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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