APPENDIX L – PARAMETER STUDIES

APPENDIX L – PARAMETER STUDIES

L-1

Slab on Prestressed Concrete I Girders The following is a summary of the procedures and results for various models using both

SAP2000 and ANSYS 6.1. For this study, only fatigue loading was considered. Each model was

analyzed with and without support diaphragms and skew angles of 0, 30, and 60 degrees were used.

Two models were further investigated with the placement of intermediate diaphragms at quarter points

and then at midspan.

Description of Bridge. The following bridge is #24 in the TTU Bridge Database.

4'-6" 10'-6" 10'-6" 10'-6" 10'-6" 4'-6"

1'-9" 47'-6" 1'-9"

Figure L-1 - Typical Cross Section

75' 75' 75' 75' 75'

4'-6"10'-6"

10'-6"

10'-6"

10'-6"

4'-6"1

6

11

16

21

2

7

12

17

22

3

8

13

18

23

4

9

14

19

24

5

10

15

20

25

Figure L-2 - Plan View

L-2

Acute CornerObtuse Corner

1

6

θ

Figure L-3 – Plan View (Skewed)

Diaphragms Placed at Midspan Diaphragms Placed at Quarter Points


θ


θ

Figure L-4 – Diaphragm Locations

12' 5'-2"

Lane 1 Shoulder

4'-6"10'-6"10'-6"

6' 2'

3'

4'

5'

6'

7'

8'

9'2'-2"

BridgeCL

MOVE1

MOVE2

MOVE3

MOVE4

MOVE5

MOVE6

MOVE7

MOVE8

Figure L-5 - Loading Locations

L-3

Table L-1 – Section Properties

Area J I33 I22 AS2 AS3AASHTO Type III Beam 560 17652 125390 12217 536 327Interior Beam (Composite) 1833 55550 542833 1474557 1225 616Exterior Beam (Composite) 1754 53545 531263 1192425 1154 613End/Support Diaphragm 810 65482 136688 21870 675 675Int. Dia. 1: 25% of TYPE III 560 4412.973 31347.59 3054.14 0 0Int. Dia. 2: 50% of TYPE III 560 8825.945 62695.18 6108.28 0 0Int. Dia. 3: 75% of TYPE III 560 13238.92 94042.76 9162.42 0 0Int. Dia. 4: 100% of TYPE III 560 17652 125390 12217 0 0

Section Properties

Description of Models:

SAP2000:

Each beam section was created in SAP’s Section Designer. Each section consisted of an

AASHTO Type III beam and the appropriate portion of deck slab. In the grillage models, the rigidity of

the transverse grillage members was not adjusted. Subsequent runs may need to be performed while

varying the stiffness of these members.

The shell models consisted of the same sections as the grillage models. Shell elements were

used to connect each beam section. The moment and shear contribution of the shell elements was

neglected.

All elements were connected at their centroids.

ANSYS:

To compare the ANSYS models to the SAP models, the beam elements had to be offset from the

shell elements. This allowed the beam and slab to act as a composite member.

L-4

Vehicle Definition:

The following figure has been taken from SAP. The standard HS20-44 vehicle was converted to

a general vehicle in order to make the necessary changes. The standard vehicle uses a 10 ft axle width

with a fixed width line. The axle width has been changed to 6 ft with two points for the axle width type.

Figure L-6 – SAP Vehicle Definition

Point loads that represented the wheel loads of HS20 truck were used for all ANSYS models.

The initial location of the vehicle was based on SAP results. Several load cases were analyzed to

determine the location of the maximum response. For the controlling load case, point loads that were to

lie within a shell element were distributed to the four nodes that made up the element.

Approximate Modeling and Run Times for each Model:

The run times for the various structure models are presented in Table L-2 and Table L-1. Models

15, 16, 21, and 22 from the tables below have not been completed. Results from these models can be

made available if necessary.

L-5

Table L-2 – Model Run Times for SAP

SAP2000

Skew Support Diaphragm

Intermediate Diaphragm Load Case Lane Definition

1 24-gm-s0-wd-le 0 YES NO MOVE1-8 Lane Eccentricity 1 hr 15 min 1 hr 5 min2 24-gm-s0-wd-fm 0 YES NO MOVE1-8 Flexible Members 1 hr 30 min 3 hr3 24-gm-s0-wod-le 0 NO NO MOVE1-8 Lane Eccentricity 10 min 1 hr 20 min4 24-gm-s0-wod-fm 0 NO NO MOVE1-8 Flexible Members 10 min 3 hr5 24-gm-s30-wd-fm 30 YES NO MOVE1-8 Flexible Members 1 hr 3 hr 40 min6 24-gm-s30-wod-fm 30 NO NO MOVE1-8 Flexible Members 10 min 3 hr 30 min7 24-gm-s60-wd-fm 60 YES NO MOVE1-8 Flexible Members 1 hr 3 hr 45 min8 24-gm-s60-wod-fm 60 NO NO MOVE1-8 Flexible Members 10 min 3 hr 30 min9 24-sm-s0-wd-le 0 YES NO MOVE1-8 Lane Eccentricity 1 hr 6 hr 30 min10 24-sm-s0-wd-fm 0 YES NO MOVE1-8 Flexible Members 1 hr 45 min 5 hr 30 min**11 24-sm-s0-wod-le 0 NO NO MOVE1-8 Lane Eccentricity 10 min 6 hr 40 min12 24-sm-s0-wod-fm 0 NO NO MOVE1-8 Flexible Members 10 min 7 hr 40 min**13 24-sm-s30-wd-fm 30 YES NO MOVE1-8 Flexible Members 2 hr 7 hr**14 24-sm-s30-wod-fm 30 NO NO MOVE1-8 Flexible Members 10 min 6 hr**15 24-sm-s60-wd-fm 60 YES NO MOVE1-8 Flexible Members - -16 24-sm-s60-wod-fm 60 NO NO MOVE1-8 Flexible Members - -23 24-gm-s0-wd-fm (with 25% inter dia @ 0.25 pts) 0 YES 1/4 Points MOVE1-8 Flexible Members 30 min 4 hr24 24-gm-s0-wd-fm (with 50% inter dia @ 0.25 pts) 0 YES 1/4 Points MOVE1-8 Flexible Members < 5 min 4 hr25 24-gm-s0-wd-fm (with 75% inter dia @ 0.25 pts) 0 YES 1/4 Points MOVE1-8 Flexible Members < 5 min 4 hr26 24-gm-s0-wd-fm (with 100% inter dia @ 0.25 pts) 0 YES 1/4 Points MOVE1-8 Flexible Members < 5 min 4 hr27 24-gm-s0-wd-fm (with 25% midspan dia) 0 YES Midspan MOVE1-8 Flexible Members 20 min 3 hr 30 min28 24-gm-s0-wd-fm (with 50% midspan dia) 0 YES Midspan MOVE1-8 Flexible Members < 5 min 3 hr 15 min29 24-gm-s0-wd-fm (with 75% midspan dia) 0 YES Midspan MOVE1-8 Flexible Members < 5 min 3 hr 25 min30 24-gm-s0-wd-fm (with 100% midspan dia) 0 YES Midspan MOVE1-8 Flexible Members < 5 min 3 hr 15 min31 24-gm-s30-wd-fm (with 25% inter dia @ 0.25 pts) 30 YES 1/4 Points MOVE1-8 Flexible Members 30 min 5 hr 32 24-gm-s30-wd-fm (with 50% inter dia @ 0.25 pts) 30 YES 1/4 Points MOVE1-8 Flexible Members < 5 min 4 hr 30 min33 24-gm-s30-wd-fm (with 75% inter dia @ 0.25 pts) 30 YES 1/4 Points MOVE1-8 Flexible Members < 5 min 5 hr34 24-gm-s30-wd-fm (with 100% inter dia @ 0.25 pts) 30 YES 1/4 Points MOVE1-8 Flexible Members < 5 min 4 hr 30 min35 24-gm-s30-wd-fm (with 25% midspan dia) 30 YES Midspan MOVE1-8 Flexible Members 20 min 4 hr 5 min36 24-gm-s30-wd-fm (with 50% midspan dia) 30 YES Midspan MOVE1-8 Flexible Members < 5 min 3 hr 50 min37 24-gm-s30-wd-fm (with 75% midspan dia) 30 YES Midspan MOVE1-8 Flexible Members < 5 min 3 hr38 24-gm-s30-wd-fm (with 100% midspan dia) 30 YES Midspan MOVE1-8 Flexible Members < 5 min 4 hr

* Includes loading

Model # Filename

** Reduced the number of shell elements

Approximate Run Time

ParametersApproximate

Modeling Time*

Model Type

Gril

lage

Shel

lG

rilla

ge

Table L-3 – Model Run Times for ANSYS

Moment Shear0 YES Max Span 1 1-8 20-27 3 hr < 5 min0 YES Max Span 2 9-16 28-35 2 hr < 5 min0 NO Max Span 1 1-8 20-27 30 min < 5 min0 NO Max Span 2 9-16 28-35 30 min < 5 min30 YES Max Span 1 1-8 20-27 3 hr 30 min < 5 min30 YES Max Span 2 9-16 28-35 2 hr < 5 min30 NO Max Span 1 1-8 20-27 30 min < 5 min30 NO Max Span 2 9-16 28-35 30 min < 5 min60 YES Max Span 1 1-8 20-27 - -60 YES Max Span 2 9-16 28-35 - -60 NO Max Span 1 1-8 20-27 - -60 NO Max Span 2 9-16 28-35 - -

* Includes loading

Approximate Run TimeFilenameModel # Load Case

Parameters

Load LocationSupport DiaphragmSkew

24-sm-s60-wd

24-sm-s60-wod

24-sm-s30-wod

24-sm-s0-wd

24-sm-s0-wod

24-sm-s30-wd

ANSYS 6.1

Approximate Modeling Time*

17

18

19

20

21

22

L-6

Program Comparison:

The results presented in Table L-4 and Table L-5 are based on models with no skew and support

diaphragms present. The ANSYS results for both moment and shear seemed to compare better to the

grillage models using flexible members to define the lane location. The results shown for the parametric

studies are based on the grillage models with flexible members.

Flexible members are frame elements with near-zero stiffness used to define a path for the live

load in SAP 2000. The other option for defining the live load path in SAP 2000 is to use the actual

frame elements (girder) as the path, and then enter and eccentricity to indicate if the live load does not

follow directly along the path of the frame elements. The flexible member method always uses an

eccentricity of zero. It is unclear how SAP 2000 applies the lane eccentricity method, therefore both

methods were investigated.

Table L-4 – SAP and ANSYS Results Comparisons, Flexure

Lane Eccentricity

Flexible Members

Lane Eccentricity

Flexible Members

1 558.21 560.36 547.92 528.83 548.222 469.74 471.40 459.26 441.24 455.321 522.34 512.73 510.01 483.02 505.332 437.89 428.50 425.41 399.97 417.691 486.47 464.13 472.11 437.32 457.882 406.61 384.75 391.56 358.90 375.541 450.61 415.51 434.20 392.61 411.662 375.34 341.03 357.71 318.83 334.601 317.35 367.78 314.63 349.37 366.842 250.85 298.24 247.77 280.75 295.031 289.57 321.96 287.21 308.38 325.032 226.90 257.27 224.27 244.50 258.411 261.79 278.96 259.80 270.11 286.522 202.96 219.24 200.77 210.84 224.951 234.01 239.74 232.39 235.57 250.092 179.01 185.04 177.27 180.45 193.50

MOVE6

MOVE7

MOVE8

Yes

MOVE2

MOVE3

MOVE4

MOVE5

SkewSAP2000

ANSYS

Maximum Moment

Grillage Shell

0

LoadBeamSupport Diaphragm

MOVE1

L-7

Table L-5 – SAP and ANSYS Results Comparison, Shear

Lane Eccentricity

Flexible Members

Lane Eccentricity

Flexible Members

1 57.49 45.12 53.77 42.81 44.292 56.52 43.36 52.86 41.32 43.401 55.25 40.02 50.63 37.27 40.482 54.32 38.35 49.76 35.70 38.711 53.00 34.69 47.49 31.95 35.452 52.13 33.11 46.67 30.24 33.981 50.76 29.31 44.35 27.09 30.682 49.93 27.82 43.58 25.17 29.301 18.68 24.05 16.65 22.45 25.992 16.68 22.66 14.65 20.55 24.711 16.53 19.09 14.86 18.30 21.512 14.55 17.78 12.92 16.40 20.331 14.46 15.43 13.09 14.89 17.402 12.47 13.74 11.22 12.93 16.301 12.46 12.76 11.36 12.40 13.542 10.50 10.83 9.55 10.37 12.52


0 Yes

MOVE1

MOVE2

MOVE3

MOVE4

Beam Load

MOVE5

MOVE6

Maximum ShearSAP2000

ANSYSGrillage Shell

MOVE7

MOVE8

L-8

2D Analysis Results:

maxM

75' 75' 75' 75' 75'

maxV

30'

k32 kk 832

14' - 30' 14'

Direction of Travel

of TravelDirection

14' - 30'14'

8k 32k k32

Figure L-7 - 2D Model with Maximum Response Location

Table L-6 - Beam Line Analysis Results

Location Reaction Shear Moment(ft) (kip) (kip) (kip-ft)0 60.82 60.82 -

30 - - 851.7675 66.20 -0 64.07 -

36 - - 688.2075 64.45 -0 64.31 -

36 & 39 - - 679.0875 64.31 -0 64.45 -

39 - - 688.2075 64.07 -0 66.20 -

45 - - 851.7675 60.82 60.82 -

70.59

69.78

69.78

70.59

5

Span

1

2

3

4

L-9

Parametric Study Results: MOMENT

Table L-7 – Flexural Results for Beam 1

Location from Barrier Load Moment DF Moment DF Moment DF Moment DF Moment DF Moment DF

2 MOVE1 560.36 0.658 544.23 0.639 467.92 0.549 573.52 0.673 564.32 0.663 520.00 0.6113 MOVE2 512.73 0.602 498.67 0.585 424.34 0.498 523.13 0.614 514.68 0.604 469.10 0.5514 MOVE3 464.13 0.545 452.03 0.531 381.42 0.448 471.93 0.554 464.18 0.545 417.43 0.4905 MOVE4 415.51 0.488 405.24 0.476 338.56 0.397 420.89 0.494 413.81 0.486 366.06 0.4306 MOVE5 367.78 0.432 359.26 0.422 298.08 0.350 370.93 0.435 364.49 0.428 316.08 0.3717 MOVE6 321.96 0.378 315.03 0.370 260.18 0.305 323.07 0.379 317.23 0.372 268.55 0.3158 MOVE7 278.96 0.328 274.02 0.322 224.49 0.264 278.23 0.327 273.27 0.321 226.09 0.2659 MOVE8 239.74 0.281 236.85 0.278 194.27 0.228 237.36 0.279 233.58 0.274 189.26 0.222

Without Support Diaphragm0 30 6030 60Skew

With Support Diaphragm0

Moment Values for Beam 1

Table L-8 – Flexural Results for Beam 6

Location from Barrier Load Moment DF Moment DF Moment DF Moment DF Moment DF Moment DF


30 60SkewWith Support Diaphragm

0

Moment Values for Beam 6Without Support Diaphragm

0 30 60

L-10

Effect of Skew Angle on Moment Distribution for Beam 1:

Skew Angle Effect on Moment Distribution for Beam 1 (MOVE1)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60

With Support Diaphragm Without Support Diaphragm


0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60


Figure L-8 - Effect of Skew Angle on Moment Distribution for Beam 1, Bridge #24

L-11



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0 10 20 30 40 50

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60


Figure L-9 - Effect of Skew Angle on Moment Distribution for Beam 6, Bridge #24

L-12

Effect of Vehicle Location on Moment Distribution for Beam 1:

Effect of Vehicle Location on Moment Distribution for Beam 1(60° Skew Angle)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

2 3 4 5 6 7 8 9

Vehicle Location (ft)

Dis

trib

utio

n Fa

ctor


Figure L-10 – 60 Degree Skew

Effect of Vehicle Location on Moment Distribution for Beam 1(With Support Diaphragm)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

0° Skew

30° Skew

60° Skew

Figure L-11 – No Skew, Support Diaphragm

L-13

Effect of Vehicle Location on Moment Distribution for Beam 1(Without Support Diaphragm)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

0° Skew

30° Skew

9

60° Skew

Figure L-12 – No Skew, No Support Diaphragm

Figure L-13, Figure L-14, and Figure L-15 show the effect of vehicle location on moment

distribution as the intermediate diaphragm stiffness is increased and location is varied. The original

properties of the diaphragm are based on an AASHTO Type III beam.

Effect of Vehicle Location on Moment Distribution for Beam 1 (0° Skew Angle with Support Diaphragms)

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9

Int. Dia. @ 1/4 pts (25%) Int. Dia. @ 1/4 pts. (50%) Int. Dia. @ 1/4 pts (75%) Int. Dia. @ 1/4 pts (100%)

Figure L-13 – Moment Distribution with Vehicle Location and Diaphragm Stiffness

L-14


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9

Int. Dia. @ Midspan (25%) Int. Dia. @ Midspan (50%) Int. Dia. @ Midspan (75%) Int. Dia. @ Midspan (100%)

Figure L-14 - Moment Distribution with Vehicle Location and Diaphragm Stiffness, No Support Diaphragms

Effect of Vehicle Location on Moment Distribution for Beam 1(30° Skew Angle with Support Diaphragms)

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor


Figure L-15 - Moment Distribution with Vehicle Location and Diaphragm Stiffness, 30 Degree Skew

L-15


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9


Figure L-16 - Moment Distribution with Vehicle Location and Diaphragm Stiffness, 30 Degree Skew, No Support Diaphragms

L-16

Effect of Intermediate Diaphragms on Moment Magnitude for Beam 1: (No Skew

Angle)

Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE1)

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000

Distance From Left Support (ft)

Mom

ent (

kip-

ft)

No Intermediate Diaphragm Int. Dia. (25% of Type III Beam) Int. Dia. (50% of Type III Beam)Int. Dia. (75% of Type III Beam) Int. Dia. (100% of Type III Beam)

Grillage Model: 0° Skew Angle with Support Diaphragm

Figure L-17 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE1, Bridge #24

Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE1)

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)

No Midspan Diaphragm Midspan Dia. (25% of Type III Beam) Midspan Dia. (50% of Type III Beam)Midspan Dia. (75% of Type III Beam) Midspan Dia. (100% of Type III Beam)


Figure L-18 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE1, Bridge #24

L-17


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-18


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-19


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-20


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-21


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-22


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-23


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-24


Angle):


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-25


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-26


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-27


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-28


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-29


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-30


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-31


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

0.0 7.5 15.0 22.5 30.0 37.5 45.0 52.5 60.0 67.5 75.0


Mom

ent (

kip-

ft)




L-32

Effect of Intermediate Diaphragms on Moment Magnitude for Beam 1: (30° Skew Angle)


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE1)

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)

No Midspan Diaphragm Int. Dia. (25% of Type III Beam) Int. Dia. (50% of Type III Beam)Int. Dia. (75% of Type III Beam) Int. Dia. (100% of Type III Beam)



L-33


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-34


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-35


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-36


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-37


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-38


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-39


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-40

Effect of Intermediate Diaphragms on Moment Magnitude for Beam 6: (30° Skew

Angle)


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-41


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-42


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-43


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-44


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-45


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-46


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-47


0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)





0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

0.000 7.500 15.000 22.500 30.000 37.500 45.000 52.500 60.000 67.500 75.000


Mom

ent (

kip-

ft)




L-48

Table L-9 – Differences for Beam 1 with Intermediate Diaphragms at Quarter Points

Distance from Barrier Load 25% 50% 75% 100% 25% 50% 75% 100%

2 MOVE1 -4.88 -7.297 -8.86 -9.974 -4.33 -5.365 -5.95 -6.3513 MOVE2 -3.60 -5.489 -6.74 -7.652 -3.46 -4.286 -4.77 -5.1124 MOVE3 -2.01 -3.281 -4.17 -4.833 -2.38 -2.969 -3.34 -3.6105 MOVE4 -0.07 -0.585 -1.03 -1.406 -1.04 -1.350 -1.58 -1.7706 MOVE5 2.31 2.703 2.79 2.893 0.61 0.646 0.58 0.4937 MOVE6 6.28 8.539 9.67 10.366 2.79 3.350 3.54 3.6078 MOVE7 11.67 15.713 17.87 19.251 5.47 6.640 7.11 7.3519 MOVE8 17.81 24.031 27.44 29.645 8.62 10.483 11.29 11.729

* Differences are based on results with no intermediate diaphragm

0 30Skew Angle

Percent Differences* for Beam 1 with Intermediate Diaphragms at Quarter Points (Support Diaphragms Present)

Table L-10 - Differences for Beam 1 with Intermediate Diaphragms at Midspan Points

Distance from Barrier Load 25% 50% 75% 100% 25% 50% 75% 100%

2 MOVE1 -4.19 -6.058 -7.42 -8.460 -3.23 -3.874 -4.19 -4.3743 MOVE2 -3.25 -4.637 -5.68 -6.499 -2.51 -2.972 -3.19 -3.3234 MOVE3 -2.10 -2.898 -3.57 -4.122 -1.62 -1.863 -1.98 -2.0355 MOVE4 -0.59 -0.689 -0.92 -1.153 -0.51 -0.492 -0.47 -0.4526 MOVE5 2.58 4.403 5.25 5.716 0.87 1.217 1.40 1.5207 MOVE6 7.51 11.180 13.15 14.394 2.65 3.489 4.18 4.6078 MOVE7 13.46 19.377 22.71 24.897 5.15 7.577 8.67 9.3009 MOVE8 20.07 28.598 33.56 36.895 8.33 11.509 12.95 13.781

* Differences are based on results with no intermediate diaphragm

Percent Differences* for Beam 1 with Intermediate Diaphragms at Midspan (Support Diaphragms Present)

Skew Angle 0 30

L-49

Moment Values for Beam 6 with Multiple Lanes Loaded:

4'-6" 10'-6" 10'-6" 10'-6" 10'-6" 4'-6"

6'MOVE8

6' 4' 6'MOVE2T

6'6' 4'

9'

4' 6'MOVE3T

Figure L-81 – Multiple Lane Loading

Moment Values for Beam 6 for Multiple Lanes Loaded with No Intermediate Diaphragms

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

500.00

550.00

600.00

650.00

700.00

750.00

0.00 7.50 15.00 22.50 30.00 37.50 45.00 52.50 60.00 67.50 75.00


Mom

ent (

kip-

ft)

1 Lane Loaded 2 Lanes Loaded 3 Lanes Loaded

Grillage Model: 0 Skew Angle with Support Diaphragm

Figure L-82 – Moment Values, Beam 6, Multiple Lanes Loaded, Bridge #24

L-50

Moment Values for Beam 6 for Multiple Lanes Loaded with Intermediate Diaphragms Placed at Quarter Points

0.0050.00

100.00150.00200.00250.00300.00350.00400.00450.00500.00550.00600.00650.00700.00750.00

0.00 7.50 15.00 22.50 30.00 37.50 45.00 52.50 60.00 67.50 75.00


Mom

ent (

kip-

ft)

1 Lane Loaded 2 Lanes Loaded 3 Lanes Loaded

Grillage Model: 0 Skew Angle with Support Diaphragm

Figure L-83 – Moment Values, Inter. Diaph. at Quarter Points, Beam 6, Multiple Lanes Loaded, Bridge #24

The comparisons shown in Figure L-82 and Figure L-83 above are based on intermediate

diaphragms with a stiffness of 100% of the AASHTO Type III beam.

L-51

Parametric Study Results: SHEAR

Effect of Skew Angle on Shear Distribution at Obtuse Corner for Beam 1:

Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE1)

0.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.750

0 10 20 30 40 50

Skew Angle (deg)

Dist

ribu

tion

Fact

or

60


ANSYS (with diaph.)


0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.150

0.2000.2500.300

0.350

0.4000.450

0.500

0.550

0.6000.650

0.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.6500.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.150

0.200

0.2500.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0


Figure L-84 - Effect of Skew Angle on Shear at Obtuse Corner for Beam 1, Bridge #24

L-52

Effect of Skew Angle on Shear Distribution at Acute Corner for Beam 1:

Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE1)

0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.750

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0



0.0500.1000.1500.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.700

0 10 20 30 40 50 6

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

0


Figure L-85 Effect of Skew Angle on Shear at Acute Corner for Beam 1, Bridge #24

L-53

Effect of Vehicle Location on Shear Distribution for Beam 1:

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner (60° Skew Angle)

0.000

0.200

0.400

0.600

0.800

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9


Figure L-86 – Shear vs. Vehicle Location, Beam 1, Bridge #24

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner (With Support Diaphragm)

0.000

0.200

0.400

0.600

0.800

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

0° Skew

30° Skew

60° Skew

Figure L-87 - Shear vs. Vehicle Location, with Support Diaphragms, Beam 1, Bridge #24

L-54

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner (Without Support Diaphragm)

0.000

0.200

0.400

0.600

0.800

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

0° Skew30° Skew

9

60° Skew

Figure L-88 - Shear vs. Vehicle Location, without Support Diaphragms, Beam 1, Bridge #24

Figure L-89, Figure L-90, Figure L-91, and Figure L-92 show the effect of vehicle location on

shear distribution as the intermediate diaphragm stiffness is increased and location is varied. The

original properties of the diaphragm are based on an AASHTO Type III beam.

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner (0° Skew Angle with Support Diaphragms)

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9


Figure L-89 - Shear vs. Vehicle Location, with Inter. Diaph. at ¼ pts, Beam 1, Bridge #24

L-55

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(0° Skew Angle with Support Diaphragms)

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9


Figure L-90 - Shear vs. Vehicle Location, with Inter. Diaph. at Midspan, Beam 1, Bridge #24

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner (30° Skew Angle with Support Diaphragms)

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9


Figure L-91 - Shear vs. Veh. Loc., with Inter. Diaph. at ¼ pts, Beam 1, 30° Skew, Bridge #24

L-56

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(30° Skew Angle with Support Diaphragms)

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

2 3 4 5 6 7 8


Dis

trib

utio

n Fa

ctor

9


Figure L-92 - Shear vs. Veh. Loc., with Inter. Diaph. at Midspan, Beam 1, 30° Skew, Bridge #24

Table L-11 – Maximum Shear Values Along Span 1 for Move1

0 30 60 0 30 60 0 30 60 0 30 600 38.46 39.27 46.34 37.91 38.90 45.82 13.76 10.08 3.86 14.79 12.76 18.915 38.46 39.27 39.19 37.91 38.90 37.82 13.76 10.08 3.86 14.79 12.76 18.91

10 31.47 32.11 33.49 31.02 31.29 30.98 11.81 10.70 6.15 12.02 10.55 16.4215 31.47 32.11 28.33 31.02 31.29 25.53 11.81 9.55 7.08 12.02 9.88 10.0120 25.87 26.18 28.33 25.30 25.14 25.53 9.22 9.55 7.62 9.44 9.88 8.5225 20.99 21.05 23.71 20.47 20.15 21.26 6.70 7.00 7.59 6.89 8.40 7.7530 18.89 21.05 19.61 20.47 20.15 18.11 6.70 7.78 6.89 6.89 6.23 8.1635 18.89 18.93 20.47 19.20 19.50 22.19 5.73 5.72 5.81 5.82 6.23 7.3540 24.13 24.00 24.19 24.51 24.64 25.63 8.49 6.72 5.04 8.48 6.63 5.3445 29.19 28.76 27.63 29.54 29.29 28.44 11.07 9.71 7.29 8.48 9.60 7.0650 29.19 28.76 27.63 29.54 29.29 28.44 11.07 9.71 7.29 11.07 9.60 7.0655 34.25 32.91 30.85 34.51 33.29 30.91 13.41 12.95 10.20 13.44 13.00 10.2460 39.45 36.52 34.02 39.56 36.66 33.55 15.36 14.82 13.78 15.51 15.03 14.6665 39.45 40.38 32.82 39.56 40.22 37.13 15.36 17.60 18.05 15.51 18.15 19.9770 45.12 44.57 23.54 44.70 44.12 41.94 16.62 20.06 23.88 17.21 20.98 25.5475 45.12 44.57 23.54 44.70 44.12 41.94 16.62 20.06 23.88 17.21 20.98 25.54

Beam 6With Diaphragm Without Diaphragm

Maximum Shear Values Along Span 1 (MOVE1)Distance

From Left Support

With Diaphragm Without DiaphragmBeam 1

L-57

Table L-12 – Maximum Shear Values Along Span 5 for Move1

0 30 60 0 30 60 0 30 60 0 30 600 45.12 46.28 52.16 44.70 46.16 52.24 16.62 12.47 6.03 17.21 13.98 12.305 45.12 46.28 46.63 44.70 46.16 46.85 16.62 12.47 6.03 17.21 13.98 12.30

10 39.45 40.29 41.55 39.56 40.46 41.70 15.36 12.99 7.22 15.51 13.22 9.3615 39.45 40.29 36.48 39.56 40.46 36.77 15.36 12.58 8.03 15.51 12.65 8.6420 34.25 34.63 36.48 34.51 34.85 36.77 13.41 12.58 9.10 13.44 12.65 9.4125 29.20 29.17 31.55 29.54 29.48 32.27 11.07 11.46 9.26 11.07 11.64 9.7930 29.20 29.17 26.84 29.54 29.48 28.23 11.07 9.77 9.32 11.07 9.96 10.3335 24.13 23.87 22.32 24.51 24.30 24.50 8.49 9.77 9.08 8.48 9.96 10.1640 18.89 18.53 18.02 19.20 19.03 20.94 5.73 7.47 8.32 5.82 7.59 8.8645 20.99 21.04 21.03 20.47 20.48 19.39 6.70 5.27 6.90 6.89 5.21 6.0650 20.99 21.04 21.03 20.47 20.48 19.39 6.70 5.27 6.90 6.89 5.21 6.0655 25.87 25.15 24.26 25.30 24.44 23.02 9.22 7.99 5.46 9.44 8.10 6.1660 31.47 28.98 27.75 31.02 28.18 27.36 11.81 9.89 8.01 12.02 10.26 11.1665 31.47 33.46 28.10 31.02 32.79 34.34 11.81 13.13 12.18 12.02 14.16 14.7870 38.46 39.00 21.70 37.91 38.74 41.56 13.76 16.28 20.32 14.79 18.69 18.0875 38.46 39.00 27.70 37.91 38.74 41.56 13.76 16.28 20.32 14.79 18.69 18.08

Beam 10With Diaphragm Without Diaphragm

Maximum Shear Values Along Span 5 (MOVE1)Distance

From Left Support

With Diaphragm Without DiaphragmBeam 5

Maximum Shear Values at End of Span for MOVE1:

1

Span 1 Span 5

V = 39.27 kipsDF = 0.646

V = 44.57 kipsDF = 0.673

V = 39.00 kipsDF = 0.641

V = 46.28 kipsDF = 0.699

5

25

V = 44.57 kipsDF = 0.673

V = 39.27 kipsDF = 0.646

V = 38.46 kipsDF = 0.632

V = 45.12 kipsDF = 0.682

1

V = 45.12 kipsDF = 0.632

25

V = 38.46 kipsDF = 0.632

5

V = 45.12 kipsDF = 0.682

V = 38.46 kipsDF = 0.632

With Support Diaphragms

V = 46.34 kipsDF = 0.762

V = 46.34 kipsDF = 0.762

V = 23.54 kipsDF = 0.356

V = 23.54 kipsDF = 0.356

1

V = 52.16 kipsDF = 0.788

25

V = 27.70 kipsDF = 0.455

5



V = 38.46 kipsDF = 0.632

V = 45.12 kipsDF = 0.682

V = 39.00 kipsDF = 0.641

V = 46.28 kipsDF = 0.699

V = 27.70 kipsDF = 0.455

V = 52.16 kipsDF = 0.788

30°

60°

Figure L-93 – Shear Values with Support Diaphragms, Bridge #24

L-58

1Without Support

DiaphragmsV = 45.82 kipsDF = 0.753

5

25

V = 41.94 kipsDF = 0.634

V = 41.94 kipsDF = 0.634

V = 52.24 kipsDF = 0.789

V = 45.82 kipsDF = 0.753

V = 41.56 kipsDF = 0.683

Without Support Diaphragms


V = 38.90 kipsDF = 0.640

V = 37.91 kipsDF = 0.623

V = 38.90 kipsDF = 0.640

V = 44.12 kipsDF = 0.666

V = 44.12 kipsDF = 0.666

1

V = 44.70 kipsDF = 0.675

1

V = 46.16 kipsDF = 0.697

25

V = 44.70 kipsDF = 0.675

V = 44.70 kipsDF = 0.675

V = 38.74 kipsDF = 0.637

5

V = 37.91 kipsDF = 0.623

V = 37.91 kipsDF = 0.623

5

25

V = 37.91 kipsDF = 0.623

V = 44.70 kipsDF = 0.675

V = 38.74 kipsDF = 0.637

V = 46.16 kipsDF = 0.697

V = 41.56 kipsDF = 0.683

V = 52.24 kipsDF = 0.789

60°

30°

Figure L-94 – Shear Values without Support Diaphragms, Bridge #24

Maximum Support Reactions for MOVE1:




R = 61.87 kipsDF = 0.876

R = 52.94 kipsDF = 0.870

R = 54.89 kipsDF = 0.778

R = 20.07 kipsDF = 0.330

R = 52.94 kipsDF = 0.870

R = 43.82 kipsDF = 0.621

R = 52.15 kipsDF = 0.739

R = 43.78 kipsDF = 0.720

1

1

1

R = 54.89 kipsDF = 0.778

R = 46.62 kipsDF = 0.660

25

R = 46.62 kipsDF = 0.660

Span 1

5

5

R = 28.00 kipsDF = 0.460

R = 43.78 kipsDF = 0.720

25

5

Span 5

25

R = 34.30 kipsDF = 0.564

60°

30°

R = 34.30 kipsDF = 0.564

R = 43.82 kipsDF = 0.621

R = 34.30 kipsDF = 0.564

R = 34.30 kipsDF = 0.564

R = 43.82 kipsDF = 0.621

R = 43.82 kipsDF = 0.621

R = 28.00 kipsDF = 0.460

R = 52.15 kipsDF = 0.739

R = 20.07 kipsDF = 0.330

R = 61.87 kipsDF = 0.876

Figure L-95 – Reaction Values with Support Diaphragms, Bridge #24

L-59




R = 52.33 kipsDF = 0.741

R = 53.73 kipsDF = 0.761

R = 48.21 kipsDF = 0.793

R = 57.26 kipsDF = 0.811

R = 48.21 kipsDF = 0.793

1

R = 47.82 kipsDF = 0.786

1

R = 54.27 kipsDF = 0.769

R = 54.27 kipsDF = 0.769

R = 52.29 kipsDF = 0.741

25

1

R = 52.29 kipsDF = 0.741

5

R = 44.26 kipsDF = 0.728

5

R = 44.14 kipsDF = 0.726

25

R = 47.82 kipsDF = 0.786

25

5

R = 45.64 kipsDF = 0.750

60°

30°

R = 52.33 kipsDF = 0.741

R = 45.64 kipsDF = 0.750

R = 45.64 kipsDF = 0.750

R = 52.33 kipsDF = 0.741

R = 52.33 kipsDF = 0.741

R = 45.64 kipsDF = 0.750

R = 44.14 kipsDF = 0.726

R = 53.73 kipsDF = 0.761

R = 44.26 kipsDF = 0.728

R = 57.26 kipsDF = 0.811

Figure L-96 – Reaction Values with Support Diaphragms, Bridge #24

Maximum Shear Along Span 1 (Beam 1)With Support Diaphragm

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0 7.5 15 22.5 30 37

Distance From L

Shea

r (k

ips)

Figure L-97 – Maximum Shear Values Along

.5 45 52.5 60 67.5 75

eft Support (ft)

No Skew30 Skew60 Skew

Span 1, with Sup. Diaph., Beam 1, Bridge #24

L-60

Maximum Shear Along Span 1 (Beam 1)Without Support Diaphragm

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

0 7.5 15 22.5 30 37.5 45 52.5 60 67.5 75


Shea

r (k

ips)


Figure L-98 – Maximum Shear Values Along Span 1, without Sup. Diaph., Beam 1, Bridge #24


0.00

5.00

10.00

15.00

20.00

25.00

30.00

0 7.5 15 22.5 30 37.5 45 52.5 60 67.5 75


Shea

r (k

ips)


Figure L-99 – Maximum Shear Values Along Span 1, with Sup. Diaph., Beam 6, Bridge #24

L-61


0.00

5.00

10.00

15.00

20.00

25.00

30.00

0 7.5 15 22.5 30 37

Distance From L

Shea

r (k

ips)

Figure L-100 – Maximum Shear Values Alon

Maximum Shear AWith Supp

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 7.5 15 22.5 30 37

Distance From L

Shea

r (k

ips)

Figure L-101 – Maximum Shear Values Alon

.5 45 52.5 60 67.5 75

eft Support (ft)


g Span 1, without Sup. Diaph., Beam 6, Bridge #24

long Span 5 (Beam 5)ort Diaphragm

.5 45 52.5 60 67.5 75

eft Support (ft)


g Span 5, with Sup. Diaph., Beam 5, Bridge #24

L-62


0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 7.5 15 22.5 30 37.5 45 52.5 60 67.5 75


Shea

r (k

ips)




0.00

5.00

10.00

15.00

20.00

25.00

0 7.5 15 22.5 30 37.5 45 52.5 60 67.5 75


Shea

r (k

ips)


Figure L-103 – Maximum Shear Values Along Span 5, with Sup. Diaph., Beam 10, Bridge #24

L-63


0.00

5.00

10.00

15.00

20.00

25.00

0 7.5 15 22.5 30 37.5 45 52.5 60 67.5 75


Shea

r (k

ips)



L-64

Discussion of Results:

Vehicle loading at support location:

Based on my understanding of SAP, the live load analysis considers all possible vehicle

locations, resulting in an envelope of shear and moment values for any location. Therefore, cutting the

lane short of the support, in my opinion, should not yield different results. I am currently in the process

of analyzing a model with the lanes stopped approximately 7.5 ft short of the support locations. I will

compare these results to the results with the lane continuous over the supports.

Assigning Frame End Length Offsets:

Assigning an end (length) offset of 2 ft (to both i

& j end) to the transverse slab members did not yield

different results. This was tested on the grillage model

with no skew and support diaphragms present. Flexible

members were used to define the lane location.

Effect of Skew Angle:

MOMENT:

As skew angle increased the moment distribution factors decreased for all loading positions

(MOVE1-8). For skew angles of 0° and 30°, the decrease, if any, in distribution factor was negligible.

However, larger decreases were shown to exist when the skew angle was increased to 60°.

SHEAR:

Increasing the skew angle caused the shear distribution factors at the obtuse corner of the bridge

to increase for all loading positions. A larger increase was shown when the skew angle was changed

from 30° to 60°.

L-65

Effect of Vehicle Location:

MOMENT:

An almost linear relationship existed between vehicle location and moment distribution factor.

As the vehicle was positioned farther away from the barrier, the distribution factor decreased. This

linear relationship was independent of intermediate diaphragm location and stiffness.

SHEAR:

Same as moment.

Effect of Support Diaphragms:

MOMENT: (Exterior Beam)

In general, support diaphragms did not seem to make a significant difference in moment

distribution factor. A slight difference was observed for larger skew angles when the vehicle was

positioned close to the beam.

SHEAR:

The effect of support diaphragms on shear distribution at the obtuse corner of the bridge was

negligible. The support diaphragms made a significant difference at the acute corner, however the

values are not critical, so the obtuse corner controls.

Effect of Intermediate Diaphragms:

The presence of intermediate diaphragms at quarter points caused the load to be better

distributed. For a 30° skew angle, the stiffness of the intermediate diaphragms seemed to be almost

negligible.

L-66

Figure L-105 - Comparison of Results for Beam 1 with Varied Lane Length

Lanes 7.5 ft Short of Supports

Flexible Members

Abu

tmen

t

Lanes Continuous

Flexible Members

Abu

tmen

t

Table L-13 – Comparison of Results for Beam 1 with Varied Lane Length

Grillage Model w/ Support Diaphragms and No Skew - Beam 1

Shortened Lane Length (Stopped 7.5' from supports)

Lanes Continuous Station

V2 M3 V2 M3 Output Case Step

Type Frame

ft Kip Kip-ft Kip Kip-ft

MOVE1 Max 1 0.000 2.98 5.31 2.98 24.23

MOVE1 Max 1 1.875 2.98 48.35 2.98 59.04

MOVE1 Max 1 3.750 2.98 120.47 2.98 123.44

MOVE1 Max 1 5.625 2.98 192.58 2.98 195.34

MOVE1 Max 1 7.500 2.98 264.69 2.98 267.24

MOVE1 Min 1 0.000 -38.46 -27.50 -38.46 -27.50

MOVE1 Min 1 1.875 -38.46 -0.39 -38.46 -0.37

MOVE1 Min 1 3.750 -38.46 -5.90 -38.46 -5.89

MOVE1 Min 1 5.625 -38.46 -11.48 -38.46 -11.48

MOVE1 Min 1 7.500 -38.46 -17.08 -38.46 -17.08

MOVE1 Max 2 0.000 4.55 268.00 4.55 268.00

MOVE1 Max 2 1.875 4.55 295.32 4.55 295.32

MOVE1 Max 2 3.750 4.55 329.48 4.55 329.48

MOVE1 Max 2 5.625 4.55 379.79 4.55 379.79

MOVE1 Max 2 7.500 4.55 436.04 4.55 436.04

MOVE1 Min 2 0.000 -31.47 -15.54 -31.47 -15.54

L-67

MOVE1 Min 2 1.875 -31.47 -21.19 -31.47 -21.19

MOVE1 Min 2 3.750 -31.47 -26.84 -31.47 -26.84

MOVE1 Min 2 5.625 -31.47 -32.47 -31.47 -32.47

MOVE1 Min 2 7.500 -31.47 -38.13 -31.47 -38.13

MOVE1 Max 3 0.000 7.68 426.50 8.13 426.50

MOVE1 Max 3 1.875 7.68 438.69 8.13 438.69

MOVE1 Max 3 3.750 7.68 453.46 8.13 453.46

MOVE1 Max 3 5.625 7.68 482.67 8.13 482.67

MOVE1 Max 3 7.500 7.68 524.86 8.13 524.86

MOVE1 Min 3 0.000 -25.87 -36.64 -25.87 -36.64

MOVE1 Min 3 1.875 -25.87 -42.45 -25.87 -42.45

MOVE1 Min 3 3.750 -25.87 -48.24 -25.87 -48.24

MOVE1 Min 3 5.625 -25.87 -54.00 -25.87 -54.00

MOVE1 Min 3 7.500 -25.87 -59.77 -25.87 -59.77

MOVE1 Max 4 0.000 13.78 514.65 13.78 514.65

MOVE1 Max 4 1.875 13.78 512.93 13.78 512.93

MOVE1 Max 4 3.750 13.78 514.60 13.78 514.60

MOVE1 Max 4 5.625 13.78 531.28 13.78 531.28

MOVE1 Max 4 7.500 13.78 560.36 13.78 560.36

MOVE1 Min 4 0.000 -20.99 -58.52 -20.99 -58.52

MOVE1 Min 4 1.875 -20.99 -64.54 -20.99 -64.54

MOVE1 Min 4 3.750 -20.99 -70.52 -20.99 -70.52

MOVE1 Min 4 5.625 -20.99 -76.56 -20.99 -76.56

MOVE1 Min 4 7.500 -20.99 -82.58 -20.99 -82.58

MOVE1 Max 5 0.000 18.71 549.37 18.89 549.37

MOVE1 Max 5 1.875 18.71 535.43 18.89 535.43

MOVE1 Max 5 3.750 18.71 524.36 18.89 524.36

MOVE1 Max 5 5.625 18.71 529.07 18.89 529.07

MOVE1 Max 5 7.500 18.71 540.87 18.89 540.87

MOVE1 Min 5 0.000 -16.56 -81.55 -16.56 -81.55

MOVE1 Min 5 1.875 -16.56 -87.91 -16.56 -87.91

MOVE1 Min 5 3.750 -16.56 -94.26 -16.56 -94.26

MOVE1 Min 5 5.625 -16.56 -100.66 -16.56 -100.66

L-68

MOVE1 Min 5 7.500 -16.56 -107.02 -16.56 -107.02

MOVE1 Max 6 0.000 24.13 548.65 24.13 548.65

MOVE1 Max 6 1.875 24.13 513.93 24.13 513.93

MOVE1 Max 6 3.750 24.13 492.96 24.13 492.96

MOVE1 Max 6 5.625 24.13 486.91 24.13 486.91

MOVE1 Max 6 7.500 24.13 482.80 24.13 482.80

MOVE1 Min 6 0.000 -12.35 -106.41 -12.43 -106.41

MOVE1 Min 6 1.875 -12.35 -113.23 -12.43 -113.23

MOVE1 Min 6 3.750 -12.35 -120.05 -12.43 -120.05

MOVE1 Min 6 5.625 -12.35 -126.87 -12.43 -126.87

MOVE1 Min 6 7.500 -12.35 -133.69 -12.43 -133.69

MOVE1 Max 7 0.000 29.20 492.33 29.19 492.33

MOVE1 Max 7 1.875 29.20 446.98 29.19 446.98

MOVE1 Max 7 3.750 29.20 412.18 29.19 412.18

MOVE1 Max 7 5.625 29.20 394.43 29.19 394.43

MOVE1 Max 7 7.500 29.20 381.54 29.19 381.54

MOVE1 Min 7 0.000 -8.70 -133.62 -8.70 -133.62

MOVE1 Min 7 1.875 -8.70 -141.02 -8.70 -141.02

MOVE1 Min 7 3.750 -8.70 -148.43 -8.70 -148.43

MOVE1 Min 7 5.625 -8.70 -155.83 -8.70 -155.83

MOVE1 Min 7 7.500 -8.70 -163.23 -8.70 -163.23

MOVE1 Max 8 0.000 34.25 391.35 34.25 391.35

MOVE1 Max 8 1.875 34.25 333.18 34.25 333.75

MOVE1 Max 8 3.750 34.25 289.43 34.25 289.43

MOVE1 Max 8 5.625 34.25 261.13 34.25 261.13

MOVE1 Max 8 7.500 34.25 234.38 34.25 237.62

MOVE1 Min 8 0.000 -4.90 -163.88 -5.11 -163.88

MOVE1 Min 8 1.875 -4.90 -171.98 -5.11 -171.98

MOVE1 Min 8 3.750 -4.90 -180.09 -5.11 -180.09

MOVE1 Min 8 5.625 -4.90 -188.19 -5.11 -188.19

MOVE1 Min 8 7.500 -4.90 -196.29 -5.11 -196.29

MOVE1 Max 9 0.000 39.45 248.53 39.45 248.53

MOVE1 Max 9 1.875 39.45 181.91 39.45 181.91

L-69

MOVE1 Max 9 3.750 39.45 131.86 39.45 131.86

MOVE1 Max 9 5.625 39.45 100.69 39.45 100.69

MOVE1 Max 9 7.500 39.45 101.50 39.45 101.50

MOVE1 Min 9 0.000 -2.81 -197.86 -2.81 -197.86

MOVE1 Min 9 1.875 -2.81 -206.74 -2.81 -206.74

MOVE1 Min 9 3.750 -2.81 -215.61 -2.81 -215.61

MOVE1 Min 9 5.625 -2.81 -224.49 -2.81 -224.49

MOVE1 Min 9 7.500 -2.81 -233.36 -2.81 -233.36

MOVE1 Max 10 0.000 45.12 95.39 45.12 100.43

MOVE1 Max 10 1.875 45.12 56.23 45.12 57.75

MOVE1 Max 10 3.750 45.12 58.28 45.12 58.28

MOVE1 Max 10 5.625 45.12 60.33 45.12 60.33

MOVE1 Max 10 7.500 45.12 62.38 45.12 62.38

MOVE1 Min 10 0.000 -1.09 -236.12 -1.09 -236.12

MOVE1 Min 10 1.875 -1.09 -245.68 -1.09 -245.68

MOVE1 Min 10 3.750 -1.09 -255.23 -1.09 -255.23

MOVE1 Min 10 5.625 -1.09 -296.54 -1.09 -296.54

MOVE1 Min 10 7.500 -1.09 -356.49 -1.09 -356.49

Table L-14 - Comparison of Results for Beam 1 with Varied Torsional Constant

Grillage Model w/ Support Diaphragms and No Skew

(Intermediate Diaphragms Placed at Quarter Points)

I's & J = 100% of Type III Beam

I's = 100% & J = 25% of Type III Beam Station

V2 M3 V2 M3

Output Case

Step Type Frame

ft Kip Kip-ft Kip Kip-ft

MOVE1 Max G1 0.000 2.59 24.83 2.58 24.82

MOVE1 Max G1 1.875 2.59 60.20 2.58 60.14

MOVE1 Max G1 3.750 2.59 120.13 2.58 120.04

MOVE1 Max G1 5.625 2.59 187.30 2.58 187.18

MOVE1 Max G1 7.500 2.59 254.47 2.58 254.32

MOVE1 Min G1 0.000 -35.88 -19.28 -35.86 -19.35

L-70

MOVE1 Min G1 1.875 -35.88 -1.45 -35.86 -1.41

MOVE1 Min G1 3.750 -35.88 -6.30 -35.86 -6.24

MOVE1 Min G1 5.625 -35.88 -11.16 -35.86 -11.08

MOVE1 Min G1 7.500 -35.88 -16.01 -35.86 -15.93

MOVE1 Max G2 0.000 5.42 256.52 5.41 256.32

MOVE1 Max G2 1.875 5.42 277.17 5.41 276.92

MOVE1 Max G2 3.750 5.42 303.89 5.41 303.58

MOVE1 Max G2 5.625 5.42 346.69 5.41 346.29

MOVE1 Max G2 7.500 5.42 395.77 5.41 395.31

MOVE1 Min G2 0.000 -27.77 -15.02 -27.74 -14.92

MOVE1 Min G2 1.875 -27.77 -19.89 -27.74 -19.78

MOVE1 Min G2 3.750 -27.77 -24.75 -27.74 -24.62

MOVE1 Min G2 5.625 -27.77 -29.62 -27.74 -29.47

MOVE1 Min G2 7.500 -27.77 -34.48 -27.74 -34.32

MOVE1 Max G3 0.000 11.02 383.66 11.02 383.14

MOVE1 Max G3 1.875 11.02 389.01 11.02 388.36

MOVE1 Max G3 3.750 11.02 416.28 11.02 415.48

MOVE1 Min G3 0.000 -24.05 -33.56 -24.01 -33.38

MOVE1 Min G3 1.875 -24.05 -38.43 -24.01 -38.24

MOVE1 Min G3 3.750 -24.05 -43.31 -24.01 -43.10

MOVE1 Max G4 0.000 9.36 412.01 9.36 414.40

MOVE1 Max G4 1.875 9.36 424.02 9.36 426.46

MOVE1 Max G4 3.750 9.36 460.50 9.36 462.84

MOVE1 Min G4 0.000 -27.26 -42.24 -27.24 -42.83

MOVE1 Min G4 1.875 -27.26 -47.38 -27.24 -47.94

MOVE1 Min G4 3.750 -27.26 -52.52 -27.24 -53.06

MOVE1 Max G5 0.000 12.87 462.32 12.87 464.64

MOVE1 Max G5 1.875 12.87 459.91 12.87 462.21

MOVE1 Max G5 3.750 12.87 460.75 12.87 463.02

MOVE1 Max G5 5.625 12.87 476.58 12.87 478.80

MOVE1 Max G5 7.500 12.87 504.47 12.87 506.63

MOVE1 Min G5 0.000 -19.87 -51.69 -19.84 -52.23

MOVE1 Min G5 1.875 -19.87 -56.88 -19.84 -57.40

L-71

MOVE1 Min G5 3.750 -19.87 -62.09 -19.84 -62.59

MOVE1 Min G5 5.625 -19.87 -67.28 -19.84 -67.76

MOVE1 Min G5 7.500 -19.87 -72.47 -19.84 -72.93

MOVE1 Max G6 0.000 19.82 495.92 19.82 498.08

MOVE1 Max G6 1.833 19.82 474.65 19.82 476.72

MOVE1 Max G6 3.667 19.82 461.03 19.82 462.99

MOVE1 Max G6 5.500 19.82 458.41 19.82 460.53

MOVE1 Max G6 7.333 19.82 467.76 19.82 469.44

MOVE1 Min G6 0.000 -13.64 -71.82 -13.60 -72.27

MOVE1 Min G6 1.833 -13.64 -76.98 -13.60 -77.41

MOVE1 Min G6 3.667 -13.64 -82.13 -13.60 -82.55

MOVE1 Min G6 5.500 -13.64 -87.29 -13.60 -87.69

MOVE1 Min G6 7.333 -13.64 -92.45 -13.60 -92.83

MOVE1 Max G7 0.000 20.34 460.46 20.30 461.70

MOVE1 Max G7 0.167 20.34 460.81 20.30 462.07

MOVE1 Min G7 0.000 -22.46 -91.94 -22.47 -92.70

MOVE1 Min G7 0.167 -22.46 -92.49 -22.47 -93.25

MOVE1 Max G8 0.000 20.23 474.96 20.19 476.34

MOVE1 Max G8 1.875 20.23 447.42 20.19 448.91

MOVE1 Max G8 3.750 20.23 434.06 20.19 435.70

MOVE1 Max G8 5.625 20.23 434.63 20.19 436.34

MOVE1 Max G8 7.500 20.23 436.79 20.19 438.55

MOVE1 Min G8 0.000 -13.88 -92.09 -13.88 -92.84

MOVE1 Min G8 1.875 -13.88 -98.29 -13.88 -99.05

MOVE1 Min G8 3.750 -13.88 -104.48 -13.88 -105.23

MOVE1 Min G8 5.625 -13.88 -110.68 -13.88 -111.43

MOVE1 Min G8 7.500 -13.88 -116.88 -13.88 -117.63

MOVE1 Max G9 0.000 27.13 445.46 27.09 447.28

MOVE1 Max G9 1.875 27.13 403.23 27.09 405.11

MOVE1 Max G9 3.750 27.13 371.31 27.09 373.23

MOVE1 Max G9 5.625 27.13 356.15 27.09 358.09

MOVE1 Max G9 7.500 27.13 345.49 27.09 347.46

MOVE1 Min G9 0.000 -8.27 -116.81 -8.27 -117.56

L-72

MOVE1 Min G9 1.875 -8.27 -123.20 -8.27 -123.95

MOVE1 Min G9 3.750 -8.27 -129.60 -8.27 -130.35

MOVE1 Min G9 5.625 -8.27 -135.99 -8.27 -136.74

MOVE1 Min G9 7.500 -8.27 -142.39 -8.27 -143.14

MOVE1 Max G10 0.000 34.52 343.92 34.49 345.90

MOVE1 Max G10 1.875 34.52 295.32 34.49 297.25

MOVE1 Max G10 3.750 34.52 269.02 34.49 270.87

MOVE1 Min G10 0.000 -5.63 -142.77 -5.62 -143.53

MOVE1 Min G10 1.875 -5.63 -149.33 -5.62 -150.09

MOVE1 Min G10 3.750 -5.63 -155.89 -5.62 -156.65

MOVE1 Max G11 0.000 31.76 272.86 31.72 271.84

MOVE1 Max G11 1.875 31.76 231.83 31.72 230.97

MOVE1 Max G11 3.750 31.76 214.71 31.72 213.99

MOVE1 Min G11 0.000 -7.84 -156.70 -7.84 -156.86

MOVE1 Min G11 1.875 -7.84 -164.91 -7.84 -165.08

MOVE1 Min G11 3.750 -7.84 -173.13 -7.84 -173.31

MOVE1 Max G12 0.000 35.34 228.46 35.31 227.69

MOVE1 Max G12 1.875 35.34 168.95 35.31 168.39

MOVE1 Max G12 3.750 35.34 124.92 35.31 124.48

MOVE1 Max G12 5.625 35.34 98.85 35.31 98.81

MOVE1 Max G12 7.500 35.34 101.21 35.31 101.18

MOVE1 Min G12 0.000 -3.52 -174.12 -3.51 -174.31

MOVE1 Min G12 1.875 -3.52 -182.60 -3.51 -182.79

MOVE1 Min G12 3.750 -3.52 -191.11 -3.51 -191.31

MOVE1 Min G12 5.625 -3.52 -199.61 -3.51 -199.82

MOVE1 Min G12 7.500 -3.52 -208.12 -3.51 -208.34

MOVE1 Max G13 0.000 42.33 99.67 42.31 99.66

MOVE1 Max G13 1.875 42.33 57.73 42.31 57.71

MOVE1 Max G13 3.750 42.33 50.20 42.31 50.33

MOVE1 Max G13 5.625 42.33 51.81 42.31 51.95

MOVE1 Max G13 7.500 42.33 53.43 42.31 53.56

MOVE1 Min G13 0.000 -0.86 -209.95 -0.86 -210.18

MOVE1 Min G13 1.875 -0.86 -218.89 -0.86 -219.13

L-73

MOVE1 Min G13 3.750 -0.86 -227.84 -0.86 -228.08

MOVE1 Min G13 5.625 -0.86 -260.27 -0.86 -260.90

MOVE1 Min G13 7.500 -0.86 -314.18 -0.86 -314.71

L-74

Slab on Steel I Girders The following is a summary of the procedures and results for various models using only

SAP2000. For this study, only fatigue loading was considered. Each model was analyzed with and

without support diaphragms and skew angles of 0, 30, and 60 degrees were used. Models were analyzed

without the presence of intermediate diaphragms in addition to intermediate diaphragms placed at varies

locations.

Description of Bridge:

The following bridge is #18 in the TTU Bridge Database.

1'-9" 40'-6" 1'-9"

44'

4'-9" 11'-6" 11'-6" 11'-6" 4'-9"

9"

66" Web (Typ.)

Figure L-106 - Typical Cross Section

1" x 21" x 39' 1.75" x 21" x 32'-4" 1" x 21" x 28'-5" 2" x 21" x 35'-7" 4" x 21" x 16'-8"

CL Bent

152'

Sec. 1 Sec. 2 Sec. 3 Sec. 4Sec. 1

1" x 21" x 99'-9"

Figure L-107 - Girder Elevation (Span 1)

L-75

4" x 21" x 6'-2"2.75" x 21" x 144'-1" 1.5" x 21" x 18'-0"

1" x 21" x 13'-9"182'

BentLC

Sec. 6Sec. 5Sec. 4 Sec. 1

Figure L-108 - Girder Elevation (Span 2)

152' 182'

4'-9"

11'-6"

11'-6"

11'-6"

4'-9"1 2

3 4

5 6

7 8

Figure L-109 - Plan View

13'-6" 25' 25' 25' 25' 25' 13'-6" 16' 25' 25' 25' 25' 25' 25' 16'

152' 182'

Figure L-110 - Cross-Frame Location (No Skew)

L-76

16' 25' 25' 25' 25' 16'

30°

19'-11" 19'-11"

Figure L-111 - Cross-Frame Location – Span 1

25'25'18'-6" 25'25' 18'-6"25'

30°

19'-11" 19'-11"


19'-11" 19'-11" 19'-11" 21'-1" 25' 25' 21'-1" 19'-11" 19'-11" 19'-11"

60°


60°

19'-11" 19'-11" 19'-11" 23'-7" 25' 25' 25' 23'-7" 19'-11" 19'-11" 19'-11"


L-77

Vehicle Loading:

The standard HS20-44 vehicle was used for all loading cases. Loading cases MOVE10-18 were

only used for the models with a 30° and 60° skew angle. This allowed the shear values at each acute

and obtuse corner to be obtained.

11'-6"4'-9" 11'-6" 4'-9"11'-6"

Lane 112'

Shoulder6'

10'2'

3'

4'

5'

6'

7'

8'

9'

MOVE16' 2'

MOVE2

MOVE3

MOVE4

MOVE5

MOVE6

MOVE8

MOVE9

MOVE79'

8'

7'

6'

5'

4'

10'

6'2'

3'MOVE10

MOVE11

MOVE12

MOVE13

MOVE14

MOVE15

MOVE16

MOVE17

MOVE18

Figure L-115 - Loading Locations

L-78

Table L-15 – Section Properties

f'c fy Area J I33 I22 AS2 AS3ksi ksi in2 in4 in4 in4 in2 in2

Sec. 1 4.0 50.0 1951 48752 1259129 1987352 1304 359Sec. 2 4.0 50.0 2078 48804 1288349 1992015 1332 358Sec. 3 4.0 50.0 2269 50938 1913600 1999014 1364 356Sec. 4 4.0 50.0 2903 53555 3109651 2022338 1435 355Sec. 5 4.0 50.0 2507 52125 2373357 2007761 1395 354Sec. 6 4.0 50.0 2110 50001 1593952 1993183 1338 357Sec. 1 4.0 50.0 1843 45856 1236482 1532287 1204 358Sec. 2 4.0 50.0 1970 30347 1265856 1538567 1231 357Sec. 3 4.0 50.0 2161 30505 1874837 1547638 1262 354Sec. 4 4.0 50.0 2795 35667 3042463 1575828 1332 353Sec. 5 4.0 50.0 2399 49177 2323199 1558511 1292 352Sec. 6 4.0 50.0 2002 47106 1563178 1540109 1237 355

- 50.0 52800 1040 191664000 2816000 44 44* Base material is concrete** Modifiers have been applied

Rigid Diaphragms**

Member

Section Properties

Exte

rior B

eam

(C

ompo

site

)*In

terio

r Bea

m

(Com

posi

te)*

Description of Models:

Each interior and exterior composite beam section was created in SAP’s Section Designer. The

transverse grillage members were created as rectangular sections, typically 8 ft in width. In order to

accommodate the skewed supports, widths between 6-11 ft were used.

Equivalent Diaphragms:

In order to model the actual cross frame members (shown in Figure L-116), an equivalent

element1 was used. To model this accurately, a linear link element was used with an effective stiffness

calculated by the following equation:

θLAEke

2sin2 ⎟⎠⎞

⎜⎝⎛= (1)

where A = area of one angle, E = modulus of elasticity, L = length of diagonal member, and θ =

angle between diagonal member and horizontal line.

1 Developed by Dr. Puckett and Mark Jablin.

L-79

L 4" x 4" x 5/16"

5'-6

" Web

θ

Figure L-116 – Actual Cross Frame Members

Using Equation 1, the effective stiffness for the intermediate diaphragms is as follows:

( )( )( )

( )ink 170 6.25sin

ftin 12ft 75.12

ksi 29000in 4.22 22

=°

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛

=ek

Rigid Diaphragms:

Rigid diaphragms were modeled as rectangular sections 8 in x 66 in. The following modifiers

were applied to the rigid sections:

Area: *100

Shear Area (AS2 & AS3): *0.1

Torsional Constant: *0.1

Moment of Inertia (I2 & I3): *1000

The use of these modifiers resulted in no loss of accuracy, zero stiffness, or instability warnings.

L-80

Table L-16 - Models Analyzed


Intermediate Diaphragm Load Case

18-gm-s0-wosd-woid-fm 0 NO NO MOVE1-918-gm-s0-wesd-woid-fm 0 YES (equiv) NO MOVE1-9 In Progress18-gm-s0-wrsd-woid-fm 0 YES (rigid) NO MOVE1-918-gm-s0-wosd-weid-fm 0 NO YES (equiv) MOVE1-918-gm-s0-wosd-wrid-fm 0 NO YES (rigid) MOVE1-918-gm-s0-wesd-weid-fm 0 YES(equiv) YES(equiv) MOVE1-9 In Progress18-gm-s0-wrsd-wrid-fm 0 YES (rigid) YES (rigid) MOVE1-918-gm-s30-wosd-woid-fm 30 NO NO MOVE1-1818-gm-s30-wesd-woid-fm 30 YES (equiv) NO MOVE1-18 In Progress18-gm-s30-wrsd-woid-fm 30 YES (rigid) NO MOVE1-1818-gm-s30-wosd-weid-fm 30 NO YES (equiv) MOVE1-1818-gm-s30-wosd-wrid-fm 30 NO YES (rigid) MOVE1-1818-gm-s30-wesd-weid-fm 30 YES(equiv) YES(equiv) MOVE1-18 In Progress18-gm-s30-wrsd-wrid-fm 30 YES (rigid) YES (rigid) MOVE1-1818-gm-s60-wosd-woid-fm 60 NO NO MOVE1-1818-gm-s60-wesd-woid-fm 60 YES (equiv) NO MOVE1-18 In Progress18-gm-s60-wrsd-woid-fm 60 YES (rigid) NO MOVE1-1818-gm-s60-wosd-weid-fm 60 NO YES (equiv) MOVE1-1818-gm-s60-wosd-wrid-fm 60 NO YES (rigid) MOVE1-1818-gm-s60-wesd-weid-fm 60 YES(equiv) YES(equiv) MOVE1-18 In Progress18-gm-s60-wrsd-wrid-fm 60 YES (rigid) YES (rigid) MOVE1-18

Gril

lage

FilenameParametersModel

Type Completed

L-81

Beam Line Analysis Results:

152' 182'

14' - 30' 14'

Direction of Travel

14' 14' - 30'

Direction of Travel

32 8k k32k

k328k 32k

Mmax Mmax

65' 106'

VmaxVmax

Span 1 Span 2

Figure L-117 - 2D Model with Maximum Response Locations

Table L-17 - Beam Line Analysis Results

Location Reaction Shear Moment(ft) (kip) (kip) (kip-ft)0 66.61 66.61 -65 - - 2043.07152 69.23 -0 70.02

106 - - 2409.14182 67.32 67.32 -

Span

1

72.08

2-

Parametric Study Results: MOMENT

Table L-18 – Moment Values, with Inter. Diaph., Beam 1, Bridge #18

Distance From Barrier

(ft)Load Moment

(kip-ft) DF Moment (kip-ft) DF Moment


(kip-ft) DF Moment (kip-ft) DF

2 MOVE1 1213.31 0.594 1184.47 0.580 1117.07 0.547 1202.90 0.589 1189.87 0.582 1140.04 0.5583 MOVE2 1135.23 0.556 1107.08 0.542 1040.32 0.509 1124.95 0.551 1112.19 0.544 1062.03 0.5204 MOVE3 1056.66 0.517 1029.30 0.504 963.22 0.471 1046.57 0.512 1034.12 0.506 983.67 0.4815 MOVE4 978.37 0.479 951.90 0.466 886.60 0.434 968.56 0.474 956.43 0.468 905.77 0.4436 MOVE5 901.10 0.441 875.67 0.429 811.82 0.397 891.67 0.436 879.91 0.431 829.42 0.4067 MOVE6 825.60 0.404 801.41 0.392 740.40 0.362 816.72 0.400 805.35 0.394 756.66 0.3708 MOVE7 752.62 0.368 729.91 0.357 671.79 0.329 744.44 0.364 733.52 0.359 686.65 0.3369 MOVE8 683.21 0.334 663.01 0.325 607.35 0.297 675.99 0.331 666.30 0.326 620.51 0.30410 MOVE9 618.15 0.303 600.36 0.294 548.25 0.268 612.07 0.300 603.35 0.295 559.91 0.274

Without Intermediate Diaphragms

0 30 60 0With Rigid Support Diaphragms


60Without Support Diaphragms

Skew Angle (deg) 30

L-82

Table L-19 – Moment Values, with Rigid Inter. Diaph., Beam 1, Bridge #18


(ft)Load Moment





With Rigid Support Diaphragms Without Support Diaphragms


6030Skew Angle (deg) 0 30 60 0

With Rigid Intermediate Diaphragms

Table L-20 – Moment Values, with Inter. Diaph., Beam 2, Bridge #18


(ft)Load Moment





600 30 60 0 30


With Rigid Support Diaphragms Without Support DiaphragmsSkew Angle (deg)


Table L-21 – Moment Values, with Rigid Inter. Diaph., Beam 2, Bridge #18


(ft)Load Moment





With Rigid Support Diaphragms Without Support DiaphragmsSkew Angle (deg) 0 30 60 0 30 60

Moment Values for Beam 2With Rigid Intermediate Diaphragms

L-83

Deformed Shape of Bridge With and Without the Presence of Rigid Intermediate Diaphragms:

Shown below is the deformed shape for MOVE1 and MOVE9.

Figure L-118 – Deformed Shape without Intermediate Diaphragms, Move1

L-84

Figure L-119 – Deformed Shape with Rigid Intermediate Diaphragms, Move1

Figure L-120 - Without Intermediate Diaphragms

Figure L-121 - With Rigid Intermediate Diaphragms

L-85


Skew Angle Effect on Moment Distribution for Beam 1 (MOVE1)Without Support Diaphragms

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60

Skew Angle Effect on Moment Distribution for Beam 1 (MOVE1)With Rigid Support Diaphragms

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 1 (MOVE2)


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600


Dis

trib

utio

n Fa

ctor



0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600


Dis

trib

utio

n Fa

ctor



With Rigid Support Diaphragms

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Figure L-122 - Effect of Skew Angle on Moment Distribution for Beam 1, MOVE1-4, Bridge #18

L-86


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0 30 60

Skew Angle (deg)

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Skew Angle (deg)

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0 30 60

Skew Angle (deg)

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With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 1 (MOVE7)


0.250

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0 30 60

Skew Angle (deg)

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0 30 60

Skew Angle (deg)

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Figure L-123 - Effect of Skew Angle on Moment Distribution for Beam 1, MOVE5-8, Bridge #18

L-87


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0 30 60


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Skew Angle (deg)

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Skew Angle (deg)

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Figure L-124 - Effect of Skew Angle on Moment Distribution for Beam 1, MOVE9, Bridge #18

L-88



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0 30 60


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0 30 60

Skew Angle (deg)

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n Fa

ctor


Skew Angle (deg)

Dis

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n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms


0.200

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Dis

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0 30 60

Skew Angle (deg)

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0 30 60

Skew Angle (deg)

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L-89


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0 30 60

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Skew Angle (deg)

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n Fa

ctor



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Skew Angle (deg)

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Skew Angle (deg)

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L-90


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0 30 60


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Skew Angle (deg)

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Skew Angle (deg)

Dis

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ctor


Figure L-127 - Effect of Skew Angle on Moment Distribution for Beam 2, MOVE9, Bridge #18


Effect of Vehicle Location on Moment Distribution for Beam 1(Without Intermediate Diaphragms - Without Support Diaphragms)

0.200

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0.650

0.700

2 3 4 5 6 7 8 9

Distance From Barrier (ft)

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ctor

10

0 Skew 30 Skew 60 Skew

Figure L-128 – Moment vs. Vehicle Location, without Inter. Diaph., without Sup. Diaph., Beam 1, Bridge #18

L-91

Effect of Vehicle Location on Moment Distribution for Beam 1(Without Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

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0.550

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0.650

0.700

2 3 4 5 6 7 8 9


Dis

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n Fa

ctor

10


Figure L-129 – Moment vs. Vehicle Location, without Inter. Diaph., with Rigid Sup. Diaph., Beam 1, Bridge #18

Effect of Vehicle Location on Moment Distribution for Beam 1(With Equivalent Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

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0.650

0.700

2 3 4 5 6 7 8 9


Dis

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n Fa

ctor

10


Figure L-130 – Moment vs. Vehicle Location, with Inter. Diaph., without Sup. Diaph., Beam 1, Bridge #18

L-92

Effect of Vehicle Location on Moment Distribution for Beam 1(With Rigid Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

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0.650

0.700

2 3 4 5 6 7 8 9


Dis

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n Fa

ctor

10


Figure L-131 – Moment vs. Vehicle Location, with Rigid Inter. Diaph., without Sup. Diaph., Beam 1, Bridge #18

Effect of Vehicle Location on Moment Distribution for Beam 1(With Rigid Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

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0.550

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0.650

0.700

2 3 4 5 6 7 8 9


Dis

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ctor

10


Figure L-132 – Moment vs. Vehicle Location, with Rigid Inter. Diaph., with Rigid Sup. Diaph., Beam 1, Bridge #18

L-93


Effect of Vehicle Location on Moment Distribution for Beam 2(Without Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

2 3 4 5 6 7 8 9


Dis

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n Fa

ctor

10


Figure L-133 – Moment vs. Vehicle Location, without Inter. Diaph., without Sup. Diaph., Beam 2, Bridge #18

Effect of Vehicle Location on Moment Distribution for Beam 2(Without Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

2 3 4 5 6 7 8 9


Dis

trib

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n Fa

ctor

10


Figure L-134 – Moment vs. Vehicle Location, without Inter. Diaph., with Rigid Sup. Diaph., Beam 2, Bridge #18

L-94

Effect of Vehicle Location on Moment Distribution for Beam 2(With Equivalent Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

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0.650

0.700

2 3 4 5 6 7 8 9


Dis

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n Fa

ctor

10


Figure L-135 – Moment vs. Vehicle Location, with Inter. Diaph., without Sup. Diaph., Beam 2, Bridge #18

Effect of Vehicle Location on Moment Distribution for Beam 2(With Rigid Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

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0.700

2 3 4 5 6 7 8 9


Dis

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ctor

10


Figure L-136 – Moment vs. Vehicle Location, with Rigid Inter. Diaph., without Sup. Diaph., Beam 2, Bridge #18

L-95

Effect of Vehicle Location on Moment Distribution for Beam 2(With Rigid Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

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2 3 4 5 6 7 8 9


Dis

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10


Figure L-137 – Moment vs. Vehicle Location, with Rigid Inter. Diaph., with Rigid Sup. Diaph., Beam 2, Bridge #18

L-96


Angle)

Effect of Intermediate Diaphragms for Beam 1 (MOVE1)

0

100

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900

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1200

1300

0 19 38 57 76 95 114 133 152

Distance From Support (ft)

Mom

ent (

kip-

ft)


0° Skew Angle Without Support Diaphragms

Figure L-138 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE1, Bridge #18


0

100

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700

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1300

0 19 38 57 76 95 114 133 15


Mom

ent (

kip-

ft)

2


0° Skew Angle With Rigid Support Diaphragms

Figure L-139 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE1, Bridge #18

L-97


0

100

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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 15


Mom

ent (

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2




L-98


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 15


Mom

ent (

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2




L-99


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 15


Mom

ent (

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2




L-100


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 15


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ent (

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2




L-101


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0 19 38 57 76 95 114 133 1


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ent (

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52





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0 19 38 57 76 95 114 133 15


Mom

ent (

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2




L-102


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0 19 38 57 76 95 114 133 1


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ent (

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52





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0 19 38 57 76 95 114 133 15


Mom

ent (

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2




L-103


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0 19 38 57 76 95 114 133 1


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ent (

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52





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0 19 38 57 76 95 114 133 15


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ent (

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2




L-104


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ent (

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0 19 38 57 76 95 114 133 1


Mom

ent (

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52




L-105


Angle)


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0 19 38 57 76 95 114 133 1


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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

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L-106


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ent (

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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

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L-107


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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

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L-108


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0 19 38 57 76 95 114 133 1


Mom

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52





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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

kip-

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30° Skew AngleWith Rigid Support Diaphragms


L-109


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52

With Rigid Intermediate Diaphragms WithoutIntermediate Diaphragms With Equivalent Intermediate Diaphragms




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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

kip-

ft)

With Rigid Intermediate Diaphragms WithoutIntermediate Diaphragms



L-110


0

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0 19 38 57 76 95 114 133 1


Mom

ent (

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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

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L-111


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0 19 38 57 76 95 114 133 1


Mom

ent (

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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

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ft)




L-112


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





0

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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

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L-113


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00


Mom

ent (

kip-

ft)




L-114


Angle)


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 1


Mom

ent (

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52




L-115


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 1


Mom

ent (

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52


60° Skew AngleWith Rigid Support Diaphragms


L-116


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0 19 38 57 76 95 114 133 1


Mom

ent (

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0 19 38 57 76 95 114 133 1


Mom

ent (

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52




L-117


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 1


Mom

ent (

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52




L-118


0

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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 1


Mom

ent (

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52




L-119


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 1


Mom

ent (

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52




L-120


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





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0 19 38 57 76 95 114 133 1


Mom

ent (

kip-

ft)

52

With Rigid Intermediate Diaphragms Without Intermediate Cross Frames



L-121


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0 19 38 57 76 95 114 133 1


Mom

ent (

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52





0

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0 19 38 57 76 95 114 133 1


Mom

ent (

kip-

ft)

52




L-122


0

100

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1100

1200

1300

0 19 38 57 76 95 114 133 1


Mom

ent (

kip-

ft)

52





0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

0 19 38 57 76 95 114 133 1


Mom

ent (

kip-

ft)

52




L-123

Effect of Intermediate Diaphragms on Moment Magnitude for Beam 2: (0° Skew Angle)


0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)





0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)




L-124


0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)





0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)




NOTE: The trends for MOVE2-8 are similar to Beam 1.

L-125


Angle)


0100200300400500600700800900

1000110012001300140015001600

0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00


Mom

ent (

kip-

ft)





0100200300400500600700800900

1000110012001300140015001600

0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00


Mom

ent (

kip-

ft)




L-126


0100200300400500600700800900

1000110012001300140015001600

0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00


Mom

ent (

kip-

ft)





0100200300400500600700800900

1000110012001300140015001600

0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00


Mom

ent (

kip-

ft)





L-127


Angle)


0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)





0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)




L-128


0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)





0100200300400500600700800900

1000110012001300140015001600

0 26 52 78 104 130 156 182


Mom

ent (

kip-

ft)





L-129

Parametric Study Results: SHEAR

Table L-22 – Shear at Obtuse Corner, Beam 1, No Intermediate Diaphragms

Distance From

Barrier (ft)

Load Shear (kips) DF Shear

(kips) DF Shear (kips) DF Shear


(kips) DF


10 MOVE9 17.88 0.258 19.96 0.288 22.76 0.329 17.70 0.256 19.93 0.288 23.17 0.335

Without Intermediate DiaphragmsWithout Support Diaphragms

060

Shear at Obtuse Corner for Beam 1

30 60Skew Angle (deg)With Rigid Support Diaphragms

0 30

Table L-23 – Shear at Obtuse Corner, Beam 1, Rigid Intermediate Diaphragms

Distance From

Barrier (ft)




(kips) DF


10 MOVE9 26.85 0.388 30.20 0.436 36.68 0.530 26.88 0.388 29.65 0.428 30.88 0.446

0 30Skew Angle (deg)With Rigid Support Diaphragms Without Support Diaphragms

30 60

With Rigid Intermediate DiaphragmsShear at Obtuse Corner for Beam 1

060

Table L-24 – Shear at Obtuse Corner, Beam 8, No Intermediate Diaphragms

Distance From

Barrier (ft)




(kips) DF


Without Support Diaphragms30 60 30 60

With Rigid Support Diaphragms0Skew Angle (deg)

Shear at Obtuse Corner for Beam 8Without Intermediate Diaphragms

0

L-130

Table L-25 – Shear at Obtuse Corner, Beam 8, Rigid Intermediate Diaphragms

Distance From

Barrier (ft)




(kips) DF


With Rigid Support Diaphragms Without Support DiaphragmsWith Rigid Intermediate Diaphragms

0 30 0

Shear at Obtuse Corner for Beam 8

30 6060Skew Angle (deg)

L-131


Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse CornerMOVE 1 - Without Support Diaphragms

0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse CornerMOVE1 - With Rigid Support Diaphragms

0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate DiaphragmsSkew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner

MOVE2 - Without Support Diaphragms

0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor


Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner

MOVE2 - With Rigid Support Diaphragms

0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner


0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor


Figure L-204 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 1, MOVE1-4,Bridge #18

L-132

Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse CornerMOVE5 - Without Support Diaphragms

0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60


0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor


Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor




0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



L-133


0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60



0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

60


Figure L-206 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 1, MOVE9,Bridge #18

L-134



0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.7500.800

0.850

0 30 60


0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor


Dis

trib

utio

n Fa

ctor



0.250

0.3000.350

0.400

0.4500.500

0.5500.600

0.6500.700

0.750

0.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse Corner


0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor




0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Cross Frames Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse Corner


0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



L-135


0.250

0.3000.350

0.400

0.4500.500

0.5500.600

0.6500.700

0.750

0.8000.850

0 30 60


0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Cross FramesSkew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.250

0.300

0.350

0.400

0.450

0.5000.550

0.600

0.650

0.700

0.750

0.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.250

0.3000.350

0.400

0.4500.500

0.5500.600

0.6500.700

0.750

0.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor




0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



0.250

0.3000.350

0.400

0.4500.500

0.550

0.6000.650

0.700

0.7500.800

0.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor



L-136


0.250

0.3000.350

0.400

0.4500.500

0.5500.600

0.6500.700

0.750

0.8000.850

0 30 60


0.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.7500.8000.850

0 30 60

Skew Angle (deg)

Dis

trib

utio

n Fa

ctor


Dis

trib

utio

n Fa

ctor

With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Figure L-209 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 8, MOVE18,Bridge #18

L-137


Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(Without Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-210 – Shear vs. Vehicle Location, without Inter. Diaph., without Sup. Diaph., Beam 1, Bridge #18

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(Without Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-211 – Shear vs. Vehicle Location, without Inter. Diaph., with Rigid Sup. Diaph., Beam 1, Bridge #18

L-138

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(With Equivalent Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-212 – Shear vs. Vehicle Location, with Inter. Diaph., without Sup. Diaph., Beam 1, Bridge #18

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(With Rigid Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-213 – Shear vs. Vehicle Location, with Rigid Inter. Diaph., without Sup. Diaph., Beam 1, Bridge #18

L-139

Effect of Vehicle Location on Shear Distribution for Beam 1 at Obtuse Corner(With Rigid Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-214 – Shear vs. Vehicle Location, with Rigid Inter. Diaph., with Rigid Sup. Diaph., Beam 1, Bridge #18


Effect of Vehicle Location on Shear Distribution for Beam 8 at Obtuse Corner(Without Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-215 – Shear vs. Vehicle Location, without Inter. Diaph., without Sup. Diaph., Beam 8, Bridge #18

L-140

Effect of Vehicle Location on Shear Distribution for Beam 8 at Obtuse Corner(Without Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-216 – Shear vs. Vehicle Location, without Inter. Diaph., with Rigid Sup. Diaph., Beam 8, Bridge #18

Effect of Vehicle Location on Shear Distribution for Beam 8 at Obtuse Corner(With Equivalent Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-217 – Shear vs. Vehicle Location, with Inter. Diaph., without Sup. Diaph., Beam 8, Bridge #18

L-141

Effect of Vehicle Location on Shear Distribution for Beam 8 at Obtuse Corner(With Rigid Intermediate Diaphragms - Without Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-218 – Shear vs. Vehicle Location, with Rigid Inter. Diaph., without Sup. Diaph., Beam 8, Bridge #18

Effect of Vehicle Location on Shear Distribution for Beam 8 at Obtuse Corner(With Rigid Intermediate Diaphragms - With Rigid Support Diaphragms)

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

2 3 4 5 6 7 8 9


Dis

trib

utio

n Fa

ctor

10


Figure L-219 – Shear vs. Vehicle Location, with Rigid Inter. Diaph., with Rigid Sup. Diaph., Beam 8, Bridge #18

L-142

Maximum Shear Values at End of Span for MOVE1 (Beam 1 & 2) and MOVE10 (Beam 7 & 8)

– WITHOUT SUPPORT DIAPHRAGMS:


V = 49.37 kipsDF = 0.713

V = 54.81 kipsDF = 0.783

V = 48.94 kipsDF = 0.735

V = 45.25 kipsDF = 0.679

60°

V = 46.22 kipsDF = 0.694

30°

V = 48.00 kipsDF = 0.721

V = 48.88 kipsDF = 0.698

V = 54.86 kipsDF = 0.792

V = 54.19 kipsDF = 0.783

V = 51.50 kipsDF = 0.736

V = 51.07 kipsDF = 0.738

V = 48.01 kipsDF = 0.713

V = 57.63 kipsDF = 0.823

V = 50.61 kipsDF = 0.752

V = 50.90 kipsDF = 0.756

V = 47.16 kipsDF = 0.701

V = 46.30 kipsDF = 0.695

V = 52.10 kipsDF = 0.753

V = 52.54 kipsDF = 0.750

V = 49.47 kipsDF = 0.7357

1 2

8

7 8

21

7

1 2

8

V = 52.10 kipsDF = 0.753

V = 46.30 kipsDF = 0.695

V = 52.54 kipsDF = 0.750

V = 49.47 kipsDF = 0.735



Figure L-220 – Shear Values without Inter. Diaph., without Sup. Diaph., Bridge #18

W ith E quivalen t Interm ediate D iaphragm s


V = 46.07 kipsD F = 0.692

V = 51 .70 k ipsD F = 0 .747

V = 52.16 kipsD F = 0.745

V = 49 .20 k ipsD F = 0 .731

V = 48 .74 k ipsD F = 0 .732

V = 50.75 kipsD F = 0.733

V = 54.81 kipsD F = 0.783

V = 47 .44 k ipsD F = 0 .705

V = 50 .76 k ipsD F = 0 .754

V = 51.14 kipsD F = 0.730

V = 54 .19 k ipsD F = 0 .783

V = 45 .85 kipsD F = 0 .688

V = 47.62 kipsD F = 0.715

V = 48 .00 k ipsD F = 0 .693

V = 58 .01 k ipsD F = 0 .828

V = 46.79 kipsD F = 0.695

V = 48 .40 k ipsD F = 0 .691

V = 50.20 kipsD F = 0.746

V = 54.79 kipsD F = 0.791

V = 45 .02 kipsD F = 0 .676

V = 51 .70 k ipsD F = 0 .747

V = 46.07 kipsD F = 0.692

V = 52.16 kipsD F = 0.745

V = 49 .20 k ipsD F = 0 .731


60°

30°

7

1 2

8

7 8

21

7

1 2

8

Figure L-221 – Shear Values with Inter. Diaph., without Sup. Diaph., Bridge #18

L-143

60°

30°


V = 47.70 kipsDF = 0.689

V = 41.64 kipsDF = 0.625

V = 47.68 kipsDF = 0.681

V = 45.32 kipsDF = 0.673

V = 52.72 kipsDF = 0.762

V = 40.80 kipsDF = 0.606

V = 51.00 kipsDF = 0.737

V = 36.40 kipsDF = 0.541

V = 38.00 kipsDF = 0.571

V = 53.51 kipsDF = 0.764

V = 35.31 kipsDF = 0.530

V = 56.25 kipsDF = 0.803

V = 28.42 kipsDF = 0.427

V = 35.60 kipsDF = 0.508

V = 35.53 kipsDF = 0.513

V = 29.84 kipsDF = 0.443

V = 38.97 kipsDF = 0.585

V = 34.86 kipsDF = 0.498

V = 37.38 kipsDF = 0.540

V = 40.36 kipsDF = 0.600

7

1 2

8

7 8

21

7

1 2

8



V = 45.32 kipsDF = 0.673

V = 47.70 kipsDF = 0.689

V = 41.64 kipsDF = 0.625

V = 47.68 kipsDF = 0.681

Figure L-222 – Shear Values with Rigid Inter. Diaph., without Sup. Diaph., Bridge #18

Maximum Shear Values at End of Span for MOVE1 (Beam 1 & 2) and MOVE10 (Beam 7 & 8)

– WITH RIGID SUPPORT DIAPHRAGMS:

V = 52.70 kipsDF = 0.761

V = 51.26 kipsDF = 0.740

V = 54.54 kipsDF = 0.788

V = 54.73 kipsDF = 0.791

30°

1

60°

V = 35.88 kipsDF = 0.539

V = 45.36 kipsDF = 0.681

V = 48.12 kipsDF = 0.722 7

1

V = 46.61 kipsDF = 0.700


V = 48.70 kipsDF = 0.731 7

1

7

V = 38.48 kipsDF = 0.572

2

V = 38.93 kipsDF = 0.556

V = 50.55 kipDF = 0.751

V = 36.32 kipsDF = 0.525

V = 58.46 kipsDF = 0.835

V = 51.68 kipsDF = 0.738

2

8

V = 50.77 kipsDF = 0.754

V = 49.87 kipsDF = 0.741

V = 53.06 kipsDF = 0.758

V = 55.21 kipsDF = 0.788 8

2

8

V = 47.57 kipsDF = 0.707



V = 52.70 kipsDF = 0.761

V = 46.61 kipsDF = 0.700

V = 49.87 kipsDF = 0.741

V = 53.06 kipsDF = 0.758

Figure L-223 – Shear Values without Inter. Diaph., with Rigid Sup. Diaph., Bridge #18

L-144

60°

1

7

30°1

7


7

1

2

8

2

8

8

2

V = 41.47 kipsDF = 0.623

V = 47.82 kipsDF = 0.691

V = 47.86 kipsDF = 0.684

V = 45.47 kipsDF = 0.675

V = 28.70 kipsDF = 0.431

V = 48.92 kipsDF = 0.734

V = 29.77 kipsDF = 0.442

V = 36.49 kipsDF = 0.527

V = 54.37 kipsDF = 0.776

V = 53.66 kipsDF = 0.775

V = 50.12 kipsDF = 0.745

V = 36.72 kipsDF = 0.524

V = 30.08 kipsDF = 0.447

V = 52.41 kipsDF = 0.787

V = 25.61 kipsDF = 0.370

V = 57.49 kipsDF = 0.821

V = 56.12 kipsDF = 0.811

V = 27.86 kipsDF = 0.418

V = 29.82 kipsDF = 0.426

V = 51.26 kipsDF = 0.761



V = 47.82 kipsDF = 0.691

V = 41.47 kipsDF = 0.623

V = 47.86 kipsDF = 0.684

V = 45.47 kipsDF = 0.675

Figure L-224 – Shear Values with Rigid Inter. Diaph., with Rigid Sup. Diaph., Bridge #18

L-145

Parametric Study Results: REACTION

Table L-26 – Reactions, No Intermediate Diaphragms

Reaction (kip) DF Reaction

(kip) DF Reaction (kip) DF Reaction



(kip) DF Reaction (kip) DF

2 MOVE1 51.54 0.774 56.28 0.781 52.43 0.779 50.44 0.757 57.41 0.797 54.27 0.806 50.67 0.761 62.47 0.867 56.00 0.8323 MOVE2 45.42 0.682 48.97 0.679 46.20 0.686 44.19 0.663 50.76 0.704 48.39 0.719 44.59 0.669 57.08 0.792 50.82 0.7554 MOVE3 39.38 0.591 41.90 0.581 40.05 0.595 38.09 0.572 44.76 0.621 42.45 0.631 38.72 0.581 52.01 0.722 45.75 0.6805 MOVE4 33.48 0.503 35.87 0.498 34.07 0.506 32.22 0.484 39.53 0.548 36.50 0.542 33.10 0.497 47.25 0.656 40.79 0.6066 MOVE5 27.81 0.418 31.29 0.434 28.32 0.421 26.64 0.400 35.01 0.486 31.14 0.463 27.68 0.416 42.83 0.594 36.00 0.5357 MOVE6 22.76 0.342 27.64 0.383 24.02 0.357 21.43 0.322 31.05 0.431 27.12 0.403 22.08 0.331 38.69 0.537 31.93 0.4748 MOVE7 19.48 0.292 24.58 0.341 20.95 0.311 16.80 0.252 27.56 0.382 23.90 0.355 16.64 0.250 35.84 0.497 28.53 0.4249 MOVE8 16.97 0.255 21.93 0.304 18.47 0.274 14.41 0.216 21.42 0.297 21.22 0.315 11.69 0.176 31.22 0.433 25.56 0.38010 MOVE9 14.91 0.224 19.57 0.272 16.37 0.243 12.65 0.190 21.56 0.299 18.88 0.280 8.92 0.134 27.83 0.386 22.94 0.341

Without Support Diaphragms - Without Intermediate DiaphragmsMaximum Reactions - Beam Line 4 (Beam 1 & 2)

60300Skew Angle (deg)BentAbutment 1

Load Position


(ft)

Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2

Table L-27 – Reactions, Equivalent Intermediate Diaphragms







Without Support Diaphragms - With Equivalent Intermediate DiaphragmsMaximum Reactions - Beam Line 4 (Beam 1 & 2)


Load Position


(ft)


L-146

Table L-28 – Reactions, Rigid Intermediate Diaphragms







Without Support Diaphragms - With Rigid Intermediate DiaphragmsMaximum Reactions - Beam Line 4 (Beam 1 & 2)


Load Position


(ft)


Table L-29 – Reactions, No Intermediate Diaphragms, Rigid Support Diaphragms







Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2BentAbutment 1Load

Position


(ft)

60300Skew Angle (deg)With Rigid Support Diaphragms - Without Intermediate Diaphragms

Maximum Reactions - Beam Line 4 (Beam 1 & 2)

L-147

Table L-30 – Reactions, Rigid Intermediate Diaphragms, Rigid Support Diaphragms







Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2BentAbutment 1Load

Position


(ft)

60300Skew Angle (deg)With Rigid Support Diaphragms - With Rigid Intermediate Diaphragms


Table L-31 - Reactions, No Intermediate Diaphragms







0Without Support Diaphragms - Without Intermediate Diaphragms


Abutment 1 Bent Abutment 2Distance From Barrier

(ft)

Load Position

Abutment 1 Bent30

Abutment 260

Abutment 1 Bent Abutment 2Skew Angle (deg)

L-148

Table L-32 – Reactions, Equivalent Intermediate Diaphragms







Abutment 1 Bent

Maximum Reactions - Beam Line 1 (Beam 7 & 8)Without Support Diaphragms - With Equivalent Intermediate Diaphragms

0 30 60Abutment 2 Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2

Skew Angle (deg)


(ft)

Load Position

Table L-33 – Reactions, Rigid Intermediate Diaphragms







Maximum Reactions - Beam Line 1 (Beam 7 & 8)Without Support Diaphragms - With Rigid Intermediate Diaphragms

Skew Angle (deg) 0 30 60


(ft)

Load Position

Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2

L-149

Table L-34 – Reactions, No Intermediate Diaphragms, Rigid Support Diaphragms







Maximum Reactions - Beam Line 1 (Beam 7 & 8)With Rigid Support Diaphragms - Without Intermediate Diaphragms



(ft)

Load Position


Table L-35 – Reactions, Rigid Intermediate Diaphragms, Rigid Support Diaphragms







Maximum Reactions - Beam Line 1 (Beam 7 & 8)With Rigid Support Diaphragms - With Rigid Intermediate Diaphragms



(ft)

Load Position


L-150

Maximum Support Reactions and Distribution Factors for MOVE1 (Beam 1 & 2) and MOVE10 (Beam 7 & 8) – WITHOUT SUPPORT DIAPHRAGMS:

R = 57.94 kipsDF = 0.804

R = 53.67 kipsDF = 0.806

60°

R = 50.67 kipsDF = 0.761

R = 50.44 kipsDF = 0.757

30°

R = 51.54 kipsDF = 0.774

R = 55.45 kipsDF = 0.832

R = 62.47 kipsDF = 0.867

R = 57.41 kipsDF = 0.796

R = 56.28 kipsDF = 0.781

R = 51.54 kipsDF = 0.774

R = 56.28 kipsDF = 0.781

R = 51.66 kipsDF = 0.767

R = 63.07 kipsDF = 0.875

R = 56.00 kipsDF = 0.832

R = 54.27 kipsDF = 0.806

R = 52.43 kipsDF = 0.779

R = 51.92 kipsDF = 0.771

R = 52.43 kipsDF = 0.779

1

7

2

8

7

1

8

2

7

1 2

8




Figure L-225 – Shear Values without Inter. Diaph., without Sup. Diaph., Bridge #18

With Equivalent Intermediate Diaphragms



R = 51.27 kipsDF = 0.770

R = 55.68 kipsDF = 0.773

R = 52.05 kipsDF = 0.773

R = 52.77 kipsDF = 0.792

R = 51.22 kipsDF = 0.761

R = 57.49 kipsDF = 0.798

R = 50.22 kipsDF = 0.754

R = 57.06 kipsDF = 0.792

R = 53.48 kipsDF = 0.794

R = 55.05 kipsDF = 0.826

R = 63.20 kipsDF = 0.877

R = 51.55 kipsDF = 0.766

R = 50.50 kipsDF = 0.758

R = 62.65 kipsDF = 0.869

R = 55.67 kipsDF = 0.827

R = 51.27 kipsDF = 0.770

R = 52.05 kipsDF = 0.773

R = 55.68 kipsDF = 0.773

60°

30°

1

7

2

8

7

1

8

2

7

1 2

8

Figure L-226 – Shear Values with Inter. Diaph., without Sup. Diaph., Bridge #18

L-151

R = 122.65 kipsDF = 1.702

R = 86.95 kipsDF = 1.305

R = 46.40 kipsDF = 0.697

60°

R = 39.10 kipsDF = 0.587

30°

R = 66.86 kipsDF = 1.004

R = 96.21 kipsDF = 1.335

R = 118.90 kipsDF = 1.650

R = 40.02 kipsDF = 0.594

R = 98.86 kipsDF = 1.372

R = 70.03 kipsDF = 1.040

R = 90.26 kipsDF = 1.341

R = 47.31 kipsDF = 0.703

R = 49.40 kipsDF = 0.742

R = 55.27 kipsDF = 0.767

R = 50.15 kipsDF = 0.745

1

7

2

8

1

7

2

8

1

7

2

8




R = 49.40 kipsDF = 0.742

R = 55.27 kipsDF = 0.767

R = 50.15 kipsDF = 0.745

Figure L-227 – Shear Values with Rigid Inter. Diaph., without Sup. Diaph., Bridge #18

Maximum Support Reactions and Distribution Factors for MOVE1 (Beam 1 & 2)

and MOVE10 (Beam 7 & 8) – WITH RIGID SUPPORT DIAPHRAGMS:

7

30°

1

60°

R = 51.04 kipsDF = 0.766

1

R = 52.06 kipsDF = 0.782

R = 55.40 kipsDF = 0.832

1

7

2

7

R = 60.93 kipsDF = 0.845

8

2

R = 56.37 kipsDF = 0.837

R = 52.22 kipsDF = 0.776

R = 52.83 kipsDF = 0.785

R = 58.17 kipsDF = 0.807

R = 61.36 kipsDF = 0.851 8

2

8

R = 49.84 kipsDF = 0.748

R = 63.52 kipsDF = 0.881

R = 57.62 kipsDF = 0.856

R = 56.74 kipsDF = 0.852

R = 63.04 kipsDF = 0.875

R = 51.07 kipsDF = 0.759




R = 52.06 kipsDF = 0.782

R = 58.17 kipsDF = 0.807

R = 52.83 kipsDF = 0.785

Figure L-228 – Shear Values without Inter. Diaph., with Rigid Sup. Diaph., Bridge #18

L-152

60°

1

7

2

8

7

30°1

7

1

2

8

8

2

R = 40.72 kipsDF = 0.611

R = 55.93 kipsDF = 0.776

R = 50.04 kipsDF = 0.743

R = 61.86 kipsDF = 0.929

R = 46.43 kipsDF = 0.690

R = 65.47 kipsDF = 0.908

R = 62.94 kipsDF = 0.935

R = 63.78 kipsDF = 0.885

R = 45.56 kipsDF = 0.684

R = 64.23 kipsDF = 0.964

R = 74.98 kipsDF = 1.040

R = 49.08 kipsDF = 0.729

R = 48.19 kipsDF = 0.723

R = 63.78 kipsDF = 0.885

R = 64.31 kipsDF = 0.955




R = 40.72 kipsDF = 0.611

R = 55.93 kipsDF = 0.776

R = 50.04 kipsDF = 0.743

Figure L-229 – Shear Values with Rigid Inter. Diaph., with Rigid Sup. Diaph., Bridge #18

L-153

Discussion of Results:

Effect of Skew Angle:

MOMENT:

As skew angle increased the moment distribution factors decreased for all loading

positions. For skew angles of 0° and 30°, the decrease, if any, in distribution factor was

negligible. However, larger decreases were shown to exist when the skew angle was

increased to 60°.

SHEAR:

Increasing the skew angle caused the shear distribution factors at the obtuse

corner of the bridge to increase for all loading positions.

Effect of Vehicle Location:

MOMENT:

An almost linear relationship existed between vehicle location and moment

distribution factor. As the vehicle was positioned farther away from the barrier, the

distribution factor decreased. This linearity was independent of support and/or

intermediate diaphragms.

SHEAR:

Vehicle location had the same effect on shear distribution as it did on moment

distribution.

Effect of Support Diaphragms:

MOMENT:

L-154

In general, support diaphragms did not seem to make a significant difference in

moment distribution factor. Rigid support diaphragms, when used in conjunction with

rigid intermediate diaphragms, seemed to have a more noticeable effect.

SHEAR:

The effect of support diaphragms on shear distribution at the obtuse corner of the

bridge was negligible. It was observed that support diaphragms caused a decrease in

shear values at the acute corner, however the values were not critical since the obtuse

corner controlled.

Effect of Intermediate Diaphragms:

MOMENT:

The equivalent intermediate diaphragms had a negligible effect on moment

distribution. Rigid intermediate diaphragms had a more pronounced effect for skew

angles of 30° and 60°.

SHEAR:

The equivalent intermediate diaphragms had a negligible effect on shear

distribution. The effect of rigid intermediate diaphragms was more significant, for all

skew angles considered, when the vehicle was positioned farther away from the girder.

L-155

APPENDIX L – PARAMETER STUDIES

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