progress report on calibration of strength iv limit...

PROGRESS REPORT ON

CALIBRATION OF STRENGTH IV LIMIT STATE IN

AASHTO LRFD BRIDGE DESIGN

SPECIFICATIONS

AASHTO T-5 Meeting

Austin, TX

July 10, 2012

Presented By

Wagdy G. Wassef, P.E., Ph.D., Modjeski and Masters, Inc.

Scope of Work (1)

• Compile a set of six straight, square, 3-

span steel I-girder bridges (Group 1)

– Center span length starts at 100 ft,

incremented by 100 ft

– Side spans 80% of center span

– Cross-section representative of 2-lane

Interstate Highway bridge with shoulders

– Gutter-to-Gutter width 44 ft, 5 Girders at 10’-2”

– Sufficiently designed to accurately provide DL

Group 1 Bridges

Bridge Span 1 (ft) Span 2 (ft) Span 3 (ft) Total Length (ft)

100 80 100 80 260

200 160 200 160 520

300 240 300 240 780

400 320 400 320 1040

500 400 500 400 1300

600 480 600 480 1560

Scope of Work (2)

• Compile set of six existing bridges (40-600

ft span lengths) (Group 2 Bridges)

– Short-span concrete slab bridge (~40 ft)

– Spliced concrete I-girder bridge (~180 ft)

– Multicell Concrete Box Girder Bridge (~250 ft)

– Steel trusses (~250 ft & ~600 ft)

– Segmental concrete box girder (~525 ft)

– Bridges assumed to be straight and square

Scope of Work (3)

• Analyze each bridge to determine maximum

positive bending moment, maximum negative

bending moment, and maximum shear for dead

loads and HL-93 live load

• Factor loads according to Strength I, existing

Strength IV, and proposed Strength IV load

combinations

• Calculate reliability index for each bridge and

each load combination (Strength I, current

Strength IV, and proposed Strength IV)

Scope of Work (4)

• Analyze each bridge for the MnDOT P413

Truck and the CalTrans P15 truck with

variable axle spacings of 18 ft, 39 ft, and 60 ft

– Permit loads assumed to be in all lanes initially

– Revised to have permit load in one lane with and

without the design load in remaining lanes for

interior girders of Group 1 Bridges

• Determine force effects due to Strength II

load combination

Strength II: Permit Vehicles

• CalTrans P15 (404 Kips)

• MnDOT P413 (255 Kips)

Existing Strength IV Combinations

Table 3.4.1-1—Load Combinations and Load Factors

Load

Combination

Limit State

DC

DD

DW

EH

EV

ES

EL

PS

CR

SH

LL

IM

CE

BR

PL

LS WA WS WL FR TU TG SE

Strength IV γp — 1.00 — — 1.00 0.50/1.20 — —

Existing Strength IV Combinations

Table 3.4.1-2—Load Factors for Permanent Loads, γp

Type of Load, Foundation Type, and

Method Used to Calculate Downdrag

Load Factor

Maximum Minimum

DC: Component and Attachments

DC: Strength IV only

1.25

1.50

0.90

0.90

1.5 1.5DC DW

For most superstructure cases when Strength IV controls, load

combination:

Proposed Strength IV Combinations

• Proposed Formula 1 =

• Proposed Formula 2 =

• Proposed Formula 3 (additional work

required =

IMLLDWDC35.1

IMLLDWDC4.1

IMLLDWDC 7.15.14.1

Group 1 Interior Girders

Strength II and Strength IV compared

to Strength I

(For Strength II: Permit Vehicles in all Lanes)

Group 1 – End Span Positive Bending

• Interior Girders

• For strength II:

Permit vehicle in all

lanes

• Impact of 1.33 applied

to permit vehicles

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.85 1.18 1.18 1.18 0.39 0.87 0.90

200 1.01 1.64 1.37 1.23 0.56 0.91 0.94

300 1.06 1.70 1.51 1.35 0.66 0.93 0.97

400 1.01 1.63 1.50 1.38 0.74 0.95 0.99

500 0.95 1.53 1.43 1.34 0.81 0.97 1.01

600 0.88 1.41 1.34 1.27 0.86 0.98 1.02

0.00

0.50

1.00

1.50

2.00

2.50

100 200 300 400 500 600

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Center Span Length (ft)

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength ICur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

For Strength II Comparison:

Permit Truck / HL93


0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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Str. II MN P413Strength I

Str. II P15-18Strength I



Cur. Str. IVStrength I

1.35 (D+L)Strength I

1.4(D+L)Strength I


•For strength II:

Permit vehicle in all

lanes

•Impact of 1.33 applied to

permit vehicles

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.90 1.12 1.12 1.12 0.39 0.87 0.90

200 1.01 1.33 1.20 1.12 0.56 0.91 0.94

300 1.02 1.31 1.22 1.15 0.66 0.93 0.97

400 1.01 1.23 1.19 1.14 0.74 0.95 0.99

500 0.99 1.16 1.13 1.11 0.81 0.97 1.01

600 0.97 1.11 1.09 1.07 0.86 0.98 1.02

Strength II Comparison:

Factored (DL + Permit Truck) /

Factored (DL+ HL93)

This is the case used for

Strength II comparisons in all

subsequent slides

Group 1 – Negative Bending


• Permit vehicle in all

lanes


to permit vehicles

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

Rat

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.99 1.22 1.23 1.15 0.53 0.90 0.93

200 0.90 1.07 1.03 1.08 0.72 0.95 0.98

300 0.90 1.03 1.01 0.99 0.81 0.97 1.01

400 0.90 0.99 0.98 0.98 0.88 0.99 1.02

500 0.90 0.97 0.96 0.96 0.92 1.00 1.03

600 0.90 0.95 0.95 0.95 0.96 1.01 1.05

Group 1 – Center Span Positive Bending

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.90 1.21 1.15 1.15 0.36 0.86 0.89

200 1.02 1.40 1.24 1.15 0.52 0.90 0.93

300 1.02 1.35 1.26 1.18 0.60 0.92 0.95

400 1.00 1.25 1.20 1.15 0.69 0.94 0.98

500 0.98 1.17 1.14 1.11 0.77 0.96 1.00

600 0.96 1.12 1.10 1.07 0.82 0.97 1.01



lanes


to permit vehicles

Group 1 – End Span Shear

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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1.4(D+L)Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.93 1.21 1.19 1.19 0.37 0.86 0.89

200 1.07 1.42 1.32 1.24 0.51 0.90 0.93

300 1.07 1.39 1.33 1.28 0.60 0.92 0.95

400 1.04 1.32 1.28 1.25 0.66 0.93 0.97

500 1.01 1.24 1.21 1.19 0.73 0.95 0.99

600 0.98 1.17 1.16 1.14 0.78 0.96 1.00



lanes


to permit vehicles

Group 1 – Shear Left of Interior Support

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 1.00 1.29 1.26 1.23 0.47 0.89 0.92

200 1.07 1.38 1.30 1.21 0.64 0.93 0.96

300 1.04 1.29 1.26 1.22 0.72 0.95 0.98

400 1.00 1.20 1.18 1.16 0.78 0.96 1.00

500 0.97 1.13 1.12 1.11 0.82 0.97 1.01

600 0.95 1.08 1.07 1.07 0.87 0.99 1.02



lanes


to permit vehicles

Group 1 – Shear Right of Interior Support

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.98 1.32 1.25 1.22 0.47 0.88 0.92

200 1.08 1.39 1.32 1.26 0.62 0.92 0.96

300 1.03 1.28 1.25 1.22 0.71 0.94 0.98

400 0.99 1.19 1.17 1.16 0.77 0.96 0.99

500 0.96 1.12 1.11 1.10 0.81 0.97 1.01

600 0.94 1.07 1.06 1.06 0.86 0.98 1.02



lanes


to permit vehicles

Group 1 Interior Girders

Strength II and Strength IV compared to Strength I

(For Strength II: Permit Vehicles in One Lane with

HL-93 Design Load in Adjacent Lanes)



• Permit vehicle in one

lane, HL-93 Design

Load in adjacent lane(s)


to permit vehicle

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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1.4(D+L)Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.88 1.01 1.01 1.01 0.39 0.87 0.90

200 0.95 1.13 1.06 1.01 0.56 0.91 0.94

300 0.97 1.12 1.08 1.04 0.66 0.93 0.97

400 0.96 1.08 1.06 1.03 0.74 0.95 0.99

500 0.96 1.05 1.04 1.02 0.81 0.97 1.01

600 0.95 1.03 1.02 1.01 0.86 0.98 1.02

Group 1 – Negative Bending



lane, HL-93 Design Load

in adjacent lane(s)


to permit vehicle

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

Rat

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.95 1.08 1.09 1.04 0.53 0.90 0.93

200 0.90 1.00 0.98 1.01 0.72 0.95 0.98

300 0.91 0.98 0.97 0.96 0.81 0.97 1.01

400 0.92 0.97 0.96 0.96 0.88 0.99 1.02

500 0.92 0.96 0.96 0.96 0.92 1.00 1.03

600 0.93 0.96 0.95 0.95 0.96 1.01 1.05

Group 1 – Center Span Positive Bending




in adjacent lane(s)


to permit vehicle

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

Rat

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.88 1.07 1.03 1.03 0.36 0.86 0.89

200 0.96 1.17 1.08 1.03 0.52 0.90 0.93

300 0.96 1.14 1.09 1.05 0.60 0.92 0.95

400 0.96 1.09 1.06 1.04 0.69 0.94 0.98

500 0.95 1.05 1.04 1.02 0.77 0.96 1.00

600 0.94 1.03 1.02 1.01 0.82 0.97 1.01

Group 1 – End Support Shear




in adjacent lane(s)


to permit vehicle

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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1.4(D+L)Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.90 1.08 1.07 1.07 0.37 0.86 0.89

200 1.00 1.23 1.17 1.12 0.51 0.90 0.93

300 1.01 1.22 1.18 1.15 0.60 0.92 0.95

400 0.99 1.18 1.15 1.13 0.66 0.93 0.97

500 0.98 1.13 1.11 1.10 0.73 0.95 0.99

600 0.96 1.09 1.08 1.07 0.78 0.96 1.00

Group 1 –Shear Left of Interior Support




in adjacent lane(s)


to permit vehicle

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.96 1.15 1.13 1.11 0.47 0.89 0.92

200 1.01 1.22 1.16 1.10 0.64 0.93 0.96

300 1.00 1.16 1.14 1.12 0.72 0.95 0.98

400 0.98 1.11 1.09 1.08 0.78 0.96 1.00

500 0.96 1.06 1.06 1.05 0.82 0.97 1.01

600 0.95 1.03 1.03 1.02 0.87 0.99 1.02

Group 1 –Shear Right of Interior Support




in adjacent lane(s)


to permit vehicle

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

100 200 300 400 500 600

Rat

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Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35 (D+L)

Strength I

1.4(D+L)

Strength I

Bridge

100 0.94 1.17 1.12 1.10 0.47 0.88 0.92

200 1.01 1.22 1.18 1.13 0.62 0.92 0.96

300 0.99 1.16 1.14 1.12 0.71 0.94 0.98

400 0.97 1.10 1.09 1.08 0.77 0.96 0.99

500 0.95 1.06 1.05 1.04 0.81 0.97 1.01

600 0.94 1.02 1.02 1.02 0.86 0.98 1.02

Group 2 Bridges – Concrete Slab

• Span Length = 41’-6”

• Slab thickness = 31”

• Reinforcement = 3.3 in2/ft

Group 2 Bridges – Spliced Concrete I-

girder

• Span Length = 206’-8”, splices at 28’-5½”

from centerline bearing

• Cross-section:

Group 2 Bridges – Steel Trusses

Bridge Span Length (ft) Truss Spacing (ft) Number of Lanes

Truss #1 250’-0” 89’-0” 6

Truss #2 617’-6” 94’-0” 6

Group 2 Bridges – Multicell Concrete Box

Girder

• Three Span Continuous – 203’-5”, 249’-3”,

203’-5”

• 11 – 11 13/16” webs spaced at 11’-4¼”

Group 2 Bridges – Precast Segmental

Box Girder

• Four span continuous – 282’-6”, 525’-0”,

525’-0”, and 312’-6”

Pier Section

Midspan Section

Group 2 – End/Simple Span Positive

Moment • Permit vehicle in all

lanes

• Impact of 1.33 applied to

permit vehicles

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Concrete Slab

Spliced PC I Girder

250' Truss 617.5' Truss MultiCell Box Girder

Segmental Box

Rat

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Bridge Example






1.35(D+L)Strength I

1.4(D+L)Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Bridge

Concrete Slab 0.91 0.98 0.98 0.98 0.65 0.92 0.96

Spliced PC I Girder 1.04 1.31 1.21 1.12 0.73 0.95 0.99

250' Truss 1.03 1.24 1.18 1.12 0.82 0.98 1.01

617.5' Truss 0.95 1.06 1.05 1.04 0.92 1.01 1.05

MultiCell Box Girder 1.02 1.21 1.14 1.09 0.84 0.98 1.01

Segmental Box 0.97 1.19 1.15 1.12 0.71 0.95 0.98

Group 2 – Negative Moment


lanes


to permit vehicles

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Concrete Slab

Spliced PC I Girder


Segmental Box

Rat

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Bridge Example

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength ICur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Bridge


Segmental Box 0.93 0.97 0.97 0.97 1.02 1.03 1.07

Group 2 – Interior Span Positive Moment


lanes


to permit vehicles

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Concrete Slab

Spliced PC I Girder


Segmental Box

Rat

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Span

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Bridge Example






1.35(D+L)Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Bridge


Segmental Box 0.97 1.12 1.09 1.07 0.86 0.99 1.03

Group 2 – Simple Support Shear


lanes


to permit vehicles

0.000.200.400.600.801.001.201.401.601.802.002.202.40

Concrete Slab

Spliced PC I Girder


Segmental Box

Rat

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ars

Bridge Example

Str. II MN P413

Strength IStr. II P15-18



Strength ICur. Str. IVStrength I

1.35(D+L)Strength I

1.4(D+L)Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Bridge

Concrete Slab 0.90 1.04 1.04 1.04 0.60 0.91 0.94

Spliced PC I Girder 1.09 1.40 1.34 1.29 0.65 0.93 0.96

250' Truss 0.96 1.12 1.10 1.08 0.82 0.98 1.01

617.5' Truss 0.91 0.99 0.99 0.98 0.92 1.01 1.05


Segmental Box 0.90 1.07 1.05 1.03 0.70 0.95 0.98

Group 2 – Shear Left of Interior Support


lanes


to permit vehicles

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Concrete Slab

Spliced PC I Girder


Segmental Box

Rat

io o

f Sh

ear

Le

ft o

f In

teri

or

Sup

po

rt

Bridge Example





Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Bridge


Segmental Box 0.97 1.05 1.05 1.04 0.99 1.02 1.06

Group 2 – Shear Right of Interior Support


lanes


to permit vehicles

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Concrete Slab

Spliced PC I Girder


Segmental Box

Rat

io o

f Sh

ear

Rig

ht

of

Inte

rio

r Su

pp

ort

Bridge Example



Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I1.35(D+L)

Strength I

1.4(D+L)Strength I

Str. II MN P413

Strength I

Str. II P15-18

Strength I

Str. II P15-39

Strength I

Str. II P15-60

Strength I

Cur. Str. IV

Strength I

1.35(D+L)

Strength I

1.4(D+L)

Strength I

Bridge


Segmental Box 0.99 1.07 1.07 1.06 1.00 1.02 1.06

Ratio of Strength II to Strength I (interior girders with permit vehicles in all lanes,

Impact = 33%)

MnDOT P413 CalTrans P15-18 ft

CalTrans P15-39ft

CalTrans P15-60ft

Min Max Min Max Min Max Min Max

M+end 0.90 1.04 0.98 1.33 0.98 1.22 0.98 1.15

M+center 0.90 1.02 1.12 1.40 1.09 1.26 1.07 1.18

M- 0.90 0.99 0.95 1.22 0.95 1.23 0.95 1.15

Vend 0.90 1.09 0.99 1.42 0.99 1.34 0.98 1.29

Vleft 0.95 1.07 1.05 1.38 1.05 1.30 1.04 1.23

Vright 0.94 1.10 1.07 1.39 1.06 1.32 1.06 1.26

* Simple span moments and shears are considered in M+end and Vend rows


CalTrans P15-39ft

CalTrans P15-60ft


M+end 0.88 1.04 0.98 1.31 0.98 1.21 0.98 1.12

M+center 0.88 1.02 1.03 1.23 1.02 1.16 1.01 1.10

M- 0.90 0.95 0.96 1.08 0.95 1.09 0.95 1.04

Vend 0.90 1.09 0.99 1.40 0.99 1.34 0.98 1.29

Vleft 0.95 1.05 1.03 1.28 1.03 1.23 1.02 1.19

Vright 0.94 1.10 1.02 1.34 1.02 1.30 1.02 1.26


Ratio of Strength II to Strength I (Interior girders with permit vehicles in one lane and

HL93 in other lanes, Impact = 33%)


CalTrans P15-39ft

CalTrans P15-60ft


M+end 0.74 0.90 0.87 1.07 0.87 1.01 0.85 0.95

M+center 0.74 0.86 0.91 1.10 0.90 1.01 0.88 0.95

M- 0.81 0.89 0.90 1.01 0.90 1.02 0.89 0.97

Vend 0.78 1.00 0.88 1.25 0.88 1.21 0.86 1.16

Vleft 0.88 0.97 0.97 1.21 0.96 1.14 0.96 1.10

Vright 0.86 1.00 0.98 1.21 0.98 1.16 0.98 1.12


Ratio of Strength II to Strength I (Interior girders with permit vehicles in one lane,

Impact of 33%)


CalTrans P15-39ft

CalTrans P15-60ft


M+end 0.82 0.98 0.92 1.22 0.92 1.13 0.92 1.07

M+center 0.82 0.97 1.06 1.27 1.03 1.16 1.02 1.09

M- 0.89 0.93 0.93 1.11 0.93 1.13 0.93 1.06

Vend 0.85 1.02 0.96 1.28 0.96 1.24 0.95 1.19

Vleft 0.92 1.00 1.02 1.27 1.02 1.19 1.01 1.14

Vright 0.90 1.05 1.02 1.27 1.02 1.22 1.01 1.19


Ratio of Strength II to Strength I (Interior girders with permit vehicles in all lanes,

Impact of 15% on Permit)


CalTrans P15-39ft

CalTrans P15-60ft


M+end 0.68 0.86 0.82 1.01 0.82 0.96 0.82 0.92

M+center 0.68 0.84 0.88 1.01 0.84 0.94 0.84 0.90

M- 0.78 0.89 0.88 0.94 0.86 0.95 0.86 0.90

Vend 0.74 0.94 0.85 1.16 0.84 1.12 0.83 1.08

Vleft 0.82 0.92 0.95 1.12 0.95 1.06 0.94 1.03

Vright 0.80 0.96 0.96 1.12 0.96 1.09 0.95 1.06


Ratio of Strength II to Strength I (Interior girders with permit vehicles in one lane,

Impact of 15% on Permit)

Ratio of Strength IV to Strength I

Current Strength IV

1.5(D)

Proposed Strength IV 1.35(D+L)

Proposed Strength IV

1.4(D+L)

Min Max Min Max Min Max

M+end 0.39 0.92 0.87 1.01 0.90 1.05

M+center 0.36 0.86 0.86 0.99 0.89 1.03

M- 0.53 1.02 0.90 1.03 0.93 1.07

Vend 0.37 0.92 0.86 1.01 0.89 1.05

Vleft 0.47 0.99 0.89 1.02 0.92 1.06

Vright 0.47 1.00 0.88 1.02 0.92 1.06


Strength IV: Reliability Analysis

Group 1 Bridges - Interior Girders

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

Be

ta

DL/(DL+LL)

Original Calibration Existing Specif ications

Proposed Formula 1 Proposed Formula 2

Strength IV: Reliability Analysis

Group 1 Bridges - Interior Girders

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

Be

ta

DL/(DL+LL)



Proposed Formula 3

Reliability Analysis – Precast Girders

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

Be

ta

DL/(DL+LL)



Reliability Analysis – Box Girders

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0

Be

ta

DL/(DL+LL)



Reliability Analysis - Trusses

2.00

2.50

3.00

3.50

4.00

4.50

0.00 0.20 0.40 0.60 0.80 1.00

Be

ta

DL/(DL+LL)

Existing Specif ications Proposed Formula 1

Proposed Formula 2

Conclusions

Strength II Comparisons (1)

• The CA-P15 trucks produce live load effects

significantly higher than the HL93

• When assumed to be in all lanes, the CA-P15

trucks produce Strength II factored design load

effects (DL + Permit) significantly higher than the

Strength I factored design load effects (DL +

HL93)

Conclusions


• The ratio between Strength II and Strength I

factored design load effects is reduced when the

permit vehicles are assumed to exist in one lane

with HL93 load in other lanes

• A larger reduction is achieved when the permit

load is assumed to have lower impact and/or

when no other loads are assumed on the bridge

concurrently with the permit load

Conclusions


• When assumed to exist in all lanes, the MN-413

truck produce Strength II design loads effects no

more than 10% higher than Strength I design

load effects

Conclusions

Strength IV Reliability Index

• The two proposed load combinations

(1.35 DL + 1.35 LL) and (1.4 DL + 1.4 LL)

Do not control over Strength I for the bridges

included in this study except in few cases and by

not more than 5% for the latter combination.

• When Strength I controls, the reliability index

does not change. When Strength IV controls

(with slight margin), the difference in the

reliability index is small

progress report on calibration of strength iv limit...

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