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Figure E.2.18: Two Cell, Cast In Place, 7'x7'Column: Post Tension Total
0.880.890.9
0.910.920.930.940.950.960.970.98
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Page 36
E-36
Figure E.2.19: Five Cell, Cast In Place, 6'x18' Column: Self Weight
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.83
0.840.850.860.870.880.890.9
0.910.920.930.94
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Figure E.2.20: Five Cell, Cast In Place, 6'x6' Column: Self Weight
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.84
0.850.860.870.880.890.9
0.910.920.930.94
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 37
E-37
Figure E.2.21: Five Cell, Cast In Place, 6'x18' Column: Live Load Total
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Figure E.2.22: Five Cell, Cast In Place, 8'x8' Column: Live Load Total
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.8
0.82
0.84
0.86
0.88
0.9
0.92
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 38
E-38
Figure E.2.23: Five Cell, Cast In Place, 6'x18' Column: Post Tension Total
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Figure E.2.24: Five Cell, Cast In Place, 8'x8' Column: Post Tension Total
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.92
0.940.960.98
11.021.041.061.081.1
1.12
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 39
E-39
Figure E.3.1: Ratio of Dead Load Stresses in Curved Bridge Relative to Straight Bridge
All Single Span fr/fs Dead Load
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
fr/fs
CIP1_6x18_sp1m_dl
CIP1_6x18_sp1s_dl
PC1_6x18_sp1m_dl
PC1_6x18_sp1s_dl
CIP2_6x18_sp1m_dl
CIP2_6x18_sp1s_dl
CIP5_6x18_sp1m_dl
CIP5_6x18_sp1s_dl
All 3-Span fr/fs Dead Load
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Length/Radius (L/R)
fr/fs
CIP1_6x18_sp3l_dl
CIP1_6x18_sp3m_dl
CIP1_6x18_sp3s_dl
CIP1_6x6_sp3l_dl
CIP1_6x6_sp3m_dl
CIP1_6x6_sp3s_dl
PC1_6x18_sp3l_dl
PC1_6x18_sp3m_dl
PC1_6x18_sp3s_dl
PC1_6x6_sp3l_dl
PC1_6x6_sp3m_dl
PC1_6x6_sp3s_dl
CIP2_6x18_sp3l_dl
CIP2_6x18_sp3m_dl
CIP2_6x18_sp3s_dl
CIP2_7x7_sp3l_dl
CIP2_7x7_sp3m_dl
CIP2_7x7_sp3s_dl
CIP5_6x18_sp3l_dl
CIP5_6x18_sp3m_dl
CIP5_6x18_sp3s_dl
CIP5_8x8_sp3l_dl
CIP5_8x8_sp3m_dl
CIP5_8x8_sp3s_dl
Page 40
E-40
Figure E.3.2: Ratio of Live Load Stresses in Curved Bridge Relative to Straight Bridge
All Single Span fr/fs Live Load Total
1
1.02
1.04
1.06
1.08
1.1
1.12
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
fr/fs
CIP1_6x18_sp1m_llt
CIP1_6x18_sp1s_llt
PC1_6x18_sp1m__llt
PC1_6x18_sp1s_llt
CIP2_6x18_sp1m_llt
CIP2_6x18_sp1s_llt
CIP5_6x18_sp1m_llt
CIP5_6x18_sp1s_llt
All 3-Span fr/fs Live Load Total
1
1.05
1.1
1.15
1.2
1.25
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Length/Radius (L/R)
fr/fs
CIP1_6x18_sp3l_lltCIP1_6x18_sp3m_lltCIP1_6x18_sp3s_lltCIP1_6x6_sp3l_lltCIP1_6x6_sp3m_lltCIP1_6x6_sp3s_lltPC1_6x18_sp3l_lltPC1_6x18_sp3m_lltPC1_6x18_sp3s_lltPC1_6x6_sp3l_lltPC1_6x6_sp3m_lltPC1_6x6_sp3s_lltCIP2_6x18_sp3l_lltCIP2_6x18_sp3m_lltCIP2_6x18_sp3s_lltCIP2_7x7_sp3l_lltCIP2_7x7_sp3m_lltCIP2_7x7_sp3s_lltCIP5_6x18_sp3l_lltCIP5_6x18_sp3m_lltCIP5_6x18_sp3s_lltCIP5_8x8_sp3l_lltCIP5_8x8_sp3m_lltCIP5_8x8_sp3s_llt
Page 41
E-41
Figure E.3.3: Ratio of Post-Tensioning Stresses in Curved Bridge Relative to Straight Bridge
All Single Span fr/fs Post Tension Total Load
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
fr/fs
CIP1_6x18_sp1m_ptt
CIP1_6x18_sp1s_ptt
PC1_6x18_sp1m_ptt
PC1_6x18_sp1s_ptt
CIP2_6x18_sp1m_ptt
CIP2_6x18_sp1s_ptt
CIP5_6x18_sp1m_ptt
CIP5_6x18_sp1s_ptt
All 3-Span fr/fs Post Tension Total Load
0.9
0.95
1
1.05
1.1
1.15
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Length/Radius (L/R)
fr/fs
CIP1_6x18_sp3l_pttCIP1_6x18_sp3m_pttCIP1_6x18_sp3s_pttCIP1_6x6_sp3l_pttCIP1_6x6_sp3m_pttCIP1_6x6_sp3s_pttPC1_6x18_sp3l_pttPC1_6x18_sp3m_pttPC1_6x18_sp3s_pttPC1_6x6_sp3l_pttPC1_6x6_sp3m_pttPC1_6x6_sp3s_pttCIP2_6x18_sp3l_pttCIP2_6x18_sp3m_pttCIP2_6x18_sp3s_pttCIP2_7x7_sp3l_pttCIP2_7x7_sp3m_pttCIP2_7x7_sp3s_pttCIP5_6x18_sp3l_pttCIP5_6x18_sp3m_pttCIP5_6x18_sp3s_pttCIP5_8x8_sp3l_pttCIP5_8x8_sp3m_pttCIP5_8x8_sp3s_ptt
Page 42
E-42
Figure E.3.4: Ratio of Dead Load Stresses in Curved Line Model Relative to Grillage Model
All Single Span fline/fgrid Dead Load
0.95
0.96
0.97
0.98
0.99
1
1.01
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Length/Radius (L/R)
fline
/fgrid
CIP1_6x18_sp1m_dl
CIP1_6x18_sp1s_dl
PC1_6x18_sp1m_dl
PC1_6x18_sp1s_dl
CIP2_6x18_sp1m_dl
CIP2_6x18_sp1s_dl
CIP5_6x18_sp1m_dl
CIP5_6x18_sp1s_dl
All 3-Span fline/fgrid Dead Load
0.94
0.95
0.96
0.97
0.98
0.99
1
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60
Length/Radius (L/R)
fline
/fgri
d
CIP1_6x18_sp3l_dlCIP1_6x18_sp3m_dlCIP1_6x18_sp3s_dlCIP1_6x6_sp3l_dlCIP1_6x6_sp3m_dlCIP1_6x6_sp3s_dlPC1_6x18_sp3l_dlPC1_6x18_sp3m_dlPC1_6x18_sp3s_dlPC1_6x6_sp3l_dlPC1_6x6_sp3m_dlPC1_6x6_sp3s_dlCIP2_6x18_sp3l_dlCIP2_6x18_sp3m_dlCIP2_6x18_sp3s_dlCIP2_7x7_sp3l_dlCIP2_7x7_sp3m_dlCIP2_7x7_sp3s_dlCIP5_6x18_sp3l_dlCIP5_6x18_sp3m_dlCIP5_6x18_sp3s_dlCIP5_8x8_sp3l_dlCIP5_8x8_sp3m_dlCIP5_8x8_sp3s_dl
Page 43
E-43
Figure E.3.5: Ratio of Live Load Stresses in Curved Line Model Relative to Grillage Model
All Single Span fline/fgrid Live Load Total
0.96
0.965
0.97
0.975
0.98
0.985
0.99
0.995
1
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Length/Radius (L/R)
fline
/f gri
d
CIP1_6x18_sp1m_llt
CIP1_6x18_sp1s_llt
PC1_6x18_sp1m_llt
PC1_6x18_sp1s_llt
CIP2_6x18_sp1m_llt
CIP2_6x18_sp1s_llt
CIP5_6x18_sp1m_llt
CIP5_6x18_sp1s_llt
All 3-Span fline/fgrid Live Load Total
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
0.00 0.50 1.00 1.50 2.00Length/Radius (L/R)
f line
/f gri
d
CIP1_6x18_sp3l_lltCIP1_6x18_sp3m_lltCIP1_6x18_sp3s_lltCIP1_6x6_sp3l_lltCIP1_6x6_sp3m_lltCIP1_6x6_sp3s_lltPC1_6x18_sp3l_lltPC1_6x18_sp3m_lltPC1_6x18_sp3s_lltPC1_6x6_sp3l_lltPC1_6x6_sp3m_lltPC1_6x6_sp3s_lltCIP2_6x18_sp3l_lltCIP2_6x18_sp3m_lltCIP2_6x18_sp3s_lltCIP2_7x7_sp3l_lltCIP2_7x7_sp3m_lltCIP2_7x7_sp3s_lltCIP5_6x18_sp3l_lltCIP5_6x18_sp3m_lltCIP5_6x18_sp3s_lltCIP5_8x8_sp3l_lltCIP5_8x8_sp3m_lltCIP5_8x8_sp3s_llt
Page 44
E-44
Figure E.3.6: Ratio of Post-Tensioning Stresses in Curved Line Model Relative to Grillage Model
All Single-Span fline/fgrid Post Tension Total
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Length/Radius (L/R)
fline
/f gri
d
CIP1_6x18_sp1m_ptt
CIP1_6x18_sp1s_ptt
PC1_6x18_sp1m_ptt
PC1_6x18_sp1s_ptt
CIP2_6x18_sp1m_ptt
CIP2_6x18_sp1s_ptt
CIP5_6x18_sp1m_ptt
CIP5_6x18_sp1s_ptt
All 3-Span fline/fgrid Post Tension Total
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
0.00 0.50 1.00 1.50 2.00
Length/Radius (L/R)
fline
/f gri
d
CIP1_6x18_sp3l_pttCIP1_6x18_sp3m_pttCIP1_6x18_sp3s_pttCIP1_6x6_sp3l_pttCIP1_6x6_sp3m_pttCIP1_6x6_sp3s_pttPC1_6x18_sp3l_pttPC1_6x18_sp3m_pttPC1_6x18_sp3s_pttPC1_6x6_sp3l_pttPC1_6x6_sp3m_pttPC1_6x6_sp3s_pttCIP2_6x18_sp3l_pttCIP2_6x18_sp3m_pttCIP2_6x18_sp3s_pttCIP2_7x7_sp3l_pttCIP2_7x7_sp3m_pttCIP2_7x7_sp3s_pttCIP5_6x18_sp3l_pttCIP5_6x18_sp3m_pttCIP5_6x18_sp3s_pttCIP5_8x8_sp3l_pttCIP5_8x8_sp3m_pttCIP5_8x8_sp3s_ptt
Page 45
E-45
Figure E.3.7: Ratio of Dead Load Shear in Curved Bridge Relative to Straight Bridge
All Single-Span Vr/Vs Dead Load
1
1.2
1.4
1.6
1.8
2
2.2
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
Vr/V
s
CIP1_6x18_sp1m_dl
CIP1_6x18_sp1s_dl
PC1_6x18_sp1m_dl
PC1_6x18_sp1s_dl
CIP2_6x18_sp1m_dl
CIP2_6x18_sp1s_dl
CIP5_6x18_sp1m_dl
CIP5_6x18_sp1s_dl
All 3-Span Vr/Vs Dead Load
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
0 0.5 1 1.5 2
Length/Radius (L/R)
Vr/V
s
CIP1_6x18_sp3l_dlCIP1_6x18_sp3m_dlCIP1_6x18_sp3s_dlCIP1_6x6_sp3l_dlCIP1_6x6_sp3m_dlCIP1_6x6_sp3s_dlPC1_6x18_sp3l_dlPC1_6x18_sp3m_dlPC1_6x18_sp3s_dlPC1_6x6_sp3l_dlPC1_6x6_sp3m_dlPC1_6x6_sp3s_dlCIP2_6x18_sp3l_dlCIP2_6x18_sp3m_dlCIP2_6x18_sp3s_dlCIP2_7x7_sp3l_dlCIP2_7x7_sp3m_dlCIP2_7x7_sp3s_dlCIP5_6x18_sp3l_dlCIP5_6x18_sp3m_dlCIP5_6x18_sp3s_dlCIP5_8x8_sp3l_dlCIP5_8x8_sp3m_dlCIP5_8x8_sp3s_dl
Page 46
E-46
Figure E.3.8: Ratio of Live Load Shear in Curved Bridge Relative to Straight Bridge
All Single-Span Vr/Vs Live Load Total
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
Vr/V
s
CIP1_6x18_sp1m_llt
CIP1_6x18_sp1s_llt
PC1_6x18_sp1m_llt
PC1_6x18_sp1s_llt
CIP2_6x18_sp1m_llt
CIP2_6x18_sp1s_llt
CIP5_6x18_sp1m_llt
CIP5_6x18_sp1s_llt
All 3-Span Vr/Vs Live Load Total
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.5 1 1.5 2
Length/Radius (L/R)
Vr/V
s
CIP1_6x18_sp3l_lltCIP1_6x18_sp3m_lltCIP1_6x18_sp3s_lltCIP1_6x6_sp3l_lltCIP1_6x6_sp3m_lltCIP1_6x6_sp3s_lltPC1_6x18_sp3l_lltPC1_6x18_sp3m_lltPC1_6x18_sp3s_lltPC1_6x6_sp3l_lltPC1_6x6_sp3m_lltPC1_6x6_sp3s_lltCIP2_6x18_sp3l_lltCIP2_6x18_sp3m_lltCIP2_6x18_sp3s_lltCIP2_7x7_sp3l_lltCIP2_7x7_sp3m_lltCIP2_7x7_sp3s_lltCIP5_6x18_sp3l_lltCIP5_6x18_sp3m_lltCIP5_6x18_sp3s_lltCIP5_8x8_sp3l_lltCIP5_8x8_sp3m_lltCIP5_8x8_sp3s_llt
Page 47
E-47
Figure E.3.9: Ratio of Post-Tensioning Shear in Curved Bridge Relative to Straight Bridge
All Single-Span Vr/Vs Post Tension Load Total
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
Vr/V
s
CIP1_6x18_sp1m_llt
CIP1_6x18_sp1s_llt
PC1_6x18_sp1m_llt
PC1_6x18_sp1s_llt
CIP2_6x18_sp1m_llt
CIP2_6x18_sp1s_llt
CIP5_6x18_sp1m_llt
CIP5_6x18_sp1s_llt
All 3-Span Vr/Vs Post Tension Load Total
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2
Length/Radius (L/R)
Vr/V
s
CIP1_6x18_sp3l_lltCIP1_6x18_sp3m_lltCIP1_6x18_sp3s_lltCIP1_6x6_sp3l_lltCIP1_6x6_sp3m_lltCIP1_6x6_sp3s_lltPC1_6x18_sp3l_lltPC1_6x18_sp3m_lltPC1_6x18_sp3s_lltPC1_6x6_sp3l_lltPC1_6x6_sp3m_lltPC1_6x6_sp3s_lltCIP2_6x18_sp3l_lltCIP2_6x18_sp3m_lltCIP2_6x18_sp3s_lltCIP2_7x7_sp3l_lltCIP2_7x7_sp3m_lltCIP2_7x7_sp3s_lltCIP5_6x18_sp3l_lltCIP5_6x18_sp3m_lltCIP5_6x18_sp3s_lltCIP5_8x8_sp3l_lltCIP5_8x8_sp3m_lltCIP5_8x8_sp3s_llt
Page 48
E-48
Figure E.3.10: Ratio of Dead Load Shear in Curved Line Model Relative to Grillage Model
All Single-Span Vline/Vgrid Dead Load Total
0.9
0.95
1
1.05
1.1
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
Vlin
e/Vg
rid
CIP1_6x18_sp1m_dl
CIP1_6x18_sp1s_dl
PC1_6x18_sp1m_dl
PC1_6x18_sp1s_dl
CIP2_6x18_sp1m_dl
CIP2_6x18_sp1s_dl
CIP5_6x18_sp1m_dl
CIP5_6x18_sp1s_dl
All 3-Span Vline/Vgrid Dead Load Total
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
0 0.5 1 1.5 2
Length/Radius (L/R)
Vlin
e/Vg
rid
CIP1_6x18_sp3l_dlCIP1_6x18_sp3m_dlCIP1_6x18_sp3s_dlCIP1_6x6_sp3l_dlCIP1_6x6_sp3m_dlCIP1_6x6_sp3s_dlPC1_6x18_sp3l_dlPC1_6x18_sp3m_dlPC1_6x18_sp3s_dlPC1_6x6_sp3l_dlPC1_6x6_sp3m_dlPC1_6x6_sp3s_dlCIP2_6x18_sp3l_dlCIP2_6x18_sp3m_dlCIP2_6x18_sp3s_dlCIP2_7x7_sp3l_dlCIP2_7x7_sp3m_dlCIP2_7x7_sp3s_dlCIP5_6x18_sp3l_dlCIP5_6x18_sp3m_dlCIP5_6x18_sp3s_dlCIP5_8x8_sp3l_dlCIP5_8x8_sp3m_dlCIP5_8x8_sp3s_dl
Page 49
E-49
Figure E.3.11: Ratio of Live Load Shear in Curved Line Model Relative to Grillage Model
All Single-Span Vline/Vgrid Live Load Total
0.9
0.95
1
1.05
1.1
1.15
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
Vlin
e/Vg
rid
CIP1_6x18_sp1m_dl
CIP1_6x18_sp1s_dl
PC1_6x18_sp1m_dl
PC1_6x18_sp1s_dl
CIP2_6x18_sp1m_dl
CIP2_6x18_sp1s_dl
CIP5_6x18_sp1m_dl
CIP5_6x18_sp1s_dl
All 3-Span Vline/Vgrid Live Load Total
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Length/Radius (L/R)
Vlin
e/V
grid
CIP1_6x18_sp3l_dlCIP1_6x18_sp3m_dlCIP1_6x18_sp3s_dlCIP1_6x6_sp3l_dlCIP1_6x6_sp3m_dlCIP1_6x6_sp3s_dlPC1_6x18_sp3l_dlPC1_6x18_sp3m_dlPC1_6x18_sp3s_dlPC1_6x6_sp3l_dlPC1_6x6_sp3m_dlPC1_6x6_sp3s_dlCIP2_6x18_sp3l_dlCIP2_6x18_sp3m_dlCIP2_6x18_sp3s_dlCIP2_7x7_sp3l_dlCIP2_7x7_sp3m_dlCIP2_7x7_sp3s_dlCIP5_6x18_sp3l_dlCIP5_6x18_sp3m_dlCIP5_6x18_sp3s_dlCIP5_8x8_sp3l_dlCIP5_8x8_sp3m_dlCIP5_8x8_sp3s_dl
Page 50
E-50
Figure E.3.12: Ratio of Post-Tensioning Shear in Curved Line Model Relative to Grillage Model
All Single-Span Vline/Vgrid Post Tension Load Total
11.021.041.061.08
1.11.121.141.161.18
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Length/Radius (L/R)
Vlin
e/Vg
rid
CIP1_6x18_sp1m_dl
CIP1_6x18_sp1s_dl
PC1_6x18_sp1m_dl
PC1_6x18_sp1s_dl
CIP2_6x18_sp1m_dl
CIP2_6x18_sp1s_dl
CIP5_6x18_sp1m_dl
CIP5_6x18_sp1s_dl
All 3-Span Vline/Vgrid Post Tension Load Total
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2
Length/Radius (L/R)
Vlin
e/Vg
rid
CIP1_6x18_sp3l_dlCIP1_6x18_sp3m_dlCIP1_6x18_sp3s_dlCIP1_6x6_sp3l_dlCIP1_6x6_sp3m_dlCIP1_6x6_sp3s_dlPC1_6x18_sp3l_dlPC1_6x18_sp3m_dlPC1_6x18_sp3s_dlPC1_6x6_sp3l_dlPC1_6x6_sp3m_dlPC1_6x6_sp3s_dlCIP2_6x18_sp3l_dlCIP2_6x18_sp3m_dlCIP2_6x18_sp3s_dlCIP2_7x7_sp3l_dlCIP2_7x7_sp3m_dlCIP2_7x7_sp3s_dlCIP5_6x18_sp3l_dlCIP5_6x18_sp3m_dlCIP5_6x18_sp3s_dlCIP5_8x8_sp3l_dlCIP5_8x8_sp3m_dlCIP5_8x8_sp3s_dl
Page 51
E-51
Figure E.4.1: Five Cell, Cast In Place, Diaphragm Analysis: Self Weight
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0-0.5 -0.4 -0.3 -0.2 -0.1 0
Gri
llage
With
Dia
phra
gm
Grillage
Mid-span Def lections
-0.008
-0.007
-0.006
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.008 -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0
Gril
lage
With
Dia
phra
gm
Grillage
Mid-span Rotations
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-4000 -3000 -2000 -1000 0
Gril
lage
With
Dia
phra
gm
Grillage
Abutment Shear
-120000
-100000
-80000
-60000
-40000
-20000
0-120000 -100000 -80000 -60000 -40000 -20000 0
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Moment
-6000
-5000
-4000
-3000
-2000
-1000
0-6000 -5000 -4000 -3000 -2000 -1000 0
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Torsion
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0-20000 -15000 -10000 -5000 0
Gril
lage
With
Dia
phra
gm
Grillage
Midspan Transverse Moment
0
100
200
300
400
500
600
700
8000 200 400 600 800
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0-2.5 -2 -1.5 -1 -0.5 0
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Outside Corner Stress (ksi)
Page 52
E-52
Figure E.4.2: Five Cell, Cast In Place, Diaphragm: Live Load Total
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0
Gri
llage
With
Dia
phra
gm
Grillage
Mid-span Def lections
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0
Gri
llage
With
Dia
phra
gm
Grillage
Mid-span Rotations
-200
-180
-160
-140
-120
-100
-80
-60
-40
-20
0-200 -150 -100 -50 0
Gril
lage
With
Dia
phra
gm
Grillage
Abutment Shear
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0-20000 -15000 -10000 -5000 0
Gril
lage
With
Dia
phra
gm
Grillage
Midspan Moment
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Torsion
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-4000 -3000 -2000 -1000 0
Gril
lage
With
Dia
phra
gm
Grillage
Midspan Transverse Moment
0
20
40
60
80
100
120
1400 20 40 60 80 100 120 140
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Axial Force
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0-0.5 -0.4 -0.3 -0.2 -0.1 0
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Outside Corner Stress (ksi)
Page 53
E-53
Figure E.4.3: Five Cell, Cast In Place, Diaphragm: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Gri
llage
With
Dia
phra
gm
Grillage
Mid-span Def lections
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002-0.002 -0.001 0 0.001 0.002
Gri
llage
With
Dia
phra
gm
Grillage
Mid-span Rotations
0
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000
Gril
lage
With
Dia
phra
gm
Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1000000 20000 40000 60000 80000 100000
Gri
llage
With
Dia
phra
gm
Grillage
Midspan Moment
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gir
der M
odel
Grillage
Midspan Torsion
-5000
0
5000
10000
15000
-5000 0 5000 10000 15000
Sing
le G
irder
Mod
el
Grillage
Midspan Transverse Moment
0
5000
10000
15000
20000
25000
300000 5000 10000 15000 20000 25000 30000
Sin
gle
Gir
der M
odel
Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Sing
le G
irder
Mod
el
Grillage
Midspan Outside Corner Stress (ksi)
Page 55
E-55
Figure E.5.1: Five Cell, Cast In Place, Diaphragm: Self Weight
SW_CIP5_Diaphragm
0.9965
0.997
0.9975
0.998
0.9985
0.999
0.9995
1
1.0005
1.001
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.997
0.9975
0.998
0.9985
0.999
0.9995
1
1.0005
1.001
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.9988
0.999
0.9992
0.9994
0.9996
0.9998
1
1.0002
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.9990.99910.99920.99930.99940.99950.99960.99970.99980.9999
11.0001
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Figure E.5.2: Five Cell, Cast In Place, Diaphragm: Live Load Total
0.994
0.995
0.996
0.997
0.998
0.999
1
1.001
1.002
0 1 2 3 4 5 6 7
With
/With
out D
iaph
ragm
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.9940.9950.9960.9970.9980.999
11.0011.0021.003
0 1 2 3 4 5 6 7
With
/With
out D
iaph
ragm
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.997
0.9975
0.998
0.9985
0.999
0.9995
1
1.0005
0 1 2 3 4 5 6 7
With
/With
out D
iaph
ragm
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0.9975
0.998
0.9985
0.999
0.9995
1
1.0005
0 1 2 3 4 5 6 7
With
/With
out D
iaph
ragm
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 56
E-56
Figure E.5.3: Five Cell, Cast In Place, Diaphragm: Post Tension Total
0.996
0.998
1
1.002
1.004
1.006
1.008
1.01
1.012
1.014
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.988
0.99
0.992
0.994
0.996
0.998
1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.998
0.9985
0.999
0.9995
1
1.0005
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.998
0.9985
0.999
0.9995
1
1.0005
1.001
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 57
E-57
Figure E.6.1: Five Cell, Cast In Place, Grid Model Hinge: Self Weight
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Sin
gle
Gird
er M
odel
Grillage
Mid-span Def lections
-0.005
-0.004
-0.003
-0.002
-0.001
0-0.005 -0.004 -0.003 -0.002 -0.001 0
Sing
le G
irde
r Mod
el
Grillage
Mid-span Rotations
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000-4000 -3000 -2000 -1000 0 1000
Sin
gle
Gird
er M
odel
Grillage
Abutment Shear
-120000
-100000
-80000
-60000
-40000
-20000
0-120000 -100000 -80000 -60000 -40000 -20000 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Moment
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
-7000 -6000 -5000 -4000 -3000 -2000 -1000 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Torsion
-20000
-15000
-10000
-5000
0
-20000 -15000 -10000 -5000 0
Sing
le G
irde
r Mod
el
Grillage
Midspan Transverse Moment
-200
-100
0
100
200
300
400
500
600
700
800
-200 0 200 400 600 800
Sin
gle
Gird
er M
odel
Grillage
Midspan Axial Force
-2.5
-2
-1.5
-1
-0.5
0
-2.5 -2 -1.5 -1 -0.5 0
Sin
gle
Gird
er M
odel
Grillage
Midspan Outside Corner Stress (ksi)
Page 58
E-58
Figure E.6.2: Five Cell, Cast In Place, Grid Model Hinge: Live Load Total
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0-0.08 -0.06 -0.04 -0.02 0
Gril
lage
With
Hin
ge
Grillage
Mid-span Def lections
-0.0006
-0.0005
-0.0004
-0.0003
-0.0002
-0.0001
0-0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0
Gril
lage
With
Hin
ge
Grillage
Mid-span Rotations
-200
-180
-160
-140
-120
-100
-80
-60
-40
-20
0-200 -150 -100 -50 0
Gril
lage
With
Hin
ge
Grillage
Abutment Shear
-20000
-18000
-16000
-14000
-12000
-10000
-8000
-6000
-4000
-2000
0-20000 -15000 -10000 -5000 0
Gril
lage
With
Hin
ge
Grillage
Midspan Moment
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0-2000 -1500 -1000 -500 0
Gri
llage
With
Hin
ge
Grillage
Midspan Torsion
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
-3500 -2500 -1500 -500
Gril
lage
With
Hin
ge
Grillage
Midspan Transverse Moment
-0.00003
19.99996
39.99996
59.99996
79.99996
99.99996
119.9999
139.9999
0.00003 50.00003 100.0000
Gril
lage
WIth
Hin
ge
Grillage
Midspan Axial Force
-0.5
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0-0.5 -0.4 -0.3 -0.2 -0.1 0
Gril
lage
With
Hin
ge
Grillage
Midspan Outside Corner Stress (ksi)
Page 59
E-59
Figure E.6.3: Five Cell, Cast In Place, Grid Model Hinge: Post Tension Total
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.40 0.1 0.2 0.3 0.4
Gril
lage
With
Hin
ge
Grillage
Mid-span Def lections
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002-0.002 -0.001 0 0.001 0.002
Gri
llage
With
HIn
ge
Grillage
Mid-span Rotations
0
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000
Gril
lage
With
Hin
ge
Grillage
Abutment Shear
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 20000 40000 60000 80000 100000
Gril
lage
With
HIn
ge
Grillage
Midspan Moment
-5000
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0-5000 -4000 -3000 -2000 -1000 0
Gril
lage
WIth
Hin
ge
Grillage
Midspan Torsion
-2000
0
2000
4000
6000
8000
10000
12000
14000
16000-2000 3000 8000 13000
Gril
lage
With
HIn
ge
Grillage
Midspan Transverse Moment
0
5000
10000
15000
20000
25000
300000 5000 10000 15000 20000 25000 30000
Gri
llage
With
Hin
ge
Grillage
Midspan Axial Force
0
0.5
1
1.5
2
2.5
3
3.50 0.5 1 1.5 2 2.5 3 3.5
Gril
alge
With
Hin
ge
Grillage
Midspan Outside Corner Stress (ksi)
Page 61
E-61
Figure E.7.1: Five Cell, Cast In Place, Grid Model Hinge: Self Weight
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S 0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Figure E.7.2: Five Cell, Cast In Place, Grid Model Hinge: Live Load Total
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 62
E-62
Figure E.7.3: Five Cell, Cast In Place, Grid Model Hinge: Post Tension Total
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Inside Corner Stress (ksi)
St_I Sp1_M Sp1_SSp3_L Sp3_M Sp3_S0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Corner Stress (ksi)
St_O Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.99
1
1.01
1.02
1.03
1.04
1.05
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Outside Shear (kips)
V_Out Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
0 1 2 3 4 5 6 7
Cur
ve/G
rid
Radius (ft)
Midspan Deflection (in)
Defl Sp1_M Sp1_SSp3_L Sp3_M Sp3_S
Page 63
E-63
Table E1: Straight DL 200 ft/Single Span - Skew Shear
Results Obtuse (Element 1) Acute (Element 21) Value Ratio Value Ratio Radial -389.35 1.00 -387.84 1.00 Skew-Left -605.00 1.55 -190.65 0.49 Skew-Both -392.94 1.01 -342.23 0.88
Table E2: Straight LL 200 ft/Single Span - Skew Shear
Results Obtuse (Element 1) Acute Value Ratio Value Ratio Radial -47.80 1.00 -47.53 1.00 Skew-Left -85.66 1.79 -10.05 0.21 Skew-Both -48.20 1.01 -35.44 0.75
Table E3: DL - 400 ft Radius, 200 ft Single Span - Skew Shear
Results Obtuse (Element 1) Acute Value Ratio Value Ratio Radial -577.89 1.00 -189.78 1.00 Skew-Left -782.91 1.35 -58.28 0.31 Skew-Both -614.14 1.06 -183.66 0.97
Table E4: LL - 400 ft Radius, 200 ft Single Span - Skew Shear
Results
Obtuse (Element 1) Acute Value Ratio Value Ratio Radial -81.62 1.00 -12.01 1.00 Skew-Left -116.15 1.42 12.53 -1.04 Skew-Both -85.08 1.04 -9.13 0.76
Table E5: DL - Straight, 200/300/200 ft Multi Span - Skew Shear
Results Obtuse (Element 1) Acute Value Ratio Value Ratio Radial -297.35 1.00 -296.59 1.00 Skew-Left -378.79 1.27 -197.35 0.67 Skew-Both -378.02 1.27 -197.66 0.67
Table E6: DL-400 ft R, 200/300/200 ft Multi Span - Skew Shear
Results Obtuse (Element 1) Acute Value Ratio Value Ratio Radial -370.00 1.00 -202.20 1.00 Skew-Left -452.84 1.22 -135.81 0.67 Skew-Both -453.89 1.23 -135.81 0.67
