ASCE Structures 2005 Final

7/29/2019 ASCE Structures 2005 Final

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STRESS IN ORTHOTROPIC STEEL DECK COMPONENTS DUE TO

VEHICULAR LOADS

WanChun Jen1 and Ben T. Yen2

1ATLSS Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA; PH

(610) 758-5613; FAX (610) 758-6568; email:[email protected] Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA; PH

(610) 758-5553; FAX (610) 758-6568; email:[email protected]

Abstract

Laboratory measurement of local stresses was made on components of a full

scale model of orthotropic deck panel of Bronx-Whitestone Bridge. Simulated wheel

load of trucks was placed on the deck at various locations along longitudinal

stiffening ribs of trapezoidal shape. The loads induced local stresses and local

bending of diaphragm web plates and rib walls. The local stresses were moderately

high in magnitude in all components of the model deck.

Introduction

Orthotropic steel decks with longitudinal, closed rib stiffeners serve the dual

function of being the upper flange of the box girder, real or equivalent, and being the

member to transfer vehicular loads to other parts of the bridges. Stresses induced by

vehicular loads are the primary cause of fatigue cracks in decks. Some analytical and

experimental studies have been conducted to examine the local stresses in deck

components in order to alleviate fatigue cracking at connections between longitudinal

ribs and transverse diaphragms (Connor 2001, Tsakopoulos 2002, Ye 2004).

After the fatigue testing in laboratory of a full scale model deck of the Bronx-

Whitestone Bridge (BWB) in New York City, stresses at various components of the

specimen were measured for examination of the regional effect of wheel loads of

trucks. This paper briefly summarizes some of the results.

Test Specimen and instrumentation

The model deck of BWB was 48 feet (14.63 m) long and 37 feet (11.28 m) wide,

1
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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as shown schematically in Figure 1. It consisted of 2 panels of continuous deck

supported by three floorbeams. The floorbeams were each supported by a wall

column, and by a stiffening girder at the other end, Figure 2. The test deck modeled

half of the bridge width with the test deck plate connected to the wall longitudinally

simulating continuity at the center line of the bridge.

REACTION WALL

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Diaphragm

A1

Floor

Beam A

Floor

Beam C

Floor

Beam B

Diaphragm

B1

N

LOADIND POSITION

Rib No.

1 2 43

Figure 1 Top View of Specimen Setup

Figure 2 Elevation of Specimen

The orthotropic deck had 5/8 in. (16 mm) thick deck plate, two longitudinal

plate stiffeners and fourteen longitudinal trough stiffeners with 5/16 in. (8 mm) thick

wall. The diaphragm web was inch (13 mm) thick.

2

Line 1

Line 5, 6

...


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The trapezoidal ribs were 13 in. (330 mm) wide at the top, 5 in. (127 mm) wide

at the bottom and the inclined walls were 14 in. (357 mm) deep. The spacing between

ribs is also 13 in. (330 mm), so the deck plate is supported uniformly for most of its

width.

A large number of strain gages and displacement transducers (LVDTS) were

placed between Diaphragm A1 and B1. The emphasis was on measuring strains in the

deck components at Diaphragm B. Figure 3 shows schematically the strain gage

locations around Rib 6 at Diaphragm B.

Loading Procedure

Hydraulic actuators applied vertical loads though rubber pads (footprints) to the

deck to simulate wheel loads of HS 25 trucks. Since linear behavior at details was

observed from strain reading during loading, each applied load was increased from

20K to 80K to exaggerate the strains in the components for easy comparison.

Figure 3 Strain Gage Location and Loading Lines, Rib 6 at Diaphragm B

Figure 4 Loading Positions

The loads were applied individually along six lines, as depicted in Figure 3.

These lines simulate the truck wheels directly over the connections of ribs wall to the

deck plate, and in between.

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Four load positions were used in each line: above Diaphragm A1, halfway

between A1 and B, above Diaphragm B and halfway between B and B1. These

positions are indicated in Figure 4.

Results

Linear Elastic Behavior

The test deck behaved linear elastically under the applied load. Figure 5 shows

as examples the load versus deflection relationship at nine LVDTs throughout the test

deck. The load was on Line 1 at Position 2. Figure 6 shows the load versus strain

relationship of four strain gages at Diaphragm B1. In all cases, the deflection and

strain increased linearly with the applied load, and return to the same original value

when the loads were removed.

Strains in the Deck Pate

The strain distributions on the bottom of deck plate along Diaphragm A1 when

the simulated load was at different positions on Line 6 are plotted in Figure 7. Line 6

was along the mid-width of Rib 8. With 80K applied at Position 1 directly over

Diaphragm A1, the maximum stress on the bottom of the deck at Rib 8 was not the

highest. The highest stress of about 7 Ksi (230 in/in strain) occurred when the load

was at Position 2 between Diaphragm A1 and B. When the 80K load was at Position

4 between two diaphragms, the bottom of the deck plate was in low tension at the

junction with the rib wall at Ribs 8, 9 and 10.

0

20

40

60

80

100

120

-0.05 0 0.05 0.1 0.15 0.2 0.25

Deflection (inch)

Load

(kips)

LVDT_1

LVDT_2

LVDT_3

LVDT_4

LVDT_5

LVDT_6LVDT_7

LVDT_8

LVDT_9

Figure 5 Load vs Deflection (Line 1, Loading Position 2)

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-800

-600

-400

-200

0

200

400

0 20 40 60 80 100 120

Strain ( in./in.)

Load(kips)

Strain Gage 46

Strain Gage 47

Strain Gage 13

Strain Gage 15

Figure 6 Load vs. Strain at Diaphragm B1 (Line 1, Loading Position 2)

-250

-200

-150

-100

-50

0

50

100

-10 0 10 20 30 40 50 60

Distance (inch)

Strain(in./

in.) Loading Position 1 Loading Position 2

Loading Position 3 Loading Position 4

Loading Position 3+4 Loading Position 2+3+4

Figure 7 Strains on the Bottom of Deck Plate along Diaphragm A1 (Loads on Line 6)

Figure 8 shows the strain distribution on the bottom of deck plate along

diaphragm B under the same loading positions of Figure 7. All stresses were low

under a 80K load, with a maximum of less than 10 Ksi (3450 in/in strain) when the

5

P = 80 K


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applied load was between diaphragms. Under a wheel load of HS 25, the maximum

live load stress under the deck would be less than 3 Ksi.

The strain distributions along Diaphragm B in Figure 8 indicate that the regional

influence of loads on deck plate stresses was confined to only the adjacent one or two

ribs.

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-100

0

100

200

300

400

500

600

-10 0 10 20 30 40 50 60 70

Distance (inch)

Strain(in./

in.)

Loading Position 1

Loading Position 2

Loading Position 3

Loading Position 4

Loading Position 3+4

Loading Position 2+3+4

Figure 8 Strains on Bottom of Deck Plate along Diaphragm B (Loads on Line 6)

Stresses in Diaphragm at Cutout

The longitudinal stiffening ribs passed though diaphragm webs at cutouts, as

shown in Figure 2 and 3. The geometry of the cutout was determined by analysis and

was one of the main reasons of fatigue testing the model deck. In the static testing of

the deck model to examine the regional effects of loads, strains on diaphragm webs at

cutouts were measured when loads were applied at various positions. Example results

are presented in Figures 9 to 10.

In Figure 9, the strains on Diaphragm B at the top of cutout for Ribs 6, 7, 8, and

9 are presented. The loads were applied along Line 3 over the connection between the

deck and a web of Rib 6. When the 80K load was at Position 2 between diaphragms,

the highest strain of about 380 in/in was induced at the cutout at the other web of

Rib 6. That is corresponding to less than 3 Ksi under a wheel load of HS 25.

Again, the influence of a wheel load on local stresses is limited to one adjacent

6

P = 80 K


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rib only, as depicted by the strains in Figure 9.

-600

-500

-400

-300

-200

-100

0

100

200

-10 10 30 50 70 90 110

Distance (inch)

ObservedstrainsatCuto

Loading Position 1

Loading Position 2

Loading Position 3

Loading Position 4

Loading Position 3+4

Loading Position 2+3+4

Figure 9 Strains at Cutout on South Face of Diaphragm B (Loads on Line 3)

-500

-400

-300

-200

-100

0

100

-10 0 10 20 30 40 50 60 70 80 90 100

Distance (inch)

Strains(in./

in.)

Line 1

Line 2

Line 3

Line 4

Line 5

Figure 10 Strains on the South Face of Diaphragm B at Cutout (Loading Position 2)

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P = 80 K

P = 80 K


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The variation of stresses on Diaphragm B at cutouts of Rib 6 to 9 for loading

Position 2 of Loading Line 1 to 5, are presented in Figure 10. Position 2 is between

diaphragms. As the loading line moved away from Rib 6 (to Lines 4 and 5), the

strains at the cutout of Rib 6 decreased. The region of effect of only one adjacent rib

is again obvious. When the applied load was on Line 5 over Rib 8, relatively high

strains developed in Rib 8. There was a connection of the diaphragm between Rib 8

and Rib 9 (as shown in Figure 2), which affected the behavior of Rib 8.

Influence Line of Strains

The strain diagrams presented so far, Figure 7 to 10, provide information on the

distribution of stresses in deck components near the point of loading. The subsequent

diagrams show the magnitude of strain at specific points as a load was applied at

different locations nearby. The results are essentially Influence Lines.

Figure 11 shows the horizontal and vertical strains on the web of Diaphragm B

at the connection of deck plate and Rib 6. The strain gage locations are given in

Figure 3. Both the horizontal and vertical strains (at gage 10x and 12y) were highest

when the 80K load was directly above. The magnitude of strains at these gages

decreased as the load was placed away. Similarly, the horizontal and vertical strains

at gage 20(x) and 22(y) were the highest when the load was directly above. When the

load was at Line 5 over Rib 7, the strain at all four gages at Rib 6 were near zero.

-400

-300

-200

-100

0

100

200

300

400

0 5 10 15 20 25 30 35 40 45 50

Loading Line Distance (inch)

Strain(

in./

in.)

Gage 10 x

Gage 20 x

Gage 12 y

Gage 22 y

Figure 11 Influence Lines of Horizontal (x) and Vertical (y) Strains on Diaphragm B

at Connection of Deck and Rib 6 (Loading Position 2)

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Line 1 2 3 4 5


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-600

-400

-200

0

200

400

600

0 5 10 15 20 25 30 35 40 45 50


Strain

(i

n./

in.)

Gage 128 N

Gage 129 S

Gage 134 N

Gage 135 S

Figure 12 Influence Lines of Strains on North and South Faces of Diaphragm B at

Top of Cutout, Rib 6 (Loading Position 2)

On Diaphragm B at the cutout of Rib 6, strains on the South surface of the

diaphragm web at the top of cutout (Figure 12) were slightly higher when the load

was at Line 2 between the rib walls than when the load was directly over the walls.

The difference in strains at back to back strain gages (128/129,134/135) indicates that

the diaphragm web was subjected to local bending. In this case, the magnitude of

bending was about the same on the two sides of Rib 6. On the other hand, the

diaphragm web plate local bending was not prominent at the lower corners of the

cutout, as the strains at back to back strain gages (130/131, and 132/133 in Figure 13)

increased or decreased similarly. All four gages had the highest strain when the

applied load was directly above, and had almost no strain when the load was one rib

away.

The rib walls were also subjected to local bending when the applied load was

nearby. The Influence Lines for strain gage pairs on the walls of Rib 6 are given in

Figure 14. The difference in strain between the gages of each pair (137/138, 139/140)

signifies local plate bending. The maximum difference was about 350 in/in in the

5/16 in. thick plate, comparing to about 400 in/in in the in. web plate of

Diaphragm B in Figure 12.

9

Line 1 2 3 4 5


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-800

-600

-400

-200

0

200

400

600

0 5 10 15 20 25 30 35 40 45 50


Strain(in./

in.)

Gage 130 N

Gage 131 S

Gage 132 N

Gage 133 S

Figure 13 Influence Lines of Strains on Diaphragm B at Lower Corner of Cutout,

Rib 6 (Loading Position 2)

-600

-400

-200

0

200

400

600

0 5 10 15 20 25 30 35 40 45 50


Strain(in./

in.)

Gage 137 N

Gage 138 S

Gage 139 N

Gage 140 S

Figure 14 Influence Lines of Strains on Web of Rib 6 (Loading Position 2)

Figure 15 shows the Influence Line of strain on the wall of Rib 6 between

Diaphragm B and B1. When the applied load was at Position 4 directly over the cross

section of the rib, the bottom of the rib had the highest strain whether the load was

over the rib wall or in between. The shape of these Influence Lines is typical for a

10

Line 1 2 3 4 5

Line 1 2 3 4 5


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continuous beam. The strains on the web of the rib about an inch from the deck and

directly below the applied load along Line 3, however, decreased without changing

sign when the load was moved away. For this Loading Line, there was practically no

local strain at the point on the opposite web of the rib.

-800

-600

-400

-200

0

200

400

600

800

1000

1200

-200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0

Distance (inch)

Strain(in./

in.)

Rib wall East Line 2

Rib bottom Line 2

Rib wall West Line 2

Rib wall East Line 3

Rib bottom Line 3

Rib wall West Line 3

Figure 15 Influence Lines of Strain on Rib 6 between Diaphragm B and B1

Discussions and Conclusions

The strains in components were measured when a simulated wheel load of trucks

was placed at various locations on the deck. Results indicate that the local stresses

induced by the wheel load were essentially zero when the wheel load was one rib

away in the transverse direction of the orthotropic deck. By considering the

configuration of trucks on the bridge, it can be concluded that wheel loads of parallel

trucks have little effect on the local stresses in deck plate, diaphragms and rib walls.

In the longitudinal direction, multiple simulated wheel loads were applied during

testing. Because of the difference in stiffness of the diaphragms with or without

floorbeams, the effect of load position on local stresses was strongly influence by the

relative position of the loads to the diaphragms. Results of strain measurement

confirmed the linear elastic behavior of the deck and thus the adequacy of

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superposition of multiple loads. Computer analysis using a finite element model also

confirmed the measured strains when one or multiple simulated wheel loads were

applied.

A limited parametric study of the deck component dimensions is being

conducted. Preliminary results indicate that were the deck plate thickness be reduced

to in. with all other thickness and dimensions being the same, the stresses in

diaphragms would increase slightly under the simulated wheel load while the stresses

in the rib walls would increase more. Obviously the relative dimensions of

components have strong effect on local stresses. For the specific replacement

orthotropic deck of BWB, it can be calculated that vehicle induced local stresses in

the components are moderately high but well within permissible values.

Acknowledgments

The funding for this study was from Pennsylvania Infrastructure Technology

Alliance (PITA) and the model deck was provided by Triborough Bridge and Tunnel

Authority of New York City (TBTA). The prototype deck panel was designed by

Weidlinger Associate Inc. of New York City and manufactured by Leonard Kunkin

Associates of Line Lexington, PA. Testing was conducted at ATLSS Research Center

of Lehigh University.

References

Connor, R. J. and Fisher, J. W. (2001), Results of Field Measurements on the

Williamsburg Bridge Orthotropic Deck," ATLSS Report 01-01.

Tsakopoulos, P. T., and Fisher, J. W. (1999), Williamsburg Bridge, Replacement

Orthotropic Deck, As-Built Full-Scale Fatigue Test," ATLSS Report 99-02.

Tsakopoulos, P. T., and Fisher, J. W. (2002), Fatigue Resistance Investigation for

the Orthotropic Deck on the Bronx-Whitestone Bridge," ATLSS Report 02-05.

Ye, Q., and Fanjiang, G. N. (2004). Analysis and Design of Steel Orthotropic

Decks, IABSE, Shanghai, China, Sep. 2004. 222-223

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ASCE Structures 2005 Final