load distribution in short bridges subjected to oversize

Dr. Sami W. Tabsh, P.E.

Department of Civil Engineering

American University of Sharjah

United Arab Emirates

WIDE TRUCK

Load Distribution in Short Bridges

Subjected to Oversize Vehicles

2

Outline

1. Introduction

2. Problem Statement

3. Objectives

4. Scope

5. Approach

6. Results

7. Conclusions

3

1. Introduction

Leading industries around the world rely heavily

on goods movement on roads:

Manufacturing

Oil and gas

Agriculture

Forest Products

Mineral Extraction

Paper

Dairy Products

Oil and gas

1. Introduction

4

Forest Products Mineral ExtractionAgriculture

5

1. Introduction

Truck weight and size are limited on bridges

because:

They reduce the useful life of the structure.

They cause damage to the deck, girders, cross-

bracing, joints, and bearings.

They result in accelerated maintenance, repair,

strengthening, or replacement work that is

required to keep structures at an acceptable level

of service.

6

1. Introduction

In the United States, federal truck weight and size

limits are:

356 kN maximum gross vehicle weight

89 kN maximum single axle weight

151 kN maximum tandem axle

2.6 m maximum gauge width

Otherwise, permits are required.

7

1. Introduction

When truck weight or

configuration exceeds the

limit, a permit is required.

For a permit truck, a DOT

engineer must check the

structural adequacy of

bridges located along the

route of the permit truck.

1. Introduction

8

Note that:

Short, heavy trucks cause more damage to a

bridge than long trucks having the same weight.

L o n g H e a v y L o a dL o n g H e a v y L o a d

S h o r t H e a v y L o a d

L o n g H e a v y L o a dL o n g H e a v y L o a d

S h o r t H e a v y L o a d

1. Introduction

9

Note also that:

Trucks having narrow gage widths are more

critical than those with wide gauges with same

weight.

S h o r t

G a u g e

W i d e

G a u g eGage Gage

10

1. Introduction

11

1. Introduction

Girder Distribution Factor (GDF)

It is the fraction of live load effect on a single girder

relative to the load effect on the whole bridge.

WxGDF

Whole superstructure One girder

Weight

W

12

1. Introduction

Properties of Girder Distribution Factors

They can be used in lieu of a refined 3-D

structural analysis.

They can be used to check the strength and

serviceability of new and existing bridges.

They are presented in the specification for

regular bridges and truck configurations.

They depend on the bridge type, geometry,

continuity, skewness, and limit state.

13

1. Introduction

GDF in AASHTO’s LRFD

Flexure: Single Lane Loaded (without multiple

presence factor)

where S = girder spacing (mm)

L = span length (mm)

ts = slab thickness (mm)

Kg = longitudinal stiffness parameter (mm4)

𝐺𝐷𝐹 = 0.05 +𝑆

6800

0.4𝑆

𝐿

0.3𝐾𝑔

𝐿 𝑡𝑠3

0.1

14

1. Introduction

GDF in AASHTO’s LRFD (Cont’d)

Shear: Single Lane Loaded (without multiple presence

factor)

where S = girder spacing (mm)

𝐺𝐷𝐹 = 0.3 +𝑆

9120

15

2. Problem Statement

Bridges subjected to overweight trucks with

standard gauge can be analyzed using common

procedures in the design specifications.

Currently, bridges subjected to oversized trucks

with nonstandard gauge require refined analysis.

Evaluation of bridges subjected to oversized trucks

can be greatly simplified by developing new girder

distribution factors that account for the increased

gauge width of oversized vehicles.

3. Objectives

• To develop flexural and shear girder distribution

factors for slab-on-steel-girder bridges subjected

to oversized trucks having nonstandard gage

configuration and width.

• To determine the sensitivity of the girder

distribution factor in flexure and in shear to

changes in the truck gage width for bridges having

various span lengths and girder spacings.

18

19

4. Scope

Slab-on-girder bridges

Composite steel I-girders

Simple spans (14.6-43.9m)

Girder spacing (1.22-3.66m)

Interior girders

Flexure at midspan and shear at the support

Single-lane and dual-lane trucks

Gauge width (1.83-5.49m)

20

4. Scope

Bridge Lengths

Three different simple spans

14.6 m

29.3 m

43.9 m

21

4. Scope

Bridge Cross-sections

1.22m girder spacing



152mm

6 spaces @ 1.22m 0.61m0.61m

203mm

4 spaces @ 2.44m1.22m1.22m

254mm

3 spaces @ 3.66m1.83m1.83m

4. Scope

Slab thickness and steel girder dimensions

22

Span Length

(m)

Girder Spacing

(m)

Slab Thickness

(mm)

Flange Thickness

(mm)

Flange Width (mm)

Web Thickness

(mm)

Web Depth (mm)

14.64

1.22 152 22 292 15 536

2.44 203 22 292 15 840

3.66 254 22 292 15 1145

29.28

1.22 152 43 423 24 628

2.44 203 43 423 24 933

3.66 254 43 423 24 1238

43.92

1.22 152 45 405 26 813

2.44 203 45 405 26 1118

3.66 254 45 405 26 1423

4. Scope

23

Truck Configurations

AASHTO HS20-44 Design Truck (325 kN)

OHBDC Level 3 Truck (740 kN)

35 kN 145 kN 145 kN4.3 m 4.3-9 m

60 kN 2 at 160 kN each 160 kN200 kN

3.6 m 6 m 7.2 m1.2 m

4. Scope

24

Trucks Configurations (Cont’d)

PennDOT P-82 Permit Truck (907 kN)

HTL-57 (507 kN)

3 at 120 kN each67 kN 4 at 120 kN each

1.2 m1.2 m1.2 m1.2 m 1.2 m3.6 m 7.2 m

4.3 m1.2 m1.2 m

4.3 m4.3 m

40 kN 2 at 94 kN each 2 at 94 kN each94 kN

25

4. Scope

Gage Widths

1.83, 2.44, 3.05 & 3.66 m

G

Single-Lane Trailer Dual-Lane Trailer

3.66, 4.88 & 5.49 m

G

a

a 1.22, 1.22 & 1.83 m

26

5. Approach

The considered bridges

will be modeled in 3-

dimensions by finite

elements and analyzed

in the linearly elastic

range under static

loading.

5. Approach

Commonly used FEA models for girder bridges

27

Model #1

Model #2Model #3

Model #4

28

5. Approach

Details of the finite element model used in study.

The FE-model was validated by Bishara et al.

(1993) based on field testing of the Parsons

Avenue Bridge in Columbus, OH.

RIGID

29

5. Approach

Bishara, A.G., Liu, M.C., & El‐Ali, N.D., “Wheel Load Distribution on Simply Supported Skew I‐Beam

Composite Bridges,” Journal of Structural Engineering, ASCE, 1993 Vol. 119, No. 2, p. 399-419.

30

5. Approach

Example of a finite element model of a 29.3 m simple

span bridge with 2.4 m girder spacing and cross-bracing

located at the quarter points.

5-girder bridge system 4-girder bridge system

31

5. Approach

Longitudinal Position of Truck

Flexure:

Place axle closest to resultant of all axles at mid-span.

35 kN 145 kN 145kN

4.3 m 4.3 m

32

5. Approach

Longitudinal Position of Truck (Cont’d)

Shear:

Place truck rear heavy axle just off the support.

35 kN 145 kN 145kN

4.3 m 4.3 mL

33

5. Approach

Transverse Position of Truck

Move the truck transversely from one side of the bridge to

the other side until the load effect in the girder under

consideration (e.g. first interior girder) is maximized.

GaugeX

34

5. Approach

Calculating the GDF

For the critical transverse truck position, determine:

Flexure: longitudinal stress in the bottom flange of all girders.

Shear: reaction at the support for all girders.

53.3 MPa

-27.9 MPa

Flexure @ midspan

5. Approach

Determining the GDF from FE Analysis

Flexure

Shear

35

𝐺𝐷𝐹𝑀 =𝑓𝑗

𝑓𝑖𝑁𝑖=1

𝐺𝐷𝐹𝑉 =𝑅𝑗

𝑅𝑖𝑁𝑖=1

f = stress in bottom flange

R = girder support reaction

36

6. Results

Critical Truck Configuration

Truck configuration effect on GDF

(Span Length=29.3m & Gage Width=1.83m)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

GD

F

Truck Location from Exterior Girder (m)

3.66 m girder

1.22 m girder

(a) Flexure

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5G

DF

Truck Location from Exterior Girder (m)

HS20

OHBDC

HTL-57

P-82

3.66 m girder

1.22 m girder

(b) Shear

3.66 spacing

1.22 spacing

3.66 spacing

1.22 spacing

37

6. Results

FEA Results for Wide Single-Lane Trailer

0

0.15

0.3

0.45

0.6

0.75

0.9

1.83 2.44 3.05 3.66

GD

F

Gage Width (m)

Girder Spacing=1.22m

0

0.15

0.3

0.45

0.6

0.75

0.9

1.83 2.44 3.05 3.66

GD

F

Gage Width (m)


L=14.6m

L=29.3m

L=43.9m

0

0.15

0.3

0.45

0.6

0.75

0.9

1.83 2.44 3.05 3.66

GD

F

Gage Width (m)


Flexure

Shear

Flexure

Shear

Flexure

Shear

6. Results

New GDFs for Wide Single-Lane Trailers

Flexure

Shear

38where G = Gauge width (mm)

𝐺𝐷𝐹𝑀 𝑆𝑖𝑛𝑔𝑙𝑒−𝐿𝑎𝑛𝑒 = 0.05 +𝑆

4 𝐺

0.4𝑆

𝐿

0.25𝐾𝑔

𝐿 𝑡𝑠3

0.3

𝐺𝐷𝐹𝑉 𝑆𝑖𝑛𝑔𝑙𝑒−𝐿𝑎𝑛𝑒 = 0.20 +𝑆

31.7

1

𝐺

0.7

39

6. Results

FEA Results for Wide Dual-Lane Trailer

0

0.15

0.3

0.45

0.6

0.75

0.9

3.66 4.27 4.88 5.49

GD

F

Gage Width (m)


0

0.15

0.3

0.45

0.6

0.75

0.9

3.66 4.27 4.88 5.49

GD

F

Gage Width (m)


L=14.6m

L=29.3m

L=43.9m

0

0.15

0.3

0.45

0.6

0.75

0.9

3.66 4.27 4.88 5.49

GD

F

Gage Width (m)


Flexure

ShearFlexure

Shear

Flexure

Shear

6. Results

New GDFs for Wide Dual-Lane Trailers

Flexure

Shear

40

where a = shortest distance between the exterior and

interior dual wheels (mm)

𝐺𝐷𝐹𝑀 𝐷𝑢𝑎𝑙−𝐿𝑎𝑛𝑒 = 0.05 +𝑆

ሻ4 (𝐺 − 𝑎

0.4𝑆

𝐿

0.25𝐾𝑔

𝐿 𝑡𝑠3

0.3

𝐺𝐷𝐹𝑉 𝐷𝑢𝑎𝑙−𝐿𝑎𝑛𝑒 = 0.19 +𝑆−915

8.75

1

𝑎

0.5 1

𝐺−2𝑎

0.4

41

6. Results

Accuracy of Developed GDF

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Pro

po

sed

GD

F

FEM-based GDF

Single Lane Trailer

Flexure

Shear

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Pro

po

sed

GD

F

FEM-based GDF

Dual Lane Trailer

Flexure

Shear

(GDF)proposed

(GDF)FEA≈ 1.082

(GDF)proposed

(GDF)FEA≈ 1.110

42

7. Conclusions

1. The HS20 truck produces the highest load effects

among the considered truck configurations.

2. The first interior girder often receives the highest

percentage of live load relative to other interior

girders.

3. Wide trucks produce lower girder distribution

factors than narrow trucks, and their effect on

shear is more critical than on flexure, especially

if the girder spacing is large.

7. Conclusions

4. The accuracy of the proposed GDF factors for

bridges subjected to oversized trucks is good.

5. When used on existing bridges subjected to

oversized vehicles, the proposed factors can

eliminate the time-consuming and complex 3-D

finite element analysis.

43

ACKNOWLEDGEMENT

Thanks are due to my former graduate student Ms

Muna M. Mitchell, currently with Walter P. Moore

in Austin, Texas, USA, for conducting the finite

element analyses.

44

Thank You

Questions?

45

load distribution in short bridges subjected to oversize

Documents