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Fatigue of Mechanical Components
Fatigue of Bolts
Professor Stephen D. Downing
Department of Mechanical Science and Engineering
© 2010 Darrell Socie, All Rights Reserved
Fatigue and Fracture
( Basic Course )
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Fatigue of Mechanical Components
Fatigue of Bolts
Fretting Fatigue
Welded J oints
Case Study
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Fatigue Strength of Bolts
Su = 785 MPa
Fatigue Design Review Task 5 – Assembly of Available Fatigue Data Relevant to Pressure Equipment Design
TWI Report No: 123337/2/01, European Commission
3.6
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K f for Bolts
SAE
Grade
Metric
Grade
Rolled
Threads
Cut
Threads
Head
Fillet
0 - 2 3.6 – 5. 8 2.2 2.8 2.1
4 - 8 6.6 – 10. 9 3.0 3.8 2.3
High strength bolts fail by crack growth.
Not much benefit, in fatigue, of very high strength bolts.
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Cut and Rolled Threads
Fatigue Design Review Task 5 – Assembly of Available Fatigue Data Relevant to Pressure Equipment Design
TWI Report No: 123337/2/01, European Commission
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Bolted J oint Loading
Force
Tensile Loading
P
P
P
Shear Loading
P
P
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Tensile Loading
kb
k j
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Bolt Preload Force
dFK T i=
K Torque factor depending on bolt friction Typically in the range of 0.1 – 0.3
T Bolt torque
Fi Preload force
D Bolt diameter
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Variability in Bolt Force
100 1000
Force
200 Data Points
Median 130
COV 0.14
99.9 %
99 %
90 %
50 %
10 %
1 %
0.1 %
Bolt Force, kN
Preload force in bolts tightened to 350 Nm
C u m u l a t i v e P r o b a b i l i t y
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Bolted J oint Analysis
δb extension
bolt
F b
δ j contraction
joint
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Bolted J oint Analysis (continued)
F b
δb δ j
Fi
preload force
kb k j
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Bolted J oint Analysis (continued)
Fb
P
P
e
P
P
e e
P
Pb
P j
Pkk
kP
jb
bb +=
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Fatigue Considerations
100
1000
10000
100
Cycles
S t r e s s A m
p l i t u d e ,
M P a
101 102 103 104 105 106 107
b ~ -0.1
10f S
1N
∆∝
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Bolt Stiffness
Fb
e
Pb
P j P
Pb
P j
P
Stiffer bolts carry more of the external force
e
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J oint Seperation
Fb
e
Fb = P
kbk j
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Bolt Stiffness
L1
L2
d
AtEA
L
EA
L
k
1k
1
k
1
k
1
t
2
1
1
b
21b
+=
+=
springs in series
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J oint Stiffness
3d
L
L
Ed8
k
2
j
π=
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J oint Stiffness
Pkk
kFP jb
bib ++=
Define joint factor, C
jb
b
ib
kk
kC
PCFP
+=
+=
kb should be small and and k j large
11.09
1
L
Ed8
L
EdL
Ed
C22
2
==π
+π
π
=
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Aluminum and Steel J oints
Steel Bolt , Steel Flange Steel Bolt , Aluminum Flange
C = 0.11 C = 0.25
L
Ed8k steel
2
f
π=
L
Ed8k umminalu
2
f
π=
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Fatigue Design
Traditional Method
Fi / AtMean stress
A l t e r n a t i n g s t r e s s
Su0
Se
Sa
tf
tiua
A2
PC
K 21
A/FSS
∆=
+−
=
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Shear Loading of Bolted J oints
Tensile Loading
P
P
P
Shear Loading
P
P
Fi FiµFiµFi
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Mechanics of Shear Loading
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Shear Failures of Bolts
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Shear Fatigue Testing
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Self Loosening of a Bolt
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Self Loosening Mechanism (Sakai)
F
−∆N
Normal force increased
Normal force decreased
Net torque produced
+∆N
−∆µN
+∆µN
Sakai, Investigations of Bolt Loosening Mechanisms, J SME 21 (159) 1978
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Loosening Fatigue limit
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Retightening of a Bolt
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Summary
Bolts have poor fatigue strength
Bolt preload must be maintained
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Fatigue of Mechanical Components
Fatigue of Bolts
Fretting Fatigue
Welded J oints
Case Study
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Fretting
www.eren.doe.gov/wind/feature.html
shaft
Relative motionbetween bearingand shaft
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Interface Stresses
P
F
Clamping Force
F
σx
τ
Stresses in the bar
Stresses in the flange
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Localized Sliding
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Fretting Mechanism
www.nrim.go.jp:8080/public/english/act/1992/1718.html
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Fretting Mechanism
High shearstresses at
local contacts
Cold weldingproduces
wear particles
Fretting fatiguecrack formed
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Fretting Cracks
100 µm
From Waterhouse, Fretting Corrosion, 1972 From ASM Fatigue and Fracture Handbook, 1996
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Fatigue Behavior
Hoeppner and Gates, “Fretting Fatigue Considerations in Engineering Design”, Wear , Vol. 70, 1981, 155-164
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Fretting Fatigue Limits
From Schijve Fatigue of Structures and Materials, Kluer, 2001
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Variables Affecting Fretting
Clamping pressure
Cyclic stress level
Sliding displacement
Coefficient of friction
Materials strength
Surface roughness
Environment
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Fretting Testing
www.nrim.go.jp:8080/public/english/act/1992/1718.html
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Clamping Pressure
www.nrim.go.jp:8080/public/english/act/1992/1718.html
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Sliding Displacement
Funk, “Test Methods to Investigate the Influences of Fretting Corrosion on the Endurance”Materialprüfung, 1969, 221-227
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Modeling
Friction stress, µpo
Contact pressure, po
Cyclic stress, σa
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Modeling (continued)
−µ−σ=σ
−K S
oflffl e1p
σffl fretting fatigue limit
σfl material fatigue limit
µ coefficient of friction
S sliding displacement, in mm
K material constant ~ 10-3 mm
Nishioka and Hirakawa, “Fundamental Investigations in Fretting Fatigue, Part 5 The Effect of Slip Amplitude”Bull. J SME, 1969, 692-697
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Friction Coefficient
Wharton, “The Effect of Different Contact Materials on the Fretting Fatigue Strength of an Aluminum Alloy”,
Wear , Vol. 26, 1973, 253-260
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Fasteners
σo
σh
p
q
θ
Farris et. Al. “Analysis of Widespread Fatigue Damage in Structural J oints, SAMPE Symposium, 1996, 65-79
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Prevention
Reduce surface shear stressReduce normal force
Reduce coefficient of friction
Eliminate stress concentrationStepped shafts with large radii
Compressive residual stressShot peening
Separation of surfacesCompliant coatings
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Eliminate Contact
K t = 3.5
Slotted hole
From Schijve Fatigue of Structures and Materials, Kluer, 2001
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Eliminate Stress Concentration
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Attachments
Fretting at the bolt hole evenwhen the bracket is unloaded
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Summary
Fretting is caused by sliding surfaces
Fretting is a long life fatigue problem
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Fatigue of Mechanical Components
Fatigue of Bolts
Fretting Fatigue
Welded Joints
Case Study
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Types of Welds
Structural welds
Spot welds
Special Processes
Laser Electron Beam
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Weld Classifications
D E
F2 G
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100
200
300
400
B
C
D
E
F F2 G W
0105 106 107 108
BS 7608 - Steel
Fatigue Life, Cycles
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Crack Growth Data
( ) 0.312 mMPaK 109.6
dN
da∆×= −
( ) 25.210 mMPaK 104.1
dN
da∆×= −
( ) 25.312 mMPaK 106.5
dNda ∆×= −
Ferritic-Pearlitic Steel:
Martensitic Steel:
Austenitic Stainless Steel:
Barsom, “Fatigue Crack Propagation in Steels of Various Yield Strengths” J ournal of Engineering for Industry, Trans. ASME, Series B, Vol. 93, No. 4, 1971, 1190-1196
5 10 100
10-7
10-6
10-8
C
r a c k G r o w t h R a t e
, m / c y c l e
∆K, MPa√m
σyield
252273392415
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0
25
50
75
100
125
105
B
C
D
E F
106 107 108
BS 7608 - Aluminum
Fatigue Life, Cycles
Sharp, “Behavior and Design of Aluminum Structures”,McGraw-Hill, 1992
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Crack Growth Data
1 10 100
Cyclic Stress Intensity, MPa√m
C r a c k G r o w t h R a
t e m / c y c l e
A533B m/cycle
6061-T6 m/cycle
10-2
10-4
10-6
10-8
10-10
10-12
3X
Steel welds are 3 timesstronger than aluminum
1
3
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Residual Stress from Welding
Y
X
X
X
X
Y
Y Y
tension
tension
compression
compression
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Weld Distortion
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Weld Toe Residual Stress
Yield
stress
Maximum stress at the weld toeis nearly the same for any cycle
∆ε
ε
σ∆ε
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Mean Stress Effects
As welded structures usually have themaximum possible mean stress
Stress relief, peening, etc. will have a
substantial effect on the fatigue life
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Butt and Fillet Weld Test Data
99% survival with 95% confidence
1000
S t r e s s R a n g e
, M P a
100
10
103 104 105 106 107
Fatigue Life, Cycles
Failures Run outs
The good welds
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Weld Terminations
1000
S t r e s s R a n g e ,
M P a
100
10
103 104 105 106 107
Fatigue Life, Cycles
Failures Run outs
99% survival with 95% confidence
The bad welds
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Sources of Inherent Scatter
Weld quality
Mean, fabrication and residual stresses
Stress concentrations (geometry)
Weldment size Material properties
Opportunities for Improvement !
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The Good and Bad
Good weld design
Bad weld design
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Typical Butt Weld
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Weld Toe
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Macroscopic LOF
3 mm
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Weld Flaws
Even good welds contain initial crack like flaws0.1 to 1 mm long. Reducing the size or eliminatingthese flaws will substantially improve fatigue lives.
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Nominal Stress ?
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Various stress distributions in a T-butt weldment with transverse fillet welds;
r
t
t1
ED
BC
A
σ peak
σ
n
σhs
FP
M
C
Θ
• Normal stress distribution in the weld throat plane (A),•Through the thickness normal stress distribution in the weld toe plane (B),
•Through the thickness normal stress distribution away from the weld (C),
•Normal stress distribution along the surface of the plate (D),
•Normal stress distribution along the surface of the weld (E),
•Linearized normal stress distribution in the weld toe plane (F).
Stress Distributions in Weldments
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Experimental Shellelements
Fine 3-D FEmesh
Coarse 3-D FEmesh
Stress magnitudes and distributions obtained from various FEmodels
Finite Element Models
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σ peak
σn σhs
Peak and Hot Spot Stress
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σ peak
t
σn
V
P
σn
V
t
σn σn
P
Physical Meaning of Hot Spot Stress
I
Mc
A
Pn +=σ
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Hot Spot SN Curves
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Weld Improvement
Reduce weld toe stresses
Stress relieve
Improve local geometry
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Macroscopic Shape
t
r
θ
0.05 0.20.150.1
2
3
4
1
r / t
tK
θ = 15º
θ = 30º
θ = 45º
θ = 60º
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K fmax
mMPatS15.01K umaxf β+=
r
t1K
t β+=
ρα+
−+=
1
1K 1K t
f
2
3
4
5
ρ =α Weld toe radius
f t K orK β ~ 0.3 axial
β ~ 0.2 bending
t
r
θ
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Spot Weld Fatigue Data
10
102
103
104
105
102 103 104 105 106 107 108
Fatigue Life, Cycles
M a x i m u m
L o a d ,
N Tensile Shear
Coach-peel
1
4
Fatigue Data Bank for Spot Welds, University of Illinois
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Spot Weld Modeling
Beams are used as " force transducers " to obtain forces and momentstransmitted through the spot welds
Forces and moments are used to calculate " structural stresses "
Spotweld “Nugget” Beam Element
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Structural Stress Calculations
Structural stresses are calculated from theforces and moments on each beam element :
Sheet 2
Nugget
Sheet 1
My
Fy
Fx
Mx
Fz
My
Fy
Fx
Mx
Fz
My
Fy
Fx
Mx
Fz
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Structural Stresses
Stresses in sheet :
θσ+θσ+σ+θσ−θσ−=θ∆ cos)M(sin)M()F(sin)F(cos)F()(S yxxyx
dt
F)F( x
x
π
=σ
dt
F)F(
y
y π=σ
2
zz
t
F744.1t6.0)F( =σ
2
xx
td
M872.1t6.0)M( =σ
2
Y Y
td
M872.1t6.0)M( =σ
Fz
Mx
t
d
Fx
Fy
My
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Structural Stress Correlation
101
102
103
104
102 103 104 105 106 107
Fatigue Life
S t r u c t u r a l S t r e s s ,
M P a
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Things Worth Remembering
Local weld toe stresses, geometry and flawscontrol the life of weldments
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Fatigue of Mechanical Components
Fatigue of Bolts
Fretting Fatigue
Welded J oints
Case Study (Merrimac Ferry)
ll b
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Collaborators
David W. Prine
Infrastructure Technology Institute
Northwestern University
Darrell Socie
Department of Mechanical EngineeringUniversity of Illinois at Urbana Champaign
Continuous Remote Monitoringof The Merrimac Free Ferry
M i Wi i
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Merrimac Wisconsin
M i F i
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Merrimac Ferries
http://www.shopstop.net/ferry/default.htm
1847 1963
M i F F
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Merrimac Free Ferry
Merrimac Ferry
M i F F
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Merrimac Free Ferry
M i F C l II
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Merrimac Ferry Colsac II
State Highway 113 over the Wisconsin River atMerrimac
Began operation in 1963
33’ wide by 80’ longCable driven (two cables)
B i D i
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Basic Design
Supported by two 10’ by 80’ barges
W ld d B B
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Welded Box Beam
C k F d i H ll
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Cracks Found in Hull
Many cracks found in the ends where theramps are attached
Cracks also found in the center of the hull that couldlead to catastrophic failure, is the ferry safe?
H L d ?
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Heavy Loads?
Remote Monitoring S stem
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Remote Monitoring System
Merrimac WIEvanston IL
Installing Strain Gages
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Installing Strain Gages
Typical Gage Installation
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Typical Gage Installation
Strain Gage Locations
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Strain Gage Locations
3
12
Data Gathering
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Data Gathering
Ferry load tested with 34,000 # county truck
Time history data for both load test and live traffic
for 16 hours to check out system
Rainflow counting and burst history recorded for ~4months until winter closing in December 1998.
Strain for Single Load Test
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Strain for Single Load Test
Gage Maximum Minimum Range
1_1 131 26 105
1_2 70 1 69
2_1 123 -158 281
2_2 44 -79 1232_3 184 -922 1106
3_1 140 -562 702
3_2 123 -61 184
Barge End
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Barge End
541.028 1100.712 Time (Secs)-875
875
Strain Gage (ustrain)
Note: strain offset indicating plastic deformation
Strain Readings
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Strain Readings
Gage Static 10-8-98 11-6-98
1_1 105 466 427
1_2 69 350
2_1 281 311 291
2_2 123 252
2_3 1106 1089
3_1 702 602 544
3_2 184 213
Live Traffic Tests:30,772 cars35 busses291 trucks
BS 7608 Steel
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BS 7608 - Steel
500
1000
FF2
GW
0105 106 107 108
Fatigue Life, Cycles
F2
Fatigue Analysis for Ends
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Fatigue Analysis for Ends
No fatigue analysis needed if there is plasticdeformation in this welded structure.
WIDoT has lowered posted limit to excludeall but passenger cars and pickup trucks.
Crack Growth Calculations
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Crack Growth Calculations
mK CdN
da∆=
m
W
af aC
dN
da
πσ∆=
∫∫
πσ∆
=f
i
a
a
m
N
0
W
af aC
dadN
Major Variables
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Major Variables
Initial and final crack sizeMaterial properties
Stress intensity factor
Loading history
Crack Growth Data
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Crack Growth Data
( ) 0.312 mMPaK 109.6
dN
da∆×= −
( ) 25.210 mMPaK 104.1
dN
da∆×= −
( ) 25.312 mMPaK 106.5
dN
da∆×= −
Ferritic-Pearlitic Steel:
Martensitic Steel:
Austenitic Stainless Steel:
From Dowling, Mechanical Behavior of Materials, 1999
Edge Cracked Plate in Tension
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Edge Cracked Plate in Tension
π
π−++
ππ=
b2
acos
)
b2
asin1(37.0
b
a02.2752.0
b2atan
ab2
baF
3
Loading History for 1 Month
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Loading History for 1 Month
0
20
40
60
80
100
120
0 300100 200 400 500
Strain Range, µε
N u m b e r o f C y c l e s
Results for Center Cracks
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Results for Center Cracks
0
2
4
6
8
10
12
0 500 1000 1500 2000
Years of Service
C r a c k L e n g t h
Results
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Results
Data shows overloads are driving end cracks.
Data shows center cracks are not being drivenby traffic loading.
Where do the strains come from to drive thecenter cracks?
Frozen Tundra of the Wisconsin River
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Frozen Tundra of the Wisconsin River
Thermal Loading
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Thermal Loading
Constant Temperature Water
Variable Temperature Air
Thermal Expansion/Contraction on Deck
Winter Tests in Ice
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Winter Tests in Ice
-15
-10
-5
0
5
10
15
A i r T e m p e r a t u r e º C
22 days
-600
-400
-200
0
200
400
S t r a i n , µ ε
Colsac III
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Colsac III
http://fun.co.columbia.wi.us/fun/colsac/construction.asp
May 16, 2003Construction
2 weeks later
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2 weeks later
The Associated Press - J une 7, 2003
MADISON — The new Merrimac Ferry, which hasbeen closed for repairs, will not operate for the
foreseeable future due to a breakdown in repairnegotiations with the contractor.
The new $2.2 million ferry, known as the ColSac III,broke down May 23 about a week after openingto the public.
New and Improved
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New and Improved
Portage Daily Register February 1,2004
The new Merrimac Ferry has spent more time beingdown for repairs than the 40 year old vessel it replaced
did in its last three years.
Since its launch on May 16, The Colsac III has brokendown 69 times and spent 48 days out of service.
The old ferry was down 48 times since 2000 but neverout of service for a full day.
More …
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More …
The last breakdown came December 2, when valvesthat control the braking system locked, stranding theboat and vehicles in the middle of the river.
J ohn Vesperman chief operations engineer, “We had topull it ashore with a huge tow truck after we were ableto free the stuck valves”
Strength Fatigue and Fracture
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Strength, Fatigue and Fracture