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
Acute CornerObtuse Corner
θ
Acute CornerObtuse Corner
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
Skew Support Diaphragm
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
2 MOVE1 267.10 0.314 253.76 0.298 203.39 0.239 267.18 0.314 254.65 0.299 220.42 0.2593 MOVE2 298.32 0.350 284.05 0.333 227.83 0.267 299.84 0.352 285.65 0.335 317.66 0.3734 MOVE3 329.33 0.387 314.05 0.369 253.00 0.297 332.15 0.390 316.30 0.371 342.64 0.4025 MOVE4 359.00 0.421 342.69 0.402 280.76 0.330 362.99 0.426 345.51 0.406 348.72 0.4096 MOVE5 386.24 0.453 368.89 0.433 306.03 0.359 391.25 0.459 373.39 0.438 354.76 0.4177 MOVE6 409.95 0.481 392.25 0.461 327.49 0.384 415.83 0.488 400.96 0.471 359.63 0.4228 MOVE7 429.02 0.504 412.11 0.484 344.71 0.405 435.61 0.511 423.53 0.497 372.70 0.4389 MOVE8 442.35 0.519 427.65 0.502 359.97 0.423 449.49 0.528 439.97 0.517 392.85 0.461
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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE3)
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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE5)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE7)
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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE2)
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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE4)
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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE6)
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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE8)
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
Figure L-8 - Effect of Skew Angle on Moment Distribution for Beam 1, Bridge #24
L-11
Effect of Skew Angle on Moment Distribution for Beam 6:
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE1)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE3)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE5)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE7)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE2)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE4)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE6)
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
With Support Diaphragm Without Support Diaphragm
Skew Angle Effect on Moment Distribution for Beam 6 (MOVE8)
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
With Support Diaphragm Without Support Diaphragm
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
With Support Diaphragm Without Support Diaphragm
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
Vehicle Location (ft)
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
Vehicle Location (ft)
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
Vehicle Location (ft)
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
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
Vehicle Location (ft)
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
Vehicle Location (ft)
Dis
trib
utio
n Fa
ctor
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-15 - Moment Distribution with Vehicle Location and Diaphragm Stiffness, 30 Degree Skew
L-15
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
Vehicle Location (ft)
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-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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-18 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE1, Bridge #24
L-17
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE2)
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-19 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE2, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE2)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-20 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE2, Bridge #24
L-18
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE3)
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-21 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE3, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE3)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-22 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE3, Bridge #24
L-19
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE4)
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-23 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE4, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE4)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-24 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE4, Bridge #24
L-20
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE5)
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-25 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE5, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE5)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-26 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE5, Bridge #24
L-21
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE6)
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-27 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE6, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE6)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-28 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE6, Bridge #24
L-22
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE7)
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-29 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE7, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE7)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-30 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE7, Bridge #24
L-23
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE8)
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-31 – Inter. Diaph. at Quarter Points, Beam 1, 0° Skew, MOVE8, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 1 (MOVE8)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-32 – Inter. Diaph. at Midspan, Beam 1, 0° Skew, MOVE8, Bridge #24
L-24
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 6: (No Skew
Angle):
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE1)
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
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-33 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE1, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE1)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-34 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE1, Bridge #24
L-25
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE2)
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
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-35 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE2, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE2)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-36 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE2, Bridge #24
L-26
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE3)
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
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-37 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE3, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE3)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-38 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE3, Bridge #24
L-27
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE4)
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
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-39 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE4, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE4)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-40 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE4, Bridge #24
L-28
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE5)
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
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-41 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE5, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE5)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-42 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE5, Bridge #24
L-29
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE6)
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
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-43 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE6, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE6)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-44 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE6, Bridge #24
L-30
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE7)
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
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-45 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE7, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE7)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-46 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE7, Bridge #24
L-31
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE8)
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
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-47 – Inter. Diaph. at Quarter Points, Beam 6, 0° Skew, MOVE8, Bridge #24
Effect of Intermediate Diaphragm Placed at Midspan for Beam 6 (MOVE8)
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
Distance From Left Support (ft)
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)
Grillage Model: 0° Skew Angle with Support Diaphragm
Figure L-48 – Inter. Diaph. at Midspan, Beam 6, 0° Skew, MOVE8, Bridge #24
L-32
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 1: (30° 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: 30° Skew Angle with Support Diaphragm
Figure L-49 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE1, Bridge #24
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-50 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE1, Bridge #24
L-33
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE2)
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: 30° Skew Angle with Support Diaphragm
Figure L-51 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE2, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE2)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-52 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE2, Bridge #24
L-34
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE3)
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: 30° Skew Angle with Support Diaphragm
Figure L-53 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE3, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE3)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-54 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE3, Bridge #24
L-35
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE4)
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: 30° Skew Angle with Support Diaphragm
Figure L-55 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE4, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE4)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-56 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE4, Bridge #24
L-36
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE5)
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: 30° Skew Angle with Support Diaphragm
Figure L-57 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE5, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE5)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-58 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE5, Bridge #24
L-37
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE6)
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: 30° Skew Angle with Support Diaphragm
Figure L-59 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE6, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE6)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-60 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE6, Bridge #24
L-38
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE7)
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: 30° Skew Angle with Support Diaphragm
Figure L-61 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE7, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE7)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-62 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE7, Bridge #24
L-39
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 1 (MOVE8)
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: 30° Skew Angle with Support Diaphragm
Figure L-63 – Inter. Diaph. at Quarter Points, Beam 1, 30° Skew, MOVE8, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 1 (MOVE8)
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 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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-64 – Inter. Diaph. at Midspan, Beam 1, 30° Skew, MOVE8, Bridge #24
L-40
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 6: (30° Skew
Angle)
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE1)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-65 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE1, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE1)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-66 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE1, Bridge #24
L-41
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE2)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-67 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE2, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE2)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-68 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE2, Bridge #24
L-42
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE3)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-69 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE3, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE3)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-70 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE3, Bridge #24
L-43
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE4)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-71 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE4, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE4)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-72 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE4, Bridge #24
L-44
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE5)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-73 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE5, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE5)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-74 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE5, Bridge #24
L-45
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE6)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-75 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE6, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE6)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-76 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE6, Bridge #24
L-46
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE7)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-77 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE7, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE7)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-78 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE7, Bridge #24
L-47
Effect of Intermediate Diaphragms Placed at Quarter Points for Beam 6 (MOVE8)
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
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: 30° Skew Angle with Support Diaphragm
Figure L-79 – Inter. Diaph. at Quarter Points, Beam 6, 30° Skew, MOVE8, Bridge #24
Effect of Intermediate Diaphragms Placed at Midspan for Beam 6 (MOVE8)
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
Distance From Left Support (ft)
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)
Grillage Model: 30° Skew Angle with Support Diaphragm
Figure L-80 – Inter. Diaph. at Midspan, Beam 6, 30° Skew, MOVE8, Bridge #24
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
Distance From Left Support (ft)
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
Distance From Left Support (ft)
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
With Support Diaphragm Without Support Diaphragm
ANSYS (with diaph.)
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE3)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE5)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE7)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE2)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE4)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE6)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Obtuse Corner (MOVE8)
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
With Support Diaphragm Without Support Diaphragm
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE3)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE5)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE7)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE2)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE4)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE6)
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
With Support Diaphragm Without Support Diaphragm
Effect of Skew Angle on Shear Distribution for Beam 1 at Acute Corner (MOVE8)
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
With Support Diaphragm Without Support Diaphragm
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
Vehicle Location (ft)
Dis
trib
utio
n Fa
ctor
9
With Support Diaphragm Without Support Diaphragm
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
Vehicle Location (ft)
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
Vehicle Location (ft)
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
Vehicle Location (ft)
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-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
Vehicle Location (ft)
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-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
Vehicle Location (ft)
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-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
Vehicle Location (ft)
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-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
With Support Diaphragms
With Support Diaphragms
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
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:
With Support Diaphragms
With Support Diaphragms
With Support Diaphragms
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
Without Support Diaphragms
Without Support Diaphragms
Without Support Diaphragms
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
Distance From Left Support (ft)
Shea
r (k
ips)
No Skew30 Skew60 Skew
Figure L-98 – Maximum Shear Values Along Span 1, without Sup. Diaph., Beam 1, Bridge #24
Maximum Shear Along Span 1 (Beam 6)With Support Diaphragm
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
Distance From Left Support (ft)
Shea
r (k
ips)
No Skew30 Skew60 Skew
Figure L-99 – Maximum Shear Values Along Span 1, with Sup. Diaph., Beam 6, Bridge #24
L-61
Maximum Shear Along Span 1 (Beam 6)Without Support Diaphragm
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)
No Skew30 Skew60 Skew
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)
No Skew30 Skew60 Skew
g Span 5, with Sup. Diaph., Beam 5, Bridge #24
L-62
Maximum Shear Along Span 5 (Beam 5)Without Support Diaphragm
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
Distance From Left Support (ft)
Shea
r (k
ips)
No Skew30 Skew60 Skew
Figure L-102 – Maximum Shear Values Along Span 5, without Sup. Diaph., Beam 5, Bridge #24
Maximum Shear Along Span 5 (Beam 10)With Support Diaphragm
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
Distance From Left Support (ft)
Shea
r (k
ips)
No Skew30 Skew60 Skew
Figure L-103 – Maximum Shear Values Along Span 5, with Sup. Diaph., Beam 10, Bridge #24
L-63
Maximum Shear Along Span 5 (Beam 10)Without Support Diaphragm
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
Distance From Left Support (ft)
Shea
r (k
ips)
No Skew30 Skew60 Skew
Figure L-104 – Maximum Shear Values Along Span 5, without Sup. Diaph., Beam 10, Bridge #24
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"
Figure L-112 - Cross-Frame Location – Span 2
19'-11" 19'-11" 19'-11" 21'-1" 25' 25' 21'-1" 19'-11" 19'-11" 19'-11"
60°
Figure L-113 - Cross-Frame Location – Span 1
60°
19'-11" 19'-11" 19'-11" 23'-7" 25' 25' 25' 23'-7" 19'-11" 19'-11" 19'-11"
Figure L-114 - Cross-Frame Location – Span 2
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
Skew Support Diaphragm
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 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
Moment Values for Beam 1
60Without Support Diaphragms
Skew Angle (deg) 30
L-82
Table L-19 – Moment Values, with Rigid 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 Moment
(kip-ft) DF Moment (kip-ft) DF
2 MOVE1 1130.59 0.553 885.33 0.433 800.87 0.392 1134.31 0.555 959.47 0.470 851.50 0.4173 MOVE2 1079.82 0.529 848.98 0.416 770.96 0.377 1083.29 0.530 919.60 0.450 821.34 0.4024 MOVE3 1028.50 0.503 811.60 0.397 740.03 0.362 1031.32 0.505 881.95 0.432 790.37 0.3875 MOVE4 988.82 0.484 773.66 0.379 712.20 0.349 991.39 0.485 843.81 0.413 761.87 0.3736 MOVE5 949.13 0.465 737.74 0.361 685.82 0.336 951.49 0.466 805.98 0.394 737.31 0.3617 MOVE6 909.14 0.445 708.76 0.347 662.72 0.324 911.31 0.446 777.84 0.381 712.58 0.3498 MOVE7 868.81 0.425 687.08 0.336 644.29 0.315 870.76 0.426 749.35 0.367 687.67 0.3379 MOVE8 828.23 0.405 664.91 0.325 625.39 0.306 829.95 0.406 720.37 0.353 662.71 0.32410 MOVE9 787.63 0.386 642.09 0.314 605.86 0.297 789.15 0.386 690.91 0.338 637.63 0.312
With Rigid Support Diaphragms Without Support Diaphragms
Moment Values for Beam 1
6030Skew Angle (deg) 0 30 60 0
With Rigid Intermediate Diaphragms
Table L-20 – Moment Values, with Inter. Diaph., Beam 2, Bridge #18
Distance From Barrier
(ft)Load Moment
(kip-ft) DF Moment (kip-ft) DF Moment
(kip-ft) DF Moment (kip-ft) DF Moment
(kip-ft) DF Moment (kip-ft) DF
2 MOVE1 1589.59 0.660 1547.30 0.642 1431.21 0.594 1567.03 0.650 1554.21 0.645 1467.38 0.6093 MOVE2 1488.82 0.618 1451.06 0.602 1339.75 0.556 1469.78 0.610 1457.42 0.605 1372.87 0.5704 MOVE3 1387.65 0.576 1353.76 0.562 1247.30 0.518 1371.48 0.569 1359.59 0.564 1277.40 0.5305 MOVE4 1286.98 0.534 1256.46 0.522 1154.91 0.479 1273.17 0.528 1261.75 0.524 1182.03 0.4916 MOVE5 1187.74 0.493 1160.22 0.482 1063.65 0.442 1175.90 0.488 1164.98 0.484 1087.87 0.4527 MOVE6 1090.73 0.453 1065.94 0.442 974.49 0.404 1080.58 0.449 1070.17 0.444 995.84 0.4138 MOVE7 996.99 0.414 974.82 0.405 888.58 0.369 988.41 0.410 978.55 0.406 907.17 0.3779 MOVE8 907.66 0.377 887.81 0.369 806.93 0.335 900.70 0.374 891.03 0.370 822.85 0.34210 MOVE9 823.58 0.342 806.33 0.335 731.20 0.304 818.32 0.340 809.08 0.336 744.53 0.309
600 30 60 0 30
Moment Values for Beam 2
With Rigid Support Diaphragms Without Support DiaphragmsSkew Angle (deg)
Without Intermediate Diaphragms
Table L-21 – Moment Values, with Rigid Inter. Diaph., Beam 2, Bridge #18
Distance From Barrier
(ft)Load Moment
(kip-ft) DF Moment (kip-ft) DF Moment
(kip-ft) DF Moment (kip-ft) DF Moment
(kip-ft) DF Moment (kip-ft) DF
2 MOVE1 1503.83 0.624 1176.27 0.488 1017.57 0.422 1507.00 0.626 1268.36 0.526 1117.60 0.4643 MOVE2 1435.73 0.596 1131.37 0.470 981.06 0.407 1438.70 0.597 1217.70 0.505 1072.41 0.4454 MOVE3 1366.50 0.567 1085.41 0.451 943.54 0.392 1369.26 0.568 1165.97 0.484 1029.47 0.4275 MOVE4 1296.58 0.538 1038.86 0.431 905.45 0.376 1299.13 0.539 1113.65 0.462 990.65 0.4116 MOVE5 1226.58 0.509 992.18 0.412 873.84 0.363 1228.93 0.510 1063.71 0.442 953.50 0.3967 MOVE6 1158.16 0.481 953.72 0.396 845.52 0.351 1160.64 0.482 1024.33 0.425 920.51 0.3828 MOVE7 1103.13 0.458 920.69 0.382 816.98 0.339 1105.36 0.459 984.74 0.409 887.26 0.3689 MOVE8 1047.68 0.435 887.58 0.368 788.90 0.327 1049.67 0.436 945.11 0.392 853.84 0.35410 MOVE9 991.68 0.412 853.77 0.354 760.69 0.316 993.44 0.412 904.79 0.376 820.39 0.341
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
Effect of Skew Angle on Moment Distribution for Beam 1:
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
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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)
Without Support Diaphragms
0.250
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0 30 60Skew Angle (deg)
Dis
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE3)Without Support Diaphragms
0.250
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0.450
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0.600
0 30 60Skew Angle (deg)
Dis
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE4)Without Support Diaphragms
0.250
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0 30 60Skew Angle (deg)
Dis
trib
utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE2)
With Rigid Support Diaphragms
0.250
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0 30 60
Skew Angle (deg)
Dis
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE3)With Rigid Support Diaphragms
0.250
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0 30 60
Skew Angle (deg)
Dis
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE4)With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
Dis
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utio
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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
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE5)Without Support Diaphragms
0.250
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0 30 60
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE5)With Rigid Support Diaphragms
0.250
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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 (MOVE6)
Without Support Diaphragms
0.250
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0 30 60Skew 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 (MOVE7)
Without Support Diaphragms
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0 30 60Skew Angle (deg)
Dis
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 1 (MOVE8)
Without Support Diaphragms
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0 30 60Skew Angle (deg)
Dis
trib
utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE6)
With Rigid Support Diaphragms
0.250
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0 30 60
Skew Angle (deg)
Dis
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 1 (MOVE7)
With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
Dis
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 1 (MOVE8)
With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
Dis
trib
utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Figure L-123 - Effect of Skew Angle on Moment Distribution for Beam 1, MOVE5-8, Bridge #18
L-87
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE9)Without Support Diaphragms
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0 30 60
Skew Angle Effect on Moment Distribution for Beam 1 (MOVE9)With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
Dis
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utio
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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
Figure L-124 - Effect of Skew Angle on Moment Distribution for Beam 1, MOVE9, Bridge #18
L-88
Effect of Skew Angle on Moment Distribution for Beam 2:
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE1)Without Support Diaphragms
0.200
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0 30 60
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE1)With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Skew Angle (deg)
Dis
trib
utio
n Fa
ctor
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE2)Without Support Diaphragms
0.200
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0 30 60Skew Angle (deg)
Dis
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE3)Without Support Diaphragms
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0 30 60Skew Angle (deg)
Dis
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE4)Without Support Diaphragms
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0 30 60Skew Angle (deg)
Dis
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE2)With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
Dis
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utio
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE3)With Rigid Support Diaphragms
0.200
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE4)With Rigid Support Diaphragms
0.200
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0 30 60
Skew Angle (deg)
Dis
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utio
n Fa
ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Figure L-125 - Effect of Skew Angle on Moment Distribution for Beam 2, MOVE1-4, Bridge #18
L-89
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE5)Without Support Diaphragms
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0 30 60
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE5)With Rigid Support Diaphragms
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0 30 60
Skew Angle (deg)
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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 2 (MOVE6)
Without Support Diaphragms
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 2 (MOVE7)
Without Support Diaphragms
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 2 (MOVE8)
Without Support Diaphragms
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE6)
With Rigid Support Diaphragms
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Skew Angle (deg)
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ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 2 (MOVE7)
With Rigid Support Diaphragms
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With Rigid Intermediate Diaphragms Without Intermediate Diaphragms Skew Angle Effect on Moment Distribution for Beam 2 (MOVE8)
With Rigid Support Diaphragms
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n Fa
ctor
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Figure L-126 - Effect of Skew Angle on Moment Distribution for Beam 2, MOVE5-8, Bridge #18
L-90
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE9)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 30 60
Skew Angle Effect on Moment Distribution for Beam 2 (MOVE9)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 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
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:
Effect of Vehicle Location on Moment Distribution for Beam 1(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
Distance From Barrier (ft)
Dis
trib
utio
n Fa
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
0.400
0.450
0.500
0.550
0.600
0.650
0.700
2 3 4 5 6 7 8 9
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
0.400
0.450
0.500
0.550
0.600
0.650
0.700
2 3 4 5 6 7 8 9
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
0.600
0.650
0.700
2 3 4 5 6 7 8 9
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
0.400
0.450
0.500
0.550
0.600
0.650
0.700
2 3 4 5 6 7 8 9
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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:
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
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
0.450
0.500
0.550
0.600
0.650
0.700
2 3 4 5 6 7 8 9
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
2 3 4 5 6 7 8 9
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
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
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
Distance From Barrier (ft)
Dis
trib
utio
n Fa
ctor
10
0 Skew 30 Skew 60 Skew
Figure L-137 – Moment vs. Vehicle Location, with Rigid Inter. Diaph., with Rigid Sup. Diaph., Beam 2, Bridge #18
L-96
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 1: (No Skew
Angle)
Effect of Intermediate Diaphragms for Beam 1 (MOVE1)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 152
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-138 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE1, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE1)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-139 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE1, Bridge #18
L-97
Effect of Intermediate Diaphragms for Beam 1 (MOVE2)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-140 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE2, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE2)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-141 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE2, Bridge #18
L-98
Effect of Intermediate Diaphragms for Beam 1 (MOVE3)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-142 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE3, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE3)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-143 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE3, Bridge #18
L-99
Effect of Intermediate Diaphragms for Beam 1 (MOVE4)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-144 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE4, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE4)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-145 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE4, Bridge #18
L-100
Effect of Intermediate Diaphragms for Beam 1 (MOVE5)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-146 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE5, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE5)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-147 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE5, Bridge #18
L-101
Effect of Intermediate Diaphragms for Beam 1 (MOVE6)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-148 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE6, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE6)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-149 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE6, Bridge #18
L-102
Effect of Intermediate Diaphragms for Beam 1 (MOVE7)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-150 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE7, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE7)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-151 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE7, Bridge #18
L-103
Effect of Intermediate Diaphragms for Beam 1 (MOVE8)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-152 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE8, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE8)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 15
Distance From Support (ft)
Mom
ent (
kip-
ft)
2
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-153 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE8, Bridge #18
L-104
Effect of Intermediate Diaphragms for Beam 1 (MOVE9)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-154 – Inter. Diaph. without Sup. Diaph., Beam 1, 0° Skew, MOVE9, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE9)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-155 – Inter. Diaph. with Sup. Diaph., Beam 1, 0° Skew, MOVE9, Bridge #18
L-105
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 1: (30° Skew
Angle)
Effect of Intermediate Diaphragms for Beam 1 (MOVE1)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-156 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE1, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE1)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-157 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE1, Bridge #18
L-106
Effect of Intermediate Diaphragms for Beam 1 (MOVE2)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-158 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE2, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE2)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-159 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE2, Bridge #18
L-107
Effect of Intermediate Diaphragms for Beam 1 (MOVE3)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-160 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE3, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE3)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-161 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE3, Bridge #18
L-108
Effect of Intermediate Diaphragms for Beam 1 (MOVE4)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-162 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE4, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE4)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew AngleWith Rigid Support Diaphragms
Figure L-163 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE4, Bridge #18
L-109
Effect of Intermediate Diaphragms for Beam 1 (MOVE5)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms WithoutIntermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-164 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE5, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE5)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms WithoutIntermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-165 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE5, Bridge #18
L-110
Effect of Intermediate Diaphragms for Beam 1 (MOVE6)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-166 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE6, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE6)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-167 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE6, Bridge #18
L-111
Effect of Intermediate Diaphragms for Beam 1 (MOVE7)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-168 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE7, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE7)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-169 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE7, Bridge #18
L-112
Effect of Intermediate Diaphragms for Beam 1 (MOVE8)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-170 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE8, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE8)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-171 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE8, Bridge #18
L-113
Effect of Intermediate Diaphragms for Beam 1 (MOVE9)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-172 – Inter. Diaph. without Sup. Diaph., Beam 1, 30° Skew, MOVE9, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE9)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0.00 19.00 38.00 57.00 76.00 95.00 114.00 133.00 152.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-173 – Inter. Diaph. with Sup. Diaph., Beam 1, 30° Skew, MOVE9, Bridge #18
L-114
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 1: (60° Skew
Angle)
Effect of Intermediate Diaphragms for Beam 1 (MOVE1)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-174 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE1, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE1)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-175 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE1, Bridge #18
L-115
Effect of Intermediate Diaphragms for Beam 1 (MOVE2)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-176 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE2, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE2)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew AngleWith Rigid Support Diaphragms
Figure L-177 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE2, Bridge #18
L-116
Effect of Intermediate Diaphragms for Beam 1 (MOVE3)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-178 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE3, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE3)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-179 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE3, Bridge #18
L-117
Effect of Intermediate Diaphragms for Beam 1 (MOVE4)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-180 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE4, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE4)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-181 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE4, Bridge #18
L-118
Effect of Intermediate Diaphragms for Beam 1 (MOVE5)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-182 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE5, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE5)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-183 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE5, Bridge #18
L-119
Effect of Intermediate Diaphragms for Beam 1 (MOVE6)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-184 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE6, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE6)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-185 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE6, Bridge #18
L-120
Effect of Intermediate Diaphragms for Beam 1 (MOVE7)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-186 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE7, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE7)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames
60° Skew Angle With Rigid Support Diaphragms
Figure L-187 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE7, Bridge #18
L-121
Effect of Intermediate Diaphragms for Beam 1 (MOVE8)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-188 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE8, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE8)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-189 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE8, Bridge #18
L-122
Effect of Intermediate Diaphragms for Beam 1 (MOVE9)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-190 – Inter. Diaph. without Sup. Diaph., Beam 1, 60° Skew, MOVE9, Bridge #18
Effect of Intermediate Diaphragms for Beam 1 (MOVE9)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 19 38 57 76 95 114 133 1
Distance From Support (ft)
Mom
ent (
kip-
ft)
52
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames
60° Skew Angle With Rigid Support Diaphragms
Figure L-191 – Inter. Diaph. with Sup. Diaph., Beam 1, 60° Skew, MOVE9, Bridge #18
L-123
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 2: (0° Skew Angle)
Effect of Intermediate Diaphragms for Beam 2 (MOVE1)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-192 – Inter. Diaph. without Sup. Diaph., Beam 2, 0° Skew, MOVE1, Bridge #18
Effect of Intermediate Diaphragms for Beam 2 (MOVE1)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-193 – Inter. Diaph. with Sup. Diaph., Beam 2, 0° Skew, MOVE1, Bridge #18
L-124
Effect of Intermediate Diaphragms for Beam 2 (MOVE9)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
0° Skew Angle Without Support Diaphragms
Figure L-194 – Inter. Diaph. without Sup. Diaph., Beam 2, 0° Skew, MOVE9, Bridge #18
Effect of Intermediate Diaphragms for Beam 2 (MOVE9)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
0° Skew Angle With Rigid Support Diaphragms
Figure L-195 – Inter. Diaph. with Sup. Diaph., Beam 2, 0° Skew, MOVE9, Bridge #18
NOTE: The trends for MOVE2-8 are similar to Beam 1.
L-125
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 2: (30° Skew
Angle)
Effect of Intermediate Diaphragms for Beam 2 (MOVE1)
0100200300400500600700800900
1000110012001300140015001600
0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-196 – Inter. Diaph. without Sup. Diaph., Beam 2, 30° Skew, MOVE1, Bridge #18
Effect of Intermediate Diaphragms for Beam 2 (MOVE1)
0100200300400500600700800900
1000110012001300140015001600
0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-197 – Inter. Diaph. with Sup. Diaph., Beam 2, 30° Skew, MOVE1, Bridge #18
L-126
Effect of Intermediate Diaphragms for Beam 2 (MOVE9)
0100200300400500600700800900
1000110012001300140015001600
0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
30° Skew Angle Without Support Diaphragms
Figure L-198 – Inter. Diaph. without Sup. Diaph., Beam 2, 30° Skew, MOVE9, Bridge #18
Effect of Intermediate Diaphragms for Beam 2 (MOVE9)
0100200300400500600700800900
1000110012001300140015001600
0.00 26.00 52.00 78.00 104.00 130.00 156.00 182.00
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
30° Skew Angle With Rigid Support Diaphragms
Figure L-199 – Inter. Diaph. with Sup. Diaph., Beam 2, 30° Skew, MOVE9, Bridge #18
NOTE: The trends for MOVE2-8 are similar to Beam 1.
L-127
Effect of Intermediate Diaphragms on Moment Magnitude for Beam 2: (60° Skew
Angle)
Effect of Intermediate Diaphragms for Beam 2 (MOVE1)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-200 – Inter. Diaph. without Sup. Diaph., Beam 2, 60° Skew, MOVE1, Bridge #18
Effect of Intermediate Diaphragms for Beam 2 (MOVE1)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-201 – Inter. Diaph. with Sup. Diaph., Beam 2, 60° Skew, MOVE1, Bridge #18
L-128
Effect of Intermediate Diaphragms for Beam 2 (MOVE9)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
60° Skew Angle Without Support Diaphragms
Figure L-202 – Inter. Diaph. without Sup. Diaph., Beam 2, 60° Skew, MOVE9, Bridge #18
Effect of Intermediate Diaphragms for Beam 2 (MOVE9)
0100200300400500600700800900
1000110012001300140015001600
0 26 52 78 104 130 156 182
Distance From Support (ft)
Mom
ent (
kip-
ft)
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
60° Skew Angle With Rigid Support Diaphragms
Figure L-203 – Inter. Diaph. with Sup. Diaph., Beam 2, 60° Skew, MOVE9, Bridge #18
NOTE: The trends for MOVE2-8 are similar to Beam 1.
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 Shear (kips) DF Shear
(kips) DF
2 MOVE1 52.70 0.761 54.54 0.788 54.73 0.791 52.10 0.753 54.19 0.783 54.86 0.7923 MOVE2 47.16 0.681 49.17 0.710 49.86 0.720 46.42 0.670 48.65 0.703 50.02 0.7224 MOVE3 41.46 0.599 43.59 0.630 44.92 0.649 40.65 0.587 42.99 0.621 45.11 0.6515 MOVE4 35.73 0.516 37.95 0.548 39.97 0.577 34.91 0.504 37.32 0.539 40.20 0.5816 MOVE5 30.08 0.434 32.37 0.468 35.10 0.507 29.32 0.423 31.76 0.459 35.38 0.5117 MOVE6 25.13 0.363 27.70 0.400 31.11 0.449 24.89 0.359 27.68 0.400 31.49 0.4558 MOVE7 22.24 0.321 24.71 0.357 27.96 0.404 22.05 0.318 24.70 0.357 28.37 0.4109 MOVE8 19.91 0.288 22.17 0.320 25.23 0.364 19.72 0.285 22.17 0.320 25.65 0.371
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)
Load Shear (kips) DF Shear
(kips) DF Shear (kips) DF Shear
(kips) DF Shear (kips) DF Shear
(kips) DF
2 MOVE1 47.82 0.691 53.66 0.775 56.12 0.811 47.70 0.689 52.72 0.761 51.00 0.7373 MOVE2 44.71 0.646 50.13 0.724 52.78 0.762 44.56 0.644 49.27 0.712 47.84 0.6914 MOVE3 41.37 0.598 46.35 0.669 49.29 0.712 41.21 0.595 45.57 0.658 44.53 0.6435 MOVE4 37.88 0.547 42.41 0.613 46.21 0.667 37.75 0.545 41.71 0.602 41.13 0.5946 MOVE5 34.59 0.500 39.13 0.565 44.10 0.637 34.62 0.500 38.27 0.553 38.10 0.5507 MOVE6 32.35 0.467 36.74 0.531 42.13 0.608 32.37 0.468 35.98 0.520 36.23 0.5238 MOVE7 30.14 0.435 34.44 0.497 40.23 0.581 30.17 0.436 33.75 0.488 34.38 0.4979 MOVE8 28.44 0.411 32.22 0.465 38.40 0.555 28.47 0.411 31.61 0.457 32.61 0.471
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)
Load Shear (kips) DF Shear
(kips) DF Shear (kips) DF Shear
(kips) DF Shear (kips) DF Shear
(kips) DF
2 MOVE10 53.06 0.758 55.21 0.788 58.46 0.835 52.54 0.750 54.81 0.783 57.63 0.8233 MOVE11 47.47 0.678 49.80 0.711 53.52 0.764 46.85 0.669 49.22 0.703 52.29 0.7474 MOVE12 41.72 0.596 44.17 0.631 48.27 0.689 41.06 0.586 43.48 0.621 46.84 0.6695 MOVE13 35.94 0.513 38.44 0.549 42.84 0.612 35.30 0.504 37.72 0.539 41.38 0.5916 MOVE14 30.26 0.432 32.75 0.468 37.38 0.534 29.66 0.424 32.05 0.458 36.30 0.5187 MOVE15 25.64 0.366 28.26 0.404 32.51 0.464 25.46 0.364 28.20 0.403 32.63 0.4668 MOVE16 22.85 0.326 25.29 0.361 29.32 0.419 22.65 0.323 25.26 0.361 29.53 0.4229 MOVE17 20.54 0.293 22.80 0.326 26.60 0.380 20.34 0.291 22.76 0.325 26.78 0.38210 MOVE18 18.57 0.265 20.60 0.294 24.17 0.345 18.36 0.262 20.55 0.293 24.30 0.347
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)
Load Shear (kips) DF Shear
(kips) DF Shear (kips) DF Shear
(kips) DF Shear (kips) DF Shear
(kips) DF
2 MOVE10 47.86 0.684 54.37 0.777 57.49 0.821 47.68 0.681 53.51 0.764 56.25 0.8033 MOVE11 44.78 0.640 50.63 0.723 53.16 0.759 44.57 0.636 49.85 0.712 51.98 0.7424 MOVE12 41.49 0.593 46.60 0.666 48.46 0.692 41.28 0.590 45.89 0.655 47.33 0.6765 MOVE13 38.08 0.544 42.40 0.606 43.65 0.623 37.89 0.541 41.76 0.596 42.44 0.6066 MOVE14 34.89 0.498 39.22 0.560 40.74 0.582 34.88 0.498 38.38 0.548 38.65 0.5527 MOVE15 32.92 0.470 36.88 0.527 38.74 0.553 32.93 0.470 36.13 0.516 36.55 0.5228 MOVE16 31.11 0.444 34.61 0.494 36.75 0.525 31.12 0.444 33.90 0.484 34.60 0.4949 MOVE17 29.38 0.420 32.54 0.465 34.81 0.497 29.39 0.420 31.93 0.456 32.65 0.46610 MOVE18 27.67 0.395 30.53 0.436 33.04 0.472 27.68 0.395 30.00 0.428 30.86 0.441
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 on Shear Distribution at Obtuse Corner for Beam 1:
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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner
MOVE3 - 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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner
MOVE4 - 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
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms
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
MOVE3 - 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
MOVE4 - 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
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
Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse CornerMOVE5 - 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
MOVE6 - 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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner
MOVE7 - 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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner
MOVE8 - 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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse Corner
MOVE6 - 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
MOVE7 - 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
MOVE8 - 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
Figure L-205 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 1, MOVE5-8,Bridge #18
L-133
Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse CornerMOVE9 - Without Support Diaphragms
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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms
Effect of Skew Angle of Shear Distribution for Beam 1 at Obtuse CornerMOVE9 - With Rigid Support Diaphragms
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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms
Figure L-206 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 1, MOVE9,Bridge #18
L-134
Effect of Skew Angle on Shear Distribution at Obtuse Corner for Beam 8:
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE10 - Without Support Diaphragms
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
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE10 - With Rigid Support Diaphragms
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 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 8 at Obtuse Corner
MOVE11 - Without Support Diaphragms
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
MOVE12 - Without Support Diaphragms
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
With Rigid Intermediate Diaphragms Without Intermediate Diaphragms With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse Corner
MOVE13 - Without Support Diaphragms
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 Diaphragms With Equivalent Intermediate Diaphragms
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse Corner
MOVE11 - With Rigid Support Diaphragms
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
MOVE12 - With Rigid Support Diaphragms
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 Diaphragms Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse Corner
MOVE13 - With Rigid Support Diaphragms
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 Diaphragms
Figure L-207 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 8, MOVE10-13,Bridge #18
L-135
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE14 - Without Support Diaphragms
0.250
0.3000.350
0.400
0.4500.500
0.5500.600
0.6500.700
0.750
0.8000.850
0 30 60
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE14 - With Rigid Support Diaphragms
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
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames With Equivalent Intermediate Diaphragms
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE15 - Without Support Diaphragms
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
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
MOVE16 - Without Support Diaphragms
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 With Equivalent Intermediate Diaphragms Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse Corner
MOVE17 - Without Support Diaphragms
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
MOVE15 - With Rigid Support Diaphragms
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
MOVE16 - With Rigid Support Diaphragms
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
MOVE17 - With Rigid Support Diaphragms
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
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n Fa
ctor
With Rigid Intermediate Diaphragms Without Intermediate Cross Frames
Figure L-208 - Effect of Skew Angle on Shear at Obtuse Corner, Beam 8, MOVE14-17,Bridge #18
L-136
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE18 - Without Support Diaphragms
0.250
0.3000.350
0.400
0.4500.500
0.5500.600
0.6500.700
0.750
0.8000.850
0 30 60
Effect of Skew Angle of Shear Distribution for Beam 8 at Obtuse CornerMOVE18 - With Rigid Support Diaphragms
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 DiaphragmsSkew Angle (deg)
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:
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
Distance From Barrier (ft)
Dis
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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:
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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
Distance From Barrier (ft)
Dis
trib
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ctor
10
0 Skew 30 Skew 60 Skew
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:
Without Intermediate 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
Without Intermediate Diaphragms
Without Intermediate Diaphragms
Figure L-220 – Shear Values without Inter. Diaph., without Sup. Diaph., Bridge #18
W ith E quivalen t Interm ediate D iaphragm s
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
W ith E quivalen t Interm ediate D iaphragm s
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°
With Rigid Intermediate Diaphragms
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
With Rigid Intermediate Diaphragms
With Rigid Intermediate Diaphragms
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
Without Intermediate Diaphragms
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
Without Intermediate Diaphragms
Without Intermediate Diaphragms
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
With Rigid Intermediate Diaphragms
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
With Rigid Intermediate Diaphragms
With Rigid Intermediate Diaphragms
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 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
Distance From Barrier
(ft)
Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2
Table L-27 – Reactions, Equivalent Intermediate Diaphragms
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE1 51.27 0.770 55.68 0.773 52.05 0.773 50.22 0.754 57.06 0.792 53.48 0.794 50.50 0.758 62.65 0.869 55.67 0.8273 MOVE2 45.13 0.678 48.28 0.670 45.77 0.680 43.97 0.660 50.56 0.701 47.40 0.704 44.41 0.667 57.26 0.794 50.46 0.7504 MOVE3 39.10 0.587 41.22 0.572 39.63 0.589 37.89 0.569 44.77 0.621 41.41 0.615 38.55 0.579 52.21 0.724 45.42 0.6755 MOVE4 33.25 0.499 35.60 0.494 33.69 0.500 32.07 0.481 39.74 0.551 35.61 0.529 32.92 0.494 47.45 0.658 40.55 0.6026 MOVE5 27.65 0.415 31.34 0.435 28.05 0.417 26.56 0.399 35.26 0.489 31.04 0.461 27.49 0.413 43.02 0.597 36.02 0.5357 MOVE6 22.79 0.342 27.85 0.386 24.07 0.358 21.43 0.322 31.34 0.435 27.31 0.406 21.98 0.330 38.84 0.539 32.13 0.4778 MOVE7 19.72 0.296 24.86 0.345 21.19 0.315 17.07 0.256 27.84 0.386 24.18 0.359 16.67 0.250 34.95 0.485 28.81 0.4289 MOVE8 17.28 0.259 22.24 0.309 18.78 0.279 14.75 0.221 24.66 0.342 21.50 0.319 11.83 0.178 31.29 0.434 25.87 0.38410 MOVE9 15.22 0.229 19.91 0.276 16.71 0.248 13.05 0.196 21.76 0.302 19.12 0.284 9.08 0.136 27.84 0.386 23.21 0.345
Without Support Diaphragms - With Equivalent Intermediate DiaphragmsMaximum Reactions - Beam Line 4 (Beam 1 & 2)
60300Skew Angle (deg)BentAbutment 1
Load Position
Distance From Barrier
(ft)
Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2
L-146
Table L-28 – Reactions, Rigid Intermediate Diaphragms
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE1 49.40 0.742 55.27 0.767 50.15 0.745 39.10 0.587 118.90 1.650 90.26 1.341 46.40 0.697 96.21 1.335 70.03 1.0403 MOVE2 45.21 0.679 49.85 0.692 45.60 0.677 34.29 0.515 112.01 1.554 85.27 1.267 40.62 0.610 91.71 1.272 66.78 0.9924 MOVE3 40.88 0.614 44.42 0.616 40.96 0.608 29.59 0.444 105.13 1.459 80.28 1.192 35.25 0.529 87.25 1.211 63.54 0.9445 MOVE4 36.48 0.548 40.29 0.559 36.33 0.540 25.13 0.377 98.25 1.363 75.28 1.118 30.28 0.455 82.80 1.149 60.29 0.8966 MOVE5 32.11 0.482 37.40 0.519 32.80 0.487 21.01 0.315 91.35 1.267 70.28 1.044 25.59 0.384 78.38 1.087 57.05 0.8477 MOVE6 30.02 0.451 35.29 0.490 30.93 0.459 17.28 0.259 84.46 1.172 65.28 0.970 20.69 0.311 73.99 1.027 53.81 0.7998 MOVE7 28.44 0.427 33.30 0.462 29.29 0.435 13.96 0.210 77.56 1.076 60.27 0.895 15.98 0.240 69.65 0.966 50.56 0.7519 MOVE8 26.83 0.403 31.52 0.437 27.64 0.411 11.07 0.166 70.69 0.981 55.25 0.821 12.18 0.183 65.35 0.907 47.30 0.70310 MOVE9 25.23 0.379 29.78 0.413 26.07 0.387 9.93 0.149 63.83 0.886 50.22 0.746 11.10 0.167 61.10 0.848 44.02 0.654
Without Support Diaphragms - With Rigid Intermediate DiaphragmsMaximum Reactions - Beam Line 4 (Beam 1 & 2)
60300Skew Angle (deg)BentAbutment 1
Load Position
Distance From Barrier
(ft)
Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2
Table L-29 – Reactions, No Intermediate Diaphragms, Rigid Support Diaphragms
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE1 52.06 0.782 58.17 0.807 52.83 0.785 51.04 0.766 60.93 0.845 56.37 0.837 49.84 0.748 63.52 0.881 57.62 0.8563 MOVE2 46.75 0.702 51.42 0.713 47.42 0.704 45.34 0.681 54.89 0.762 51.39 0.763 43.59 0.654 58.47 0.811 53.42 0.7934 MOVE3 41.45 0.622 44.57 0.618 42.03 0.624 39.75 0.597 48.40 0.672 46.05 0.684 37.67 0.566 53.01 0.735 49.06 0.7295 MOVE4 36.19 0.543 38.00 0.527 36.68 0.545 34.31 0.515 41.68 0.578 40.49 0.601 32.11 0.482 47.40 0.658 44.61 0.6636 MOVE5 30.99 0.465 32.30 0.448 31.41 0.467 29.06 0.436 35.46 0.492 34.87 0.518 26.83 0.403 42.10 0.584 40.13 0.5967 MOVE6 25.89 0.389 27.86 0.387 26.37 0.392 24.08 0.362 30.93 0.429 29.34 0.436 21.84 0.328 38.05 0.528 35.70 0.5308 MOVE7 21.34 0.320 24.84 0.345 22.05 0.328 19.86 0.298 27.49 0.381 25.29 0.376 17.72 0.266 34.40 0.477 31.47 0.4679 MOVE8 18.25 0.274 22.23 0.308 19.68 0.292 16.01 0.240 24.43 0.339 22.63 0.336 14.16 0.213 31.00 0.430 28.25 0.42010 MOVE9 16.29 0.245 19.91 0.276 17.69 0.263 14.44 0.217 21.68 0.301 20.35 0.302 11.76 0.177 27.86 0.387 25.53 0.379
Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2BentAbutment 1Load
Position
Distance From Barrier
(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
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE1 40.72 0.611 55.93 0.776 50.04 0.743 45.86 0.689 63.78 0.885 62.94 0.935 48.19 0.723 63.78 0.885 64.31 0.9553 MOVE2 38.64 0.580 50.82 0.705 46.04 0.684 41.53 0.624 60.55 0.840 59.82 0.889 42.44 0.637 60.68 0.842 61.33 0.9114 MOVE3 36.90 0.554 45.43 0.630 42.00 0.624 37.32 0.560 57.54 0.798 56.88 0.845 37.21 0.559 57.71 0.801 58.36 0.8675 MOVE4 35.17 0.528 40.31 0.559 37.95 0.564 33.28 0.500 54.62 0.758 54.06 0.803 32.43 0.487 54.90 0.762 55.57 0.8256 MOVE5 33.43 0.502 37.42 0.519 34.00 0.505 29.44 0.442 51.76 0.718 51.24 0.761 27.90 0.419 52.14 0.723 52.80 0.7847 MOVE6 31.69 0.476 35.32 0.490 31.31 0.465 25.87 0.388 48.90 0.678 48.41 0.719 24.11 0.362 49.44 0.686 50.05 0.7438 MOVE7 29.92 0.449 33.33 0.462 29.54 0.439 22.39 0.336 46.04 0.639 45.55 0.677 20.50 0.308 46.80 0.649 47.29 0.7029 MOVE8 28.13 0.422 31.55 0.438 27.88 0.414 20.97 0.315 43.18 0.599 42.63 0.633 17.18 0.258 44.17 0.613 44.55 0.66210 MOVE9 26.46 0.397 29.81 0.414 26.29 0.390 19.93 0.299 40.31 0.559 39.66 0.589 16.03 0.241 41.55 0.576 41.81 0.621
Abutment 2BentAbutment 1Abutment 2BentAbutment 1Abutment 2BentAbutment 1Load
Position
Distance From Barrier
(ft)
60300Skew Angle (deg)With Rigid Support Diaphragms - With Rigid Intermediate Diaphragms
Maximum Reactions - Beam Line 4 (Beam 1 & 2)
Table L-31 - Reactions, No Intermediate Diaphragms
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE10 51.54 0.774 56.28 0.781 52.43 0.779 53.67 0.806 57.94 0.804 51.66 0.767 55.45 0.832 63.07 0.875 51.92 0.7713 MOVE11 45.42 0.682 48.97 0.679 46.20 0.686 47.92 0.719 51.46 0.714 45.39 0.674 50.28 0.755 57.70 0.801 45.88 0.6814 MOVE12 39.38 0.591 41.90 0.581 40.05 0.595 42.07 0.632 45.56 0.632 39.23 0.583 45.30 0.680 52.68 0.731 40.04 0.5955 MOVE13 33.48 0.503 35.87 0.498 34.07 0.506 36.18 0.543 40.50 0.562 33.28 0.494 40.45 0.607 47.99 0.666 34.40 0.5116 MOVE14 27.81 0.418 31.29 0.434 28.32 0.421 30.53 0.458 36.09 0.501 27.60 0.410 35.77 0.537 43.60 0.605 28.94 0.4307 MOVE15 22.76 0.342 27.64 0.383 24.02 0.357 26.02 0.391 32.24 0.447 22.27 0.331 31.36 0.471 39.56 0.549 23.24 0.3458 MOVE16 19.48 0.292 24.58 0.341 20.95 0.311 22.62 0.340 28.84 0.400 18.27 0.271 27.79 0.417 35.77 0.496 17.64 0.2629 MOVE17 16.97 0.255 21.93 0.304 18.47 0.274 19.83 0.298 25.77 0.358 16.03 0.238 24.72 0.371 32.27 0.448 12.61 0.18710 MOVE18 14.91 0.224 19.57 0.272 16.37 0.243 17.48 0.262 22.99 0.319 14.21 0.211 22.01 0.330 28.97 0.402 10.69 0.159
0Without Support Diaphragms - Without Intermediate Diaphragms
Maximum Reactions - Beam Line 1 (Beam 7 & 8)
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
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE10 51.27 0.770 55.68 0.773 52.05 0.773 52.77 0.792 57.49 0.798 51.22 0.761 55.05 0.826 63.20 0.877 51.55 0.7663 MOVE11 45.13 0.678 48.28 0.670 45.77 0.680 46.82 0.703 51.10 0.709 44.89 0.667 49.83 0.748 57.81 0.802 45.43 0.6754 MOVE12 39.10 0.587 41.22 0.572 39.63 0.589 40.91 0.614 45.47 0.631 38.74 0.575 44.92 0.674 52.79 0.732 39.52 0.5875 MOVE13 33.25 0.499 35.60 0.494 33.69 0.500 35.10 0.527 40.54 0.562 32.85 0.488 40.18 0.603 48.11 0.667 33.83 0.5026 MOVE14 27.65 0.415 31.34 0.435 28.05 0.417 30.16 0.453 36.21 0.502 27.26 0.405 35.64 0.535 43.71 0.606 28.33 0.4217 MOVE15 22.79 0.342 27.85 0.386 24.07 0.358 26.22 0.394 32.44 0.450 22.18 0.329 31.62 0.475 39.65 0.550 22.77 0.3388 MOVE16 19.72 0.296 24.86 0.345 21.19 0.315 23.00 0.345 29.05 0.403 18.57 0.276 28.13 0.422 35.83 0.497 17.41 0.2599 MOVE17 17.28 0.259 22.24 0.309 18.78 0.279 20.21 0.303 25.96 0.360 16.45 0.244 25.09 0.377 32.29 0.448 12.61 0.18710 MOVE18 15.22 0.229 19.91 0.276 16.71 0.248 17.81 0.267 23.16 0.321 14.69 0.218 22.36 0.336 28.96 0.402 11.03 0.164
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)
Distance From Barrier
(ft)
Load Position
Table L-33 – Reactions, Rigid Intermediate Diaphragms
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE10 49.40 0.742 55.27 0.767 50.15 0.745 86.95 1.305 122.65 1.702 40.02 0.594 66.86 1.004 98.86 1.372 47.31 0.7033 MOVE11 45.21 0.679 49.85 0.692 45.60 0.677 82.20 1.234 115.51 1.603 35.21 0.523 63.96 0.960 94.05 1.305 41.53 0.6174 MOVE12 40.88 0.614 44.42 0.616 40.96 0.608 77.45 1.163 108.36 1.503 30.50 0.453 61.07 0.917 89.24 1.238 36.15 0.5375 MOVE13 36.48 0.548 40.29 0.559 36.33 0.540 72.70 1.091 101.21 1.404 26.03 0.387 58.18 0.873 84.43 1.171 31.19 0.4636 MOVE14 32.11 0.482 37.40 0.519 32.80 0.487 67.93 1.020 94.06 1.305 21.90 0.325 55.33 0.831 79.64 1.105 26.51 0.3947 MOVE15 30.02 0.451 35.29 0.490 30.93 0.459 63.16 0.948 86.90 1.206 18.16 0.270 52.48 0.788 74.87 1.039 21.63 0.3218 MOVE16 28.44 0.427 33.30 0.462 29.29 0.435 58.37 0.876 79.74 1.106 14.83 0.220 49.62 0.745 70.13 0.973 17.24 0.2569 MOVE17 26.83 0.403 31.52 0.437 27.64 0.411 53.56 0.804 72.60 1.007 12.34 0.183 46.78 0.702 65.41 0.908 14.44 0.21410 MOVE18 25.23 0.379 29.78 0.413 26.07 0.387 48.73 0.732 65.45 0.908 11.68 0.173 43.92 0.659 60.73 0.843 13.46 0.200
Maximum Reactions - Beam Line 1 (Beam 7 & 8)Without Support Diaphragms - With Rigid Intermediate Diaphragms
Skew Angle (deg) 0 30 60
Distance From Barrier
(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
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE10 52.06 0.782 58.17 0.807 52.83 0.785 55.40 0.832 61.36 0.851 52.22 0.776 56.74 0.852 63.04 0.875 51.07 0.7593 MOVE11 46.75 0.702 51.42 0.713 47.42 0.704 50.55 0.759 55.34 0.768 46.49 0.691 52.63 0.790 57.81 0.802 44.81 0.6664 MOVE12 41.45 0.622 44.57 0.618 42.03 0.624 45.35 0.681 48.87 0.678 40.83 0.606 48.39 0.727 52.42 0.727 38.83 0.5775 MOVE13 36.19 0.543 38.00 0.527 36.68 0.545 39.93 0.599 42.19 0.585 35.29 0.524 44.06 0.661 47.15 0.654 33.18 0.4936 MOVE14 30.99 0.465 32.30 0.448 31.41 0.467 34.44 0.517 35.98 0.499 29.92 0.444 39.72 0.596 42.84 0.594 27.78 0.4137 MOVE15 25.89 0.389 27.86 0.387 26.37 0.392 29.02 0.436 32.09 0.445 24.89 0.370 35.44 0.532 38.93 0.540 22.68 0.3378 MOVE16 21.34 0.320 24.84 0.345 22.05 0.328 24.51 0.368 28.77 0.399 20.63 0.306 31.29 0.470 35.33 0.490 18.71 0.2789 MOVE17 18.25 0.274 22.23 0.308 19.68 0.292 21.69 0.326 25.78 0.358 17.45 0.259 27.88 0.419 31.97 0.444 14.98 0.22310 MOVE18 16.29 0.245 19.91 0.276 17.69 0.263 19.37 0.291 23.10 0.320 15.76 0.234 25.04 0.376 28.87 0.401 13.27 0.197
Maximum Reactions - Beam Line 1 (Beam 7 & 8)With Rigid Support Diaphragms - Without Intermediate Diaphragms
Skew Angle (deg) 0 30 60
Distance From Barrier
(ft)
Load Position
Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2
Table L-35 – Reactions, Rigid Intermediate Diaphragms, Rigid Support Diaphragms
Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF Reaction
(kip) DF Reaction (kip) DF
2 MOVE10 40.72 0.611 55.93 0.776 50.04 0.743 61.86 0.929 65.47 0.908 46.43 0.690 64.23 0.964 74.98 1.040 49.08 0.7293 MOVE11 38.64 0.580 50.82 0.705 46.04 0.684 58.46 0.878 62.42 0.866 42.10 0.625 61.51 0.923 71.78 0.996 43.33 0.6444 MOVE12 36.90 0.554 45.43 0.630 42.00 0.624 55.40 0.832 59.40 0.824 37.89 0.563 58.80 0.883 68.59 0.952 38.09 0.5665 MOVE13 35.17 0.528 40.31 0.559 37.95 0.564 52.51 0.788 56.41 0.783 33.85 0.503 56.15 0.843 65.42 0.908 33.30 0.4956 MOVE14 33.43 0.502 37.42 0.519 34.00 0.505 49.68 0.746 53.42 0.741 30.03 0.446 53.63 0.805 62.26 0.864 29.14 0.4337 MOVE15 31.69 0.476 35.32 0.490 31.31 0.465 46.88 0.704 50.53 0.701 26.45 0.393 51.13 0.768 59.14 0.821 25.45 0.3788 MOVE16 29.92 0.449 33.33 0.462 29.54 0.439 44.09 0.662 47.43 0.658 23.26 0.345 48.62 0.730 56.00 0.777 21.83 0.3249 MOVE17 28.13 0.422 31.55 0.438 27.88 0.414 41.27 0.620 44.43 0.616 22.17 0.329 46.13 0.693 52.89 0.734 19.75 0.29310 MOVE18 26.46 0.397 29.81 0.414 26.29 0.390 38.39 0.576 41.41 0.575 21.19 0.315 43.70 0.656 49.77 0.691 18.52 0.275
Maximum Reactions - Beam Line 1 (Beam 7 & 8)With Rigid Support Diaphragms - With Rigid Intermediate Diaphragms
Skew Angle (deg) 0 30 60
Distance From Barrier
(ft)
Load Position
Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2 Abutment 1 Bent Abutment 2
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
Without Intermediate Diaphragms
Without Intermediate Diaphragms
Without Intermediate Diaphragms
Figure L-225 – Shear Values without Inter. Diaph., without Sup. Diaph., Bridge #18
With Equivalent Intermediate Diaphragms
With Equivalent Intermediate Diaphragms
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
With Rigid Intermediate Diaphragms
With Rigid Intermediate Diaphragms
With Rigid Intermediate Diaphragms
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
Without Intermediate Diaphragms
Without Intermediate Diaphragms
Without Intermediate Diaphragms
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
With Rigid Intermediate Diaphragms
With Rigid Intermediate Diaphragms
With Rigid Intermediate Diaphragms
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
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