Calibration of AASHTO LRFD for Filled Grid Decks Based on Historical Performance Christopher Higgins...

Calibration of AASHTO LRFD for Filled Grid Decks Based on Historical Performance

Christopher Higgins and O. Tugrul TuranChristopher Higgins and O. Tugrul TuranSchool of Civil and Construction EngineeringSchool of Civil and Construction Engineering

Oregon State University Oregon State University andand

Mark Kaczinski and Phil GaseMark Kaczinski and Phil GaseBridge Grid Flooring Manufacturing AssociationBridge Grid Flooring Manufacturing Association

International Bridge ConferenceJune 8, 2011

•Widely used in practice

•Light weight compared to conventionally reinforced decks

•Two way bending (orthotropic behavior)

Source: www.bgfma.org

Source: www.bgfma.org

Introduction & Background

Main Bars (Strong Direction) Cross Bars (Weak Direction)


4 4 4

4 2 2 42 ( , )x y

w w wD H D p x y

x x y y

1 2 xyH D D

2 2

12 2( )x x

w wM D D

x y

2 2

12 2( )y y

w wM D D

y x

2

2xy xy

wM D

x y

•Orthotropic Thin Plate Theory

•Non-homogenous biharmonic equation.

•Stiffnesses can be determined experimentally

1

: Flexural rigidity in the strong direction

: Flexural rigidity in the weak direction

: Torsional rigidity contribution from

the strong and the weak direction rigidities

: Torsional rigidity

( ,

x

y

xy

D

D

D

D

w x ) : Deflection

( , ) : Applied transverse load in

the Cartesiancoordinate system

y

p x y


4 4 4

4 2 2 42 ( , )x y

w w wD H D p x y

x x y y

1 2 xyH D D

2 2

12 2( )x x

w wM D D

x y

2 2

12 2( )y y

w wM D D

y x

2

2xy xy

wM D

x y

• D = 0, plate acts like a one –way slab or beam.• D = ∞, plate behaves like a collection of separate strips.

D = 0D = 0 D = ∞D = ∞

D = 2D = 2


AASHTO-LRFD (2004) section 4.6.2.1.8

Higgins 2003, Higgins 2004

x yH D Dx yH D D x yH D D, ,


•One-way slab, (Prior to AASHTO-LRFD, 1994)

•Orthotropic Thin Plate Theory (AASHTO-LRFD, 1994) , Single patch at the center

•Orthotropic Thin Plate Theory (AASHTO-LRFD, 2004),

Tandem axle and multiple patches,

Fatigue Limit State

Deflection equations

0.25 20ln 12.0 35transverseM ClpD S

0.29 0.46150 ln 12.0 1908parallel

lM Cp D S D

1100 2.5

IM Pl


0.25 20ln 12.0 35transverseM ClpD S

0.29 0.46150 ln 12.0 1908parallel

lM Cp D S D

1100 2.5

IM Pl

:Strong direction moment,

m. bars transverse to traffic dir.transverseM

:Strong direction moment,

m. bars parallel to traffic dir.

parallelM

: X

Y

DDD

: Continuity Factor (0.8 for continuous spans)

(1.0 for simply supported)

C

L, S: Span Length

C=0.8

C=1.0


•Many of the decks were constructed more than 30 years ago and AASHTO-LRFD(2004) not calibrated against historically successful performance

•BGFMA selected 26 decks, design details and supporting information provided

•Min. 10; max. 51 years in service.


Comparison of AASHTO LRFD 2004 and AASHTO LRFD 1994

Moment main bars transverse to traffic

X

Y

DD

D Region generally used in practice

Strength Limit State Comparison


Moment main bars parallel to traffic

X

Y

DD

D Region generally used in practice

Strength Limit State Comparison

Comparison of AASHTO LRFD 2004, AASHTO LRFD 1994 and Table A4

AASHTO-LRFD (2004), AASHTO-LRFD (1994) moment values for D=1.0 and C=0.8, and AASHTO-LRFD (2004) deck slab design table positive moment values (A4)

Span Length (in)

Mo

me

nt

(kip

-in

/in)

40 60 80 100 120 140 160 1802.5

5

7.5

10

12.5

15

17.5

20AASHTO LRFD Table A4-1 (Multiplied by =1.75)AASHTO LRFD 2004(Perpendicular to traffic) (C=0.8)AASHTO LRFD 2004 (Parallel to traffic) (C=0.8)AASHTO LRFD 1994 (Perpendicular to traffic) (C=0.8) (Design Truck)AASHTO LRFD 1994 (Parallel to traffic) (C=0.8) (Design Truck)

Comparison of AASHTO LRFD 2004, AASHTO LRFD 1994 and Table A4

AASHTO-LRFD (2004), AASHTO-LRFD (1994) moment values for D=1.0 and C=0.8, and AASHTO-LRFD (2004) deck slab design table negative moment values (A4).

Span Length (in)

Mo

me

nt

(kip

-in

/in)

40 60 80 100 120 140 160 1800

5

10

15

20

25AASHTO LRFD Table A4-1 (Multiplied by =1.75)AASHTO LRFD 2004(Perpendicular to traffic) (C=0.8)AASHTO LRFD 2004 (Parallel to traffic) (C=0.8)AASHTO LRFD 1994 (Perpendicular to traffic) (C=0.8) (Design Truck)AASHTO LRFD 1994 (Parallel to traffic) (C=0.8) (Design Truck)


Strength Limit State Comparison, 26 Decks

AASHTO-LRFD-1994 Moment (Kip-in/in) (Design Truck)

AA

SH

TO

-LR

FD

-20

04 M

om

ent

(Kip

-in

/in)

8 10 12 14 16 18 20 228

10

12

14

16

18

20

22Perpendicular to trafficParallel to traffic

Demands somewhat higher now.

ADTT

MP

osi

tive

yie

ldin

g/M

AA

SH

TO

-LR

FD

-200

4 (

C=

0.8

)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.5

1

1.5

2

2.5


Max= 2.32Min=1.27Mean=1.6458% above 1.5

Strength Limit State (Positive Moment)

Comparison of AASHTO LRFD Design Demands with Available Resistance

M+ “Capacity” is adequate

Max= 2.77Min=1.08Mean=1.4835% above 1.5

ADTT

MN

egat

ive

yie

ldin

g/M

AA

SH

TO

-LR

FD

-200

4 (

C=

0.8)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.5

1

1.5

2

2.5

3

3.5Perpendicular to trafficParalle to traffic

Strength Limit State (Negative Moment)

Comparison of AASHTO LRFD Design Demands with Available Resistance

M- “Capacity” is adequate

D (pos.) D (neg.) Number of Spans Supports

Case 1 Cracked NA Single Rigid

Case 2 Uncracked NA Single Rigid

Case 3 Cracked Cracked 3 Span Rigid

Case 4 Uncracked Uncracked 3 Span Rigid

Case 5 Cracked Uncracked 3 Span Rigid

Case 6 Uncracked Cracked 3 Span Rigid

Case 7 Cracked NA Single Flexible

Case 8 Uncracked NA Single Flexible

Case 9 Cracked Cracked 3 Span Flexible

Case 10 Uncracked Uncracked 3 Span Flexible

Case 11 Cracked Uncracked 3 Span Flexible

Case 12 Uncracked Cracked 3 Span Flexible

Super structure flexibility: Slightly reduced negative moments, slightly increased positive moments for strength.

Distributed stiffness due to cracking not significant.

Strength Limit State with FEA: Superstructure and Distributed Stiffness

Bridge Number (ranked in deflection/span length order)

Def

lec

tio

n/S

pan

Le

ng

th

0 2 4 6 8 10 12 14 16 18 20 22 24 260.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035 Perpendicular to trafficParallel to trafficL/360 (AISC BLDGS)L/800 (AASHTO LRFD 2004)

Deflection Criteria

ADTT

SR

(p

osi

tiv

e b

end

ing

) (k

si)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

1

2

3

4

5

6

7

8Perpendicular to trafficParallel to trafficCategory C

SR<5ksi Inf. Life

Fatigue Limit State (Positive Moment)

Fatigue Limit State (Negative Moment)

ADTT

SR

(n

egat

ive

ben

din

g)

(ksi

)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

5

10

15

20

25

Perpendicular to trafficParallel to trafficCategory C

1/3

n

A( F)

N

N (365)(75)n(ADTT)

8A 44.0x10

Bridge # Name ADTT Y. in ser. N occurredC=0.8

SR neg. (ksi) Fat. L. (Years)

1 Green Island 890 27 26,312,850 7.5 10.9

2 Quincy Memorial 623 25 17,054,625 6.3 26.0

3 Country Road 18 NA 16 NA 12.2 NA

4 Meadowcroft Bridge 3 10 19,710 11.2 >75 years

5 Gold Star Bridge 6958 34 259,046,340 12.4 0.3

6 Mackinac Bridge 830 51 46,351,350 10.1 4.7

7 Interstate 55 7014 28 215,049,240 12.2 0.3

8 Pennsylvania Turnpike 7020 22 169,111,800 12.1 0.3

9 Tarentum Bridge 1855 21 42,655,725 12.2 1.2

10 US Route 6 220 20 4,818,000 11.5 12.0

11 Jerome Street Bridge 1007 19 20,950,635 11.9 2.4

12 Ohio State Route 360 17 6,701,400 11.5 7.3

13 Crown Point Bridge (Per.) 296 17 5,510,040 15.2 3.9

14 North Main Street 625 15 10,265,625 11.7 4.0

15 Crown Point Bridge (Par.) 296 17 5,510,040 13.6 5.3

16 Tobin Bridge 9000 28 275,940,000 8.5 0.7

17 WB I-70 7700 29 244,513,500 14.7 0.2

18 Cairo Bridge 40 29 1,270,200 8.4 >75 years

19 Gypsy Bridge NA 28 NA 9.7 NA

20 US 219 204 25 5,584,500 8.8 28.8

21 Daybrook Bridge NA 23 NA 10.8 NA

22 State Route 601 1348 16 23,616,960 12.4 1.6

23 West Street 595 15 9,772,875 11.2 4.8

24 Westbound GA 1265 15 20,777,625 13.8 1.2

25 Upper Buckeye Bridge NA 14 NA 11.7 NA

26 Smithfield Bridge 1140 13 16,227,900 14.5 1.1

Fatigue Limit State, 26 Decks

Fatigue Limit State

Tandem Axle Weight (kips)

Co

un

t

Summer I5

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 480

5000

10000

15000

20000

25000

30000

35000

40000

Tandem Axle Weight (kips)

Co

un

t

Summer I84

0 5 10 15 20 25 30 35 40 45 500

2000

4000

6000

8000

10000

12000

14000

16000

Fatigue Limit State

Elkins and Higgins, 2006

Fatigue Limit State

Elkins and Higgins, 2006

Front axle location (in)

Str

on

g d

ire

cti

on

ne

gat

ive

mo

me

nt

(k

ip-i

n/i

n)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800-6

-5

-4

-3

-2

-1

0

1

2Rigid Supports (=0.75, IM=1.15) (tandem patch)


Str

on

g d

ire

cti

on

ne

gat

ive

mo

me

nt

(kip

-in

/in

)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800-6

-5

-4

-3

-2

-1

0

1

2Rigid Supports (=0.75, IM=1.15) (single patch)


Str

on

g d

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750-5

-4

-3

-2

-1

0

1

L=5 ft

D=1.0 (=0.75, IM=1.15)D=2.0 (=0.75, IM=1.15)D=2.5 (=0.75, IM=1.15)D=8.0 (=0.75, IM=1.15)D=10.0 (=0.75, IM=1.15)


Str

on

g d

ire

cti

on

ne

gat

ive

mo

men

t (k

ip-i

n/in

)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 792-5

-4

-3

-2

-1

0

1

L=5 ft



Str

on

g d

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 100 200 300 400 500 600 700 800 900 1000-7

-6

-5

-4

-3

-2

-1

0

1

L=10 ft



Str

on

g d

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 100 200 300 400 500 600 700 800 900 1000-7

-6

-5

-4

-3

-2

-1

0

1

L=10 ft



Str

on

g d

irec

tio

n n

egat

ive

mo

men

t (k

ip-i

n/in

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200-8

-7

-6

-5

-4

-3

-2

-1

0

1

L=15 ft



Str

on

g d

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200-8

-7

-6

-5

-4

-3

-2

-1

0

1

L=15 ft


•SR/2 (transverse)

Fatigue Limit State : Transverse M-

N= 2 Big 1 Small Rainflow counting!

N = 4 Moderate 1 SmallRainflow counting!


Str

on

g d

irec

tio

n n

egat

ive

mo

men

t (k

ip-i

n/in

)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 680-3

-2

-1

0

1

L=5



Str

on

g d

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 50 100 150 200 250 300 350 400 450 500 550 600 650-3

-2

-1

0

1

L=5

D=1.0 (=0.75,IM=1.15)D=2.0 (=0.75,IM=1.15)D=2.5 (=0.75,IM=1.15)D=8.0 (=0.75,IM=1.15)D=10.0 (=0.75,IM=1.15)

•SR/2.5 (parallel)

Fatigue Limit State: Parallel M-


Str

on

g D

irec

tio

n n

egat

ive

mo

men

t (k

ip-i

n/in

)

0 100 200 300 400 500 600 700 800-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

L=10

D=2.5 (=0.75, IM=1.15)D=2.5 (=0.75, IM=1.15) (extremums)

N = 4 Big 2 SmallRainflow counting

N = 2 Moderate 6 SmallRainflow counting


Str

on

g d

irec

tio

n n

egat

ive

mo

men

t (k

ip-i

n/in

)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 680-3

-2

-1

0

1

L=5



Str

on

g d

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 50 100 150 200 250 300 350 400 450 500 550 600 650-3

-2

-1

0

1

L=5

D=1.0 (=0.75,IM=1.15)D=2.0 (=0.75,IM=1.15)D=2.5 (=0.75,IM=1.15)D=8.0 (=0.75,IM=1.15)D=10.0 (=0.75,IM=1.15)


Str

on

g D

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 100 200 300 400 500 600 700 800-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

L=10



Str

on

g D

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 100 200 300 400 500 600 700 800-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

L=10

D=1.0 (=0.75, IM=1.15) (extremums)D=2.0 (=0.75, IM=1.15) (extremums)D=2.5 (=0.75, IM=1.15) (extremums)D=8.0 (=0.75, IM=1.15) (extremums)D=10.0 (=0.75, IM=1.15) (extremums)


Fatigue Limit State: Parallel M-


Str

on

g D

ire

cti

on

ne

ga

tiv

e m

om

en

t (k

ip-i

n/i

n)

0 100 200 300 400 500 600 700 800 890-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

L=15


Front axle location (in)S

tro

ng

Dir

ec

tio

n n

eg

ati

ve

mo

me

nt

(kip

-in

/in

)0 100 200 300 400 500 600 700 800 900

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

L=15


Distance from CL of girder (in)

No

rmal

ize

neg

ativ

e m

om

ent

acc

ord

ing

to

CL

of

the

gir

der

0 3 6 90.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1Span Length = 4 ftSpan Length = 5 ftSpan Length = 6 ftSpan Length = 7 ftSpan Length = 7.5 ftSpan Length = 8 ftSpan Length = 9 ftSpan Length = 10 ft

M2=0.9xM1

Normalized negative moment (from Table A4-1 AASHTO-LRFD)).

Fatigue Limit State : Design Section

Bridge # Name ADTT Inst. Y. Y. in ser. n N occurredC=0.8

SR neg. (ksi) Fat. L. (Years)

1 Green Island 890 1981 27 5 43,854,750 3.4 Inf. life2 Quincy Memorial 623 1983 25 8 45479000 2.2 Inf. life3 Country Road 18 NA 1992 16 5 NA 5.5 NA4 Meadowcroft Bridge 3 2002 6 5 32,850 5.0 Inf. life5 Gold Star Bridge 6958 1974 34 5 431,743,900 5.6 2.06 Mackinac Bridge 830 1957 51 8 123,603,600 3.6 Inf. life7 Interstate 55 7014 1980 28 5 358,415,400 5.5 2.18 Pennsylvania Turnpike 7020 1986 22 5 281,853,000 5.5 2.19 Tarentum Bridge 1855 1987 21 5 71,092,875 5.5 7.9

10 US Route 6 220 1988 20 5 8,030,000 5.2 >75 years11 Jerome Street Bridge 1007 1989 19 5 34,917,725 5.3 15.712 Ohio State Route 360 1991 17 5 11,169,000 5.2 48.113 Crown Point Bridge (Per.) 296 1991 17 5 9,183,400 6.8 25.514 North Main Street 625 1993 15 5 17,109,375 5.3 26.315 Crown Point Bridge (Par.) 296 1991 17 7 12,856,760 4.88 Inf. life16 Tobin Bridge 9000 1980 28 8 735,840,000 3.1 Inf. life17 WB I-70 7700 1979 29 5 407,522,500 6.6 1.118 Cairo Bridge 40 1979 29 5 2,117,000 3.8 Inf. life19 Gypsy Bridge NA 1980 28 5 NA 4.4 Inf. life20 US 219 204 1983 25 8 14,892,000 3.2 Inf. life21 Daybrook Bridge NA 1985 23 5 NA 4.9 Inf. life22 State Route 601 1348 1992 16 5 39,361,600 5.6 10.423 West Street 595 1993 15 5 16,288,125 5.0 Inf. life24 Westbound GA 1265 1993 15 5 34,629,375 6.2 8.025 Upper Buckeye Bridge NA 1994 14 5 NA 5.3 NA26 Smithfield Bridge 1140 1995 13 5 27,046,500 6.5 7.6

•SR/2 (transverse)


•3 in. away from the CL of the support (SRx0.9)

•9/26 less than years in service

Fatigue Limit State, 26 Decks

ADTT

MP

os

itiv

e yi

eld

ing/M

AA

SH

TO

-LR

FD

-200

4 (

C=

0.8)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.5

1

1.5

2

2.5


C=0.8

C=1.0

All the main bars cracked over the continuous supports

If: Fatigue cracking over the supports

• Negative fatigue moment could be ignored

Strength Limit State

ADTT

SR

(p

osi

tive

ben

din

g)

(ksi

)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

1

2

3

4

5

6

7

8Perpendicular to trafficParallel to trafficCategory C

Fatigue Limit State

Fatigue Limit State

Bridge #Actual

Span (ft)

Limiting Span Lengths for different limit states

Strength (ft) Deflection L/800 (ft) Fatigue M+ (ft)

1 10.17 12.88 8.05 209.812 4.83 10.78 5.76 90.633 8.17 23.72 8.35 30.014 10.00 30.97 9.12 61.025 6.67 7.03 5.55 137.396 5.00 7.33 4.96 99.567 6.50 11.77 5.89 99.378 6.42 11.77 5.87 99.379 6.50 11.77 5.89 99.37

10 6.33 24.39 7.01 205.5211 6.12 11.77 5.77 99.3212 6.33 24.28 7.01 204.6613 6.37 7.18 5.49 181.6214 6.38 17.97 6.52 2681.2615 8.00 10.25 6.12 33.0516 6.46 8.02 6.00 96.8417 7.13 7.84 6.18 2941.2018 4.50 8.09 5.40 260.6919 6.17 8.09 6.00 260.6920 4.25 7.26 5.10 106.5421 5.25 7.06 5.55 298.9622 4.67 4.83 5.08 93.0323 5.50 5.73 5.50 45.8924 4.33 4.70 4.90 147.9225 8.25 14.20 7.48 47.8726 6.00 6.88 5.73 1215.49

Theoretical spans were determined•Strength: C=1.0; M+ only with first yeild limit

•Deflection: AASHTO-LRFD Prescribed deflection

•Fatigue: C=1.0; AASHTO-LRFD Prescribed fatigue SR (Strength/3) to limit of 5 ksi

•L/800 was the most conservative

•New service level stresses were determined for L/800

Limits on Possible Span Lengths

• Current AASHTO-LRFD moment provisions are not substantially higher than those specified for RC decks in traditional design

• Suite of decks not controlled by the strength or positive fatigue moment

• All 26 decks are limited by negative fatigue moment

• Negative fatigue moment can be reduced by a factor of 2.2 (for design say 2) for transverse to traffic and 2.8 (for design say 2.5) for parallel to traffic cases

• Additional analyses and/or tests around the negative moment region may help identify additional load distribution that may reduce stress range over the support for fatigue design

• Design approach would be: use the current design for Strength I with C=1.0, detail to obtain infinite life for positive fatigue moment, and limit the service level deflections to L/800

Conclusions and Recommendations

Calibration of AASHTO LRFD for Filled Grid Decks Based on Historical Performance Christopher Higgins...

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