Download - Vedeld 2 - VIV Fatigue Calculation
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
1/36
VIV Fatigue Calculation
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
2/36
Slide 2
Vortex Induced Vibrations (VIV)
Let us try to calculate the fatigue life of a span!
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
3/36
Slide 3
Fatigue - overview
Strength
Probability
2-Design criteria
2-Resistance
S
N
4,5-Load effects
(cyclic stresses)
6, 7-
Structural response
3-Environment
WavesCurrent
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
4/36Slide 4
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
Reduced Velocity VR
Normalised
vibrationamplitudeA/D
IN-LINE
CROSS-FLOW
U/f0D
Summary Response Model Basic Concepts
CF induced
IN-LINE
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
5/36
Slide 5
Exercise
Calculate the fatigue life of a 40m long free span at 300m water depth.
0 m
75 m
500 m
500 m
100 m
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
6/36
Slide 6
Basic data
Pipe dimensionsOutside diameter D 500 mm
Wall thickness t 13.2 mm
Operational parameters
Operational pressure Pop 100 barg @ +30m
Operational temperature Top ambient
Content density cont 153 kg/m3
Residual lay tension Heff 200 kN
Design life Tlife 25 years
Environment
Weibull parameter - Shape 1.718
Weibull parameter - Scale 0.133 m/s
Weibull parameter - Location 0.005 m/s
Current reference height zr
3.0 m
Current to pipe angle 90
Incoming turbulence Ic 5 %
Water depth d 300 m
Seabed
Medium sand
Corrosion coating asphalt
Thickness tcorr 6.0 mmDensity corr 1900 kg/m
3
Concrete coating
Thickness tcon 50.0 mm
Density con 2240 kg/m3
Structural damping 0.5 %
SN curve F1 free corrosion
Slope parameter m 3
Fatigue constant Log(C) 11.222
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
7/36
Slide 7
Practical information
The presented information should be used for allexercises during day 1
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
8/36
Slide 8
VIV Load and Response
Let us start look at the loading mechanism
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
9/36
Slide 9
CR
OSS-FLOW
In-line and Cross-flow VIV
Flow
IN-LINE
IN-LINE
CROSS-FLOW
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
10/36
Slide 10
Vortex shedding frequency- Strouhal number
D
UStfs =
The frequency at which the
vortices are shed from a
fixed cylinder
Oscillations in the lift force
occur at the Strouhal
frequency
Oscillations in the drag
force occur at twice the
Strouhal frequency
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
11/36
Slide 11
Response Model - example
Provides amplitude versus loading
Swing different lengths
or Pendulum
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
12/36
Slide 12
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
Reduced Velocity VR
VibrationamplitudeA/D
IN-LINE
CROSS-FLOW
U/f0D
widthelmod
cycleperlength
Df
UV
0
R ==
Response Models
CF induced
IN-LINE
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
13/36
Slide 13
Lock-in phenomena - cross-flow
the vortex shedding locks-on
to the natural frequency
St
1
Df
U
Df
Uff
s0
s0
==
=
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
14/36
Slide 14
Exercise Calculate Amplitude
Given:
- Current velocity, U = 0.6 m/s
- Natural frequency, f0
= 0.773 Hz
- Reduced frequency should be used for
calculation of reduced velocity
- In-line Response Model (next sheet)
Use Response Model to estimate vibration
amplitude, A/D and fill value into spreadsheet
1.1,0,0 == ff
d
ff
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
15/36
Slide 15
In-line Response Model
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0 1.0 2.0 3.0 4.0 5.0
VR
(A
y/D)
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
16/36
Slide 16
Calculation sheet
UC
p(UC
) VR,d
AY
/D SIL
Ni
=a/Sm ni
=Tyear
p(UC
)f1
ni
/Ni
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
17/36
Slide 17
Challenge
Break a wire by hand
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
18/36
Slide 18
Reflection
Fatigue failure
Relation between Stress Range and Number of cycles to failure
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
19/36
Slide 19
Fatigue Calculation
Damage accumulation by Miner-Palmgren:
Number of stress cycles:
Number of cycles to failure by SN curve:
=i
ifat
NnD
Tf)(Pn vi =
mii SaN
=
1
10
100
1000
1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
No of cycles, N
StressR
ange,
S
NSW
SSW
(a1;m1)
(a2;m2)
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
20/36
Slide 20
SN curve (F1 free corrosion)
10
100
1000
1.E+04 1.E+05 1.E+06 1.E+07 1.E+08
N
S(MPa
)
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
21/36
Slide 21
Vibration mode
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
22/36
Slide 22
Modal stress
Curvature, , of free span vibratingwith a given mode 2nd derivative
of mode
Modal stress found by curvature
E(D-t)/2
Ain, modal stress for maximum mode
amplitude = OD given by multiplying
modal stress by OD Ain = 445 MPa (given value from FE
analysis)
Vibration stress range:
S = 2 Ain
(Ay
/D)
Safety factor on stress range
3.1, == ssd SS
Exercise Calculate Stress Range & Number
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
23/36
Slide 23
Ca a S a g &of Cycles to Failure
Calculate Stress Range
Calculate Number of cycles to failure
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
24/36
Slide 24
Calculation sheet
UC
p(UC
) VR,d
AY
/D SIL,d
Ni
=a/Sm ni
=Tyear
p(UC
)f1
ni
/Ni
0
0,1
0,2
0,3
0,4
0,5
0,6 0,00 1,40 0,05
0,7
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
25/36
Slide 25
Exercise Fatigue Damage & Life
Estimate number of stress cycles per year, n(Hint : vibration frequency = natural frequency)
Calculate fatigue damage (per year)
Find fatigue life (inverse of fatigue damage per year)
Multiply with utilization factor 0.5
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
26/36
Slide 26
Calculation sheet
UC
p(UC
) VR,d
AY
/D SIL
Ni
=a/Sm ni
=Tyear
p(UC
)f1
ni
/Ni
0
0,1
0,2
0,3
0,4
0,5
0,6 0,00 1,40 0,05
0,7
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
27/36
Slide 27
Reflection Current
Will the current be constant over time (years) or vary?
L di ib i f
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
28/36
Slide 28
Long-term distribution of current
Ui(m/s)
F(Ui) f(Ui)= Pi Exposure
(days/year)
0 0.00000 0 0
0.1 0.42517 0.42517 155
0.2 0.85220 0.42703 156
0.3 0.97972 0.12752 47
0.4 0.99840 0.01868 70.5 0.99992 0.0015199 1
0.6 1.00000 7.3066E-05 0
0.7 1.00000 2.1580E-06 0
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
29/36
Slide 29
Exercise Fatigue life for current distribution
Use approach for one current flow velocity and calculate for a long-termcurrent distribution
Find fatigue life (in years)
C l l ti h t
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
30/36
Slide 30
Calculation sheet
UC
p(UC
) VR,d
AY
/D SIL
Ni
=a/Sm ni
=Tyear
p(UC
)f1
ni
/Ni
0
0,1
0,2
0,3
0,4
0,5
0,6 0,000073066 1,40 0,05 56,4 930793 1781 0,001913588
0,7
S
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
31/36
Slide 31
Summary
This exercise follows the principles of VIV fatigue calculation according toDNV RP-F105
Safety factors are included as specified Normal safety classification
and Well defined span.
In addition:
- Cross-flow VIV (in a similar way)
- Cross-flow induced Inline VIV- Direct wave load
and a lot of details.
R fl ti i l i i t
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
32/36
Slide 32
Reflection main learning points
.
Fatigue overview
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
33/36
Slide 33
Fatigue - overview
Strength
Probability
2-Design criteria
2-Resistance
S
N
4,5-Load effects(cyclic stresses)
6, 7-
Structural response
3-Environment
WavesCurrent
S R M d l B i C t
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
34/36
Slide 34
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0Reduced Velocity VR
Vib
rationamplitude
A/D
IN-LINE
CROSS-FLOW
U/f0D
Summary Response Model Basic Concepts
CF induced
IN-LINE
Calculation sheet Results
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
35/36
Slide 35
Calculation sheet - Results
UC
p(UC
) VR,d
AY
/D SIL
Ni
=a/Sm ni
=Tyear
p(UC
)f1
ni
/Ni
0 0 0 0 0 inf 0 0
0.1 0.42517 0.2325298 0 0 inf 10364509 0
0.2 0.42703 0.46505961 0 0 inf 10409850 0
0.3 0.12752 0.69758941 0 0 inf 3108597 0
0.4 0.01868 0.93011921 0.002102086 2.44 11511283020 455368 3.95584E-05
0.5 0.0015199 1.16264902 0.025356892 29.40 6558240 37051 0.005649549
0.6 0.000073066 1.39517882 0.048611698 56.37 930793 1781 0.001913588
0.7 0.000002158 1.62770862 0.071866503 83.34 288069 53 0.000182617
-
7/31/2019 Vedeld 2 - VIV Fatigue Calculation
36/36
Slide 36
http://www.dnv.com/