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Advancing Disc Bearing Specifications AASHTO T-2
Columbus, OH June 24, 2014
Paul Bradford, PE, PhD PB Engineering Consultant
PBENG
How does it work? - Compression
Urethane tries to expand laterally
Friction inhibits expansion
Disc bulges
Disc Bearing Limits – Motivation
1. No change since the 1970’s, increase in allowables has not kept up with other materials
2. Excellent field performance for 40 years 3. Tested to much higher levels 4. Higher demands 5. Turn towards elastomeric bearing design methods
Current Disc Bearing Limits;
1. Stress (currently 5.0 ksi) 2. Strain (currently 10%) 3. No lower bound Shape Factor 4. No shape factor influence on allowables • Thin pads can accommodate higher stresses, but not high strains • Thick pads can accommodate higher strains, but not high stresses
S=2.00
S=1.50
S=3.00
Shape Factor
Proposed Disc Bearing Limits
0.24c
S
0.14c
7.00 ksic
1.40S
3.
4.
[N/A, 0.20]
Is…
[0.10]
[5.00]
[N/A]
Analogous to AASHTO 14.7.5.3.2-3, implicitly sets limits on stress, strain, and shape factor combinations
Individual upper limits based on testing and field history
2.
1.
0.24c
S
Thin Pads
1 1.5 2 2.5 3 3.50.06
0.08
0.1
0.12
0.14
S( )
S
0.24c
S
SeS = Se Product + Strain Limit
0.14c
2
0.241
ES
S
Thinner Pads
21 cE S
0.24c
S
1 1.5 2 2.55
5.5
6
6.5
7
S( )
S
SeS = Se Product + Stress Limit
7.00 ksic
6c cS Gent & Lindley Solution, BE 1/76
c cC S Stanton & Roeder, NCHRP 248 (1982) C varies according to aspect ratio, C = 6.0 for circular bearings
Se product - indicator of the max shear strain due to compression
26CE GS
2.00c GS
c C cE
0.33cS
Equivalent criteria
• Material independent • Allows for design comparisons between different materials
(AASHTO 14.7.5.3.2-3)
Se Product
Se Product was (is) an implicit constraint in AASHTO specifications
Linear FEA Studies
Axisymmetric section
Baseline: S = 2.0 Pad, 62D, E = 10 ksi, nu = 0.485
Linear FEA Studies
S = 2.0 Pad, 62D, 10% strain
S=2.00, = 0.10, E = 10
Baseline: S = 2.0, 10% strain, 62D
Peak core shear stress = 1.93 ksi
-8000
-6000
-4000
-2000
0
2000
4000
6000
0 1 2 3 4 5 6 7
Stre
ss (
psi
)
Radial Coordinate (in)
Stresses
SRR
STT
SZZ
SRZ
Groove area
0.2C E
1.9 ksiC For baseline pad
Other durometers? Analyses were run with E = 10:
For proposed pad designs
1.7 ksi 2.3 ksiC
Required Coefficient of Friction;
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2 2.5 3 3.5 4 4.5 5 5.5 6
CO
F R
Radial Coordinate (in.)
COFR
Baseline and Prop S2,e10 Prop S1.5,e14 Prop S3, e8
• No real change in required coefficient of friction • Move to slightly higher shape factors reduces the average COFR
SeS Validation Test Program
Test Series 1 - Durometer
15.38 OD
3.56 ID
1.88 TH
175.69 A
1.94 S
0.12 ea
Dur E Ec e s d R P
42D 2.20 10.48 0.12 1.296 0.23 0.030 228
52D 4.00 19.05 0.12 2.357 0.23 0.030 414
62D 10.00 47.63 0.12 5.893 0.23 0.030 1035
72D 16.00 76.21 0.09 7.000 0.17 0.022 1230
Test Series 2 - Shape Factor
Material - 62D
10.00 E
15.38 OD
3.56 ID
175.71 A
S TH Ec ea e s d R P
1.50 2.43 32.50 0.140 0.140 4.55 0.34 0.044 799 1.94 1.88 47.64 0.124 0.124 5.89 0.23 0.030 1035
2.50 1.46 72.50 0.096 0.096 6.96 0.14 0.018 1223 3.00 1.21 100.00 0.080 0.070 7.00 0.08 0.011 1230
Test Program
Test Series 3 - Coupon Tests
0.25 Sample Thickness
E>> 2.20 4.00 10.00 16.00
(in) (in2) 42D 52D 62D 72D 42D 52D 62D 72D 42D 52D 62D 72D
S D A ea e e e e s s s s Ec Ec Ec Ec
1.50 1.50 1.77 0.140 0.140 0.140 0.140 0.135 1.00 1.82 4.55 7.00 7.2 13.0 32.5 52.0
2.00 2.00 3.14 0.120 0.120 0.120 0.120 0.088 1.32 2.40 6.00 7.00 11.0 20.0 50.0 80.0
2.50 2.50 4.91 0.096 0.096 0.096 0.096 0.060 1.53 2.78 6.96 7.00 16.0 29.0 72.5 116.0
3.00 3.00 7.07 0.080 0.080 0.080 0.070 0.044 1.76 3.20 7.00 7.00 22.0 40.0 100.0 160.0
42D 52D 62D 72D 42D 52D 62D 72D
d d d d P P P P
0.035 0.035 0.035 0.034 1.8 3.2 8.0 12.4
0.030 0.030 0.030 0.022 4.1 7.5 18.8 22.0
0.024 0.024 0.024 0.015 7.5 13.7 34.2 34.4
0.020 0.020 0.018 0.011 12.4 22.6 49.5 49.5
Test Sequence
Test Name Test Series Description
1 Exercise 1,2, 3 150% Compression-Deflection
2 Baseline 1,2, 3 100% Compression-Deflection
3 Rotation 1, 2 125% Design Rotation @ .75 Static + .50 Dynamic
4 Post Rotation 1, 2 100% Compression-Deflection
5 Degradation 1 X Vertical Load at Y Temperature in Z Vibration Environment for H hours, where XYZ-H is TBD
6 Post Degradation 1 100% Compression-Deflection
Project Brg Tests – 11 projects, 38 bearings, circa Fall 2012
• 350 kips to 2800 kips • 5.0 to 7.5 ksi • 62D material
Test Program
Test Program – Project Documentation
7.5 ksi, 0.02 radians
• Material • Temperature • Procedure • Equipment • Design
Mean 0.023 0.027
STDev 0.201 0.213
Calc FEA
Test-Predicted Deviation Analysis
?
23zz c iG r
r
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
No
rma
lize
d S
tre
ss
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
p0
rr
zz
v M
v 1
2
, 32 0, 1 0i
rr r c rr
rr
r
Analytical Solutions
Disc with frictionless surfaces…
cfE
2
31 i
c
rE
Stress normalized by E
SEt
KA f
2
13
irf
Material Tests
0
10000
20000
30000
40000
50000
60000
70000
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Forc
e &
Dis
pla
cem
en
t
TIme (s)
Test Data
d x 12,000 F
Scale Displacement
Force
Linear Solid Model
Ks Km
c
F
Standard Linear Solid
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Forc
e (
kip
s)
Time (s)
Force vs Time
F Test
Fit
FRlx
F-Ks
F-KmD
-0.02
-0.015
-0.01
-0.005
0
0.005
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dF
dF
Force Error (lbs)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0.0000 0.0020 0.0040 0.0060 0.0080 0.0100
Force at Constant Velocity Free expansion test
V=.010
V=.020
Ks only
Displacement (Inches)
Force (kips)
9.617 E
350.715 K'
172.348 K''
0.491 Loss factor
0.246 Damping ratio
2.00 S
48.09 Ec
1478.699 K'
172.348 K''
0.117 Loss factor
0.058 Damping ratio
Free Expansion Results Hypothetical Bonded Results
Ks Km
c
F
0?
Ks related to molecular network configuration (entropy & int. energy) c, Km related to sliding of molecular segments
Moving Forward - 2014
Complete; • SeS Validation • Equipment, fine tune load testing procedure • Material Test, algorithm, software • Finite Elements Results
Acknowledgements:
AASHTO T2 Joints & Bearings Committee RJ Watson, Inc.
PBENG
Thank You
