Open Grid Bridge Deck Research

Christopher Higgins, Ph.D., P.E. and

Peter Fetzer

AASHTO T-8 Technical Subcommittee

June 17, 2013

Outline

•Background •Experimental Program •Experimental Results •Finite Element Analysis •AASHTO-LRFD Design Approach •Conclusions

Research Need • Present AASHTO-LRFD Specification prescribes interior strip

width for open grid as : 1.25P + 4.0Sb where P is axle load, Sb is spacing of main bars • Commonly results in large SW (~72 in.) Parallel strips limited

to 40 in. • Edge loading commonly controls actual strength (no

provisions for edge strips) • No consideration of weak direction which influences fatigue

resistance • No consideration of orthotropic properties that control load

distribution in grid elements

Design Tables

Research Needs • BGFMA funded research to

improve understanding and design of open grid decks

• Move open grid deck design to LRFD

Test Specimens

•Deck Types & Configurations Diagonal Welded Rectangular Welded Lightweight Riveted Heavy Duty Riveted

All hot-dipped galvanized

• Weld Types Standard Weld and Two Alternatives

Weld Types Rectangular Grid

Experimental Program

•Orthogonal stiffness property tests •Load distribution tests: •Main bar spacing • Span length • Simple/Continuous Span

•Fatigue characterization tests • Strong Direction •Weak Direction

Stiffness Dx

Stiffness Dy

Twisting Stiffness Dxy

2

4xyP LDw

= ×

Load Distribution Tests

Grid deck specimens placed on stringer supports

- Six different grid specimens Multiple span lengths

Single and multiple patches (axle) Positive and negative moments in main bars Simple & Continuous

Weak Direction Strains Along a Single Cross Bar

Rectangular Grid

Main Bar and Cross Bar Location

Mic

rost

rain

at B

otto

m o

f Mid

span

Cro

ss B

ar (

µε ) (T

+/C

-)

Stre

ss a

t Bot

tom

of M

idsp

an C

ross

Bar

(ksi

) (T

+/C

-)

-400 -11.6

-300 -8.7

-200 -5.8

-100 -2.9

0 0.0

100 2.9

200 5.8

300 8.7

400 11.6

500 14.5

600 17.4M65.1

C65.1

M65.2

C65.2

M65.3

C65.3

M65.4

C65.4

M65.5

C65.5

M65.6

C65.6

M65.7

C65.7

M65.8

C65.8

M65.9

C65.9

M65.10

C65.10

M65.11

C65.11

M65.12

C65.12

Tension at top weld

10 kip patch load

Crossbar Strains: Critical Location Identified

Main Bar and Cross Bar Location

Mic

rost

rain

at B

otto

m o

f Mid

span

Cro

ss B

ar (

µε ) (T

+/C

-)

Stre

ss a

t Bot

tom

of M

idsp

an C

ross

Bar

(ksi

) (T

+/C

-)

-400 -11.6

-300 -8.7

-200 -5.8

-100 -2.9

0 0.0

100 2.9

200 5.8

300 8.7

400 11.6

500 14.5

600 17.4

700 20.3

800 23.2M65.1

C65.1

M65.2

C65.2

M65.3

C65.3

M65.4

C65.4

M65.5

C65.5

M65.6

C65.6

M65.7

C65.7

M65.8

C65.8

M65.9

C65.9

M65.10

C65.10

M65.11

C65.11

M65.12

C65.12

Absolute Maximum

Crossbar Strains: Critical Location Identified

Test #

Mic

rost

rain

at

C65

.5 P

roje

cted

to

To

p o

f C

ross

Bar

(

µε ) (C

+/T

-)

Str

ess

at C

65.5

Pro

ject

ed t

o T

op

of

Cro

ss B

ar (

ksi)

(C

+/T

-)

92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113-300 -8.7

-200 -5.8

-100 -2.9

0 0.0

100 2.9

200 5.8

300 8.7

400 11.6

500 14.5

600 17.4Influence of Moving Patch, Top of Crossbar

Strength Tests

July 3, 2013 15

Patch at edge of deck

Fatigue Tests of Grid Deck System

Fatigue Cracks in Main Bars Near Support

Fatigue Cracks in Cross Bars

Fatigue Results of Grid Deck System

N25

Stre

ss R

ange

(ks

i)

1,000 2,000 3,000 5,000 10,000 20,000 50,000 100,000 200,000 500,000 1,000,000 2,000,000 5,000,0002

3

4

567

10

20

30

40

506070

100

A

BB'C, C'D

E

E'

Outer Main BarInner Main BarCross Bar

Cross bar

Main bars

Subcomponent Fatigue Tests

Produce tension at top of weld detail

‘P’ Crack initiated from puddle weld

Observed Weak-Direction Fatigue Cracks

‘S’ Crack initiated from puddle weld into serration

Observed Weak-Direction Fatigue Cracks

‘N’ Crack initiated at serration ‘F’ Crack initiated at fillet weld

Weak-Direction Fatigue Results

N20t

Stre

ss R

ange

(ksi

)

1,000 2,000 5,000 10,000 100,000 1,000,000 5,000,0002

345

7

10

20

304050

70

100

ABB'C, C'DE

E'

4.0RECT2.5TYP44.0RECT2.5TYP54.0RECT2.5TYP6

Model for System Fatigue • Highly redundant internally • Weak-direction controls fatigue limit state • Need more than 1 bar to crack • System fatigue when cracking over wheel patch

dimension (5 adjacent bars transverse; 3 parallel ) • Monte Carlo simulation of fatigue life for 5 bar

system (5000 trials using statistical data from tests) • Longest lived bar controls system life • Get mean and standard dev. of system • Take 95% lower bound probability of shorter life

System Fatigue Category

July 3, 2013 25

7.5DIAG2.5TYP1 36,189 6,640 24,993 E'7.5DIAG2.5TYP2 95,420 12,497 74,864 E'7.5DIAG2.5TYP3 250,210 33,051 195,847 E4.0RECT2.5TYP4 29,449 6,957 18,006 E'4.0RECT2.5TYP5 465,169 113,734 278,092 E4.0RECT2.5TYP6 1,061,814 105,030 889,056 B'

95% Confidence Lower Bound

Standard Dev.AverageSpecimenFatigue

Category

Normalized to 20 ksi stress range

Residual Tensile Stresses • Positive moment puts welds into compression

• Residual tensile stresses from fabrication means

compression cycles can contribute to fatigue • Conducted fatigue test – 2 million cycles of compression,

then tensile fatigue tests followed Compression cycles consumed ~80% of life compared to specimens not subject to compression cycles

• Resulted in equivalent residual tension of 10.1 ksi

• Research by GangaRao et al. (1989) 6.2 ~ 3.3 ksi

Finite Element Analyses

• ABAQUS 6.11-1 • Uniformly Thick Plate • Element Type S4R • Thickness = 2.449 in. • Orthotropic Stiffness Properties:

3

3

3

12(1 )

12(1 )

12

xx

x y

yy

x y

xy

E tDv v

E tD

v v

GtD

=−

=−

=

y (in.)

Stro

ng D

irec

tion

Mom

ent (

k-in

/in) A

long

Mid

span

of N

orth

Spa

n

0 4 8 12 16 20 24 28 32 36 40 44 46-12

-10

-8

-6

-4

-2

0

2M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 CL

Test 92 FEATest 92Test 101 FEATest 101Test 113 FEATest 113

Rectangular Grid

Comparison with Finite Element Analyses Strong Direction

y (in.)

Wea

k D

irec

tion

Mom

ent (

k-in

/in) A

long

Mid

span

of N

orth

Spa

n

0 4 8 12 16 20 24 28 32 36 40 44 46-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 CL

Test 92 FEATest 92Test 101 FEATest 101Test 113 FEATest 113

Comparison with Finite Element Analyses Weak Direction

Rectangular Grid

New Design Moment Equations • FEA shows good correlation for strong and weak directions

over wide range of orthotropic properties • Based on orthotropic place model and FEA simulations • Design truck and tandem tire patches marched across a

simple span (individual patch controls) • Determine critical locations for maximum positive

moments, strong and weak directions for both transverse and parallel orientations

• Depends on parameters: D, L, α from stiffness tests •

•

2 xy

x y

DD D

α =

x

y

DDD

= 36" 84"2 5000.01 1.0

LDα

≤ ≤≤ ≤

≤ ≤

Range for L, D, α:

Proposed Strength Design Moment Equations 0.106 0.905

_ _ _ 0.101

0.723

_ _ _ 0.383 0.106

0.035 1.002

_ _ _ 0.067

_ _

0.618

0.346

0.385

transverse strong positive strength

transverse weak positive strength

parallel strong positive strength

parallel weak positiv

D LM C

LMD

D LM C

M

α

α

α

=

=

=

0.926

_ 0.486 0.120

0.120e strength

LD α

=

Example Moment Demand Strength I

Transverse direction Strong-direction Positive moment Simple Span = 6 ft

Proposed Strength Design

Specimen Proposed Demand Capacity Proposed

D α LBGFMA * (in) Mu,avg (k-in) φMp,footprint (k-in) Mu,avg/φMp,footprint

8.0RECT2.0TYP4 22.7 0.02 60 369 357 1.03

8.0RECT2.0TYP5 23.6 0.02 61.2 375 357 1.05

8.0RECT2.0TYP6 21.2 0.02 61.2 376 357 1.06

8.0RECT2.5TYP4 15.0 0.02 60 356 357 1.00

8.0RECT2.5TYP5 17.1 0.02 61.2 367 357 1.03

8.0RECT2.5TYP6 12.8 0.02 61.2 358 357 1.00

7.5DIAG2.5TYP1 9.6 0.03 61.2 324 366 0.88

7.5DIAG2.5TYP2 10.0 0.03 61.2 326 366 0.89

7.5DIAG2.5TYP3 9.9 0.03 61.2 328 366 0.90

4.0RECT2.5TYP4 24.3 0.02 75.6 364 494 0.74

4.0RECT2.5TYP5 29.1 0.03 75.6 359 494 0.73

4.0RECT2.5TYP6 24.0 0.02 75.6 357 494 0.72

37-R-L-5x1/4 61.3 0.09 24.8 73 70 1.04

37-R-5x1/4 439.6 0.19 42.6 68 70 0.97

Pres

ent s

pan

tabl

es o

k

Fatigue Design • Tire patches control design • Compare with WIM data (5000 ADTT year of data) • Five 10-kip axles (66.5 kip GVW vs 62 kip GVW AASHTO Fatigue) • LL = 1.0, IM = 1.33 = 6.65 kip patch (~ 6.9 kip fatigue tandem)

• Equivalent # of Cycles: • Account for axles of different weight in terms of fatigue cycles

and stress ranges • Equivalent 13.8 kip patch (AASHTO fatigue truck) induced cycles

per "real" truck = 0.56 (6.653/13.83)x5 Axles

• Compute life given fatigue categories of decks

0.723

_ _ _ 0.383 0.106

0.128transverse weak residual fatigue

LMD α

=

0.811

_ _ _ 0.428 0.220

0.041transverse weak negative fatigue

LMD α

=

Proposed Fatigue Design Moment Equations • Need independent critical locations for negative

moment & positive moment induced stresses • Recalibrated using fatigue load factors:

• IM = 1.15; LL = 0.75 (patch load =13.8 kips)

+

• Compressive up to maximum residual stress = 10.1 ksi • Transverse more critical due to N and SR

Design Options for Fatigue • Control location of wheel lines relative to stringers • Increase stiffness at free edges • Use targeted enhanced welds in regions across deck • Reduce span length • Use heavier grid on shorter span • Designers/owners can now choose alternatives to

get desired life and can implement into bridge management plans

Summary and Conclusions • Behavior of open grid decking is better understood

• Stiffness properties can be computed or determined

empirically

• Good correlation with analytical orthotropic plate model using stiffness properties

• LRFD compatible design equations and methodologies were developed for strength and fatigue design -> into Specs

• Open grid decks can now be designed to achieve desired level of performance

Questions?

Developing Design Moments Specimen D x (k-in2/in) D y (k-in2/in) D xy (k-in2/in) D α

7.5DIAG2.5TYP1 21,971 2300 108 9.6 0.037.5DIAG2.5TYP2 23,403 2337 112 10.0 0.037.5DIAG2.5TYP3 23,880 2404 105 9.9 0.034.0RECT2.5TYP4 51,926 2139 97 24.3 0.024.0RECT2.5TYP5 44,513 1530 106 29.1 0.034.0RECT2.5TYP6 51,547 2151 116 24.0 0.02

37-R-L-5x1/4 22,514 367 125 61.3 0.0937-R-5x1/4 34,597 79 153 440 0.19

36" 84"2 5000.01 1.0

LDα

≤ ≤≤ ≤

≤ ≤Range for L, D, α:

Proposed Strength Design Moment Equation

7.5DIAG2.5TYP1 4.0RECT2.5TYP4 37-R-L-5x1/4 37-R-5x1/4Design Eqn. 36.3 49.8 32.5 37.1Lab. Results 29.5 42.7 24.4 26.0

% Diff. -19 -14 -25 -30Design Eqn. NA 3.4 NA NALab. Results NA 3.7 NA NA

% Diff. NA 8 NA NADesign Eqn. 25.5 32.7 20.3 20.6Lab. Results 22.5 31.1 21.2 20.8

% Diff. -12 -5 5 1Design Eqn. NA 2.2 NA NALab. Results NA 2.6 NA NA

% Diff. NA 19 NA NA

Mtransverse_strong_positive_strength

Mtransverse_weak_positive_strength

Mparallel_strong_positive_strength

Mparallel_weak_positive_strength