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
Shape Factor S=1.50 S=2.00 S=3.00
Proposed Disc Bearing Limits Is 1. 2. c c 0.14 7.00 ksi [0.10] [5.00] Individual upper limits based on testing and field history 3. S c 0.24 [N/A, 0.20] Analogous to AASHTO 14.7.5.3.2-3, implicitly sets limits on stress, strain, and shape factor combinations 4. S 1.40 [N/A]
SeS = Se Product + Strain Limit S c 0.24 c 0.24 S c 0.14 0.14 0.12 ( S) 0.1 0.08 0.06 1 1.5 2 2.5 3 3.5 S Thin Pads
S c 0.24 SeS = Se Product + Stress Limit E 2 1 S c 0.24E 1 S S 2 c 7.00 ksi 7 6.5 ( S) 6 5.5 5 1 1.5 2 2.5 S Thinner Pads
Se product - indicator of the max shear strain due to compression c 6S Gent & Lindley Solution, BE 1/76 c c CS c Stanton & Roeder, NCHRP 248 (1982) C varies according to aspect ratio, C = 6.0 for circular bearings
Se Product was (is) an implicit constraint in AASHTO specifications EC E c C c 6GS 2 c S c 2.00GS 0.33 (AASHTO 14.7.5.3.2-3) Equivalent criteria Se Product Material independent Allows for design comparisons between different materials
Linear FEA Studies Baseline: S = 2.0 Pad, 62D, E = 10 ksi, nu = 0.485 Axisymmetric section
Linear FEA Studies S=2.00, = 0.10, E = 10 S = 2.0 Pad, 62D, 10% strain
Baseline: S = 2.0, 10% strain, 62D Stress (psi) Peak core shear stress = 1.93 ksi 6000 4000 Stresses Groove area 2000 0-2000 -4000-6000 -8000 0 1 2 3 4 5 6 7 Radial Coordinate (in) SRR STT SZZ SRZ
For baseline pad For proposed pad designs C 1.9 ksi 1.7 ksi 2.3 ksi C Other durometers? Analyses were run with E = 10: C 0.2 E
Required Coefficient of Friction; COF R COF R 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 2 2.5 3 3.5 4 4.5 5 5.5 6 Radial Coordinate (in.) 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 COF R
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 Sample 0.25 Thickness E>> 2.20 4.00 10.00 16.00 (in) (in 2 ) 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
Test-Predicted Deviation Analysis Calc FEA Mean 0.023 0.027 STDev 0.201 0.213 Material Temperature Procedure Equipment Design
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Analytical Solutions Disc with frictionless surfaces 2 ri rr, r 2c 0, 3 rr r 1 0 r G 3 r 2 zz c i Normalized Stress 2.5 2.0 1.5 1.0 0.5 0.0 v1 vm p 0 rr E r 3 2 i 1 Ef c 2 f 1 r i 3 c -0.5-1.0 zz -1.5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 r Stress normalized by E E t KS A f
Material Tests
Force & Displacement Test Data 70000 60000 50000 40000 30000 Force Scale Displacement 20000 10000 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 TIme (s) d x 12,000 F
Linear Solid Model Standard Linear Solid F Ks Km c
Force (kips) 4.500 Force vs Time 4.000 3.500 3.000 2.500 2.000 1.500 F Test Fit FRlx F-Ks F-KmD 1.000 0.500 0.000 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Time (s)
Force Error (lbs) 0.005 df 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.005-0.01-0.015-0.02 df
10.00 Force at Constant Velocity Free expansion test 9.00 8.00 Force (kips) 7.00 6.00 5.00 4.00 V=.010 V=.020 Ks only 3.00 2.00 1.00 0.00 0.0000 0.0020 0.0040 0.0060 0.0080 0.0100 Displacement (Inches)
F Free Expansion Results Ks Km c 0? Hypothetical Bonded Results 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 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
Thank You Acknowledgements: AASHTO T2 Joints & Bearings Committee RJ Watson, Inc. PBENG