APPENDIX W
HIGH CYCLE FATIGUE ASSESMENT OF PIPING SYSTEMS (Draft 3/25/09)
W300 Application
This appendix addresses the fatigue evaluation of B31.3 piping subjected to cyclic
loadings when the total number of significant stress cycles due to all causes exceeds
100,000. A significant stress cycle is defined as a cycle with a computed stress range
greater than 41.4 Mpa (6.0 ksi). The allowable displacement stress range requirements of
302, using the computed stress range in accordance with 319, provides an acceptable
method of evaluating piping systems for fatigue when the number of significant stress
cycles is less than 100,000. The piping cyclic loadings may be due to thermal expansion,
anchor motion, vibration, inertial loads, wave motion or other sources.
Fatigue due to pressure cycling is not addressed in this appendix but must be considered
in design. The methodology in ASME BPV Section VIII Division 2 may be applied to
address pressure cycling.
The design, fabrication, examination and testing requirements of this Appendix are in
addition to the requirements of Chapters I through IX.
W301 Nomenclature
CF = Welded Joint Fatigue Curve Coefficient, SI (US)
CME = Conversion factor, = 1.0 for stress in MPa and = 6.8948 for stress in Ksi
dt =
Fatigue damage due to thermal stress with constant amplitude
dw =
Fatigue damage due to wave stress with variable amplitude
E=
Modulus of elasticity for the displacement cycle under consideration MPa
(Ksi)
Ea =
Modulus of elasticity at ambient temperature MPa (Ksi)
fI =
Fatigue Improvement Factor from ASME BPV Section VIII Division 2
fE =
Environmental Correction Factor (See Table W302.2)
fMT = Material Temperature Correction Factor
Γ=
Gamma Function
h=
Weibull stress range shape distribution parameter
k=
fatigue strength thickness exponent
Ld =
Piping Cyclic Design Life (Years)
Lw =
Design Storm Period of Occurrence (Years)
m =
Welded Joint Fatigue Curve Exponent
Ni =
cycles for condition i
q=
Weibull stress range scale distribution parameter which can be expressed
in terms of stress range
Saw = Allowable maximum probable stress range during Nw wave cycles MPa
(ksi)
SEi =
computed displacement stress range for condition i corresponding to
cycles Ni, MPa (ksi)
TE =
Effective component thickness at weld joint, mm (in)
_
T =
component nominal thickness at weld joint, mm (in)
SEW = Computed maximum stress range due to wave motion MPa (ksi)
Nw = Design Storm Wave height associated cycles
Nd =
Design number of pipe stress cycles
Ni =
number of cycles for loading condition, i.
Nti =
allowable number of cycles for loading condition, i.
Vo =
average zero-crossing frequency (hz)
W302 Design for Fatigue
The fatigue design procedure in this appendix addresses two types of cyclic loading:
Fatigue loading where the loading spectrum may be reduced to a series of stress range –
cycle pairs and fatigue loading where the loading spectrum may be represented by a two
parameter Weibull distribution. Fatigue damage is the summation based on the linear
damage rule. The fatigue design analysis methodology in this appendix is based on the
following general requirements:
a) In the absence of more directly applicable data the stress intensification
factors shown in Appendix D for elbows, bends and B16.9 tees may be used.
The stress intensification factors for other components are the responsibility of
the designer and their validity documented in the engineering design.
b) Integral construction is recommended. Fabricated components such as
unreinforced branch connections, pad reinforced branch connections, and
miter elbows are not recommended.
c) The maximum stress range from all sources of loadings shall not exceed the
displacement stress range requirements of 302.3.5 with f = 1.0.
d) The maximum longitudinal stress due to pressure, weight and inertial forces
due to wave loading shall meet the requirements of 302.3.6.
W302.1 Fatigue damage due to Cyclic Stress Range from other than Wave Motion
The maximum stress range SE shall be computed in accordance with 319 and meet the
allowable displacement stress range requirements of 302.3.5 with f=1.0. The stress range
– cycle pairs (SEi, Ni) shall be established from a stress – cycle histogram by the Rainflow
method of ASME BPV Section VIII Division 2 Annex 5.B. Fatigue damage shall be
computed as follows.
Allowable Fatigue Cycles for load case i:
f
Nti = I
fE
 f MT  CF 


 S T k 
 Ei E 
m
(W-1)
Where,
E
Ea
fI = 1.0 unless otherwise documented in the engineering design.
fMT =
_
for
T ≤ 16 mm (0.625 in.)
TE = T
for
16 mm (0.625 in.) < T < 150 mm (6 in.)
TE = 150 mm (6 in.)
for
T ≥ 150 mm (6 in.)
TE = 16 mm (0.625 in.)
_
_
_
Fatigue Damage due to Displacement Loadings:
dt := 
Ni
N ti
Where dt must be less than 1.0.
(W-2)
Table W302.1 Fatigue Material Coefficients
CF (SI) (US)
m
Ferritic and Stainless
14137 (999.1)
3.13
Steels
Aluminum
2303 (162.8)
3.61
SI units include SEi (MPa) and TE (mm) in equation W-1
US units include SEi (Ksi) and TE (in) in equation W-1
k
.222
.222
In the absence of more directly applicable data the values of fE, for the affect of the
environment on the fatigue life of carbon steel piping at temperatures less than 200F,
provided in Table W302.2 may be used. The values of fE for other materials shall be
specified and the basis documented in the engineering design.
Table W302.2Environmental Fatigue Factors for Carbon Steel Piping, T≤200F
Environment
fE
Air
1.0
Seawater with Cathodic Protection
2.51
Seawater with free corrosion
3.0
W302.2 Fatigue damage due to Cyclic Stress Range from Wave Motion
This paragraph addresses variable amplitude random loadings where the long term stress
range distribution may be represented by a two-parameter Weibull distribution. The
specific requirements are written for wave loadings for applications such as floating
offshore platforms, however the methodology may be applied to other applications where
the Weibull distribution applies.
When designing for wave motion the design sea state shall be specified by the owner.
The sea state shall be characterized by a two parameter wave-scatter diagram of
significant wave height and zero upcrossing period. The stress range is assumed
proportional to wave height and the Weibull stress range shape distribution parameter and
average zero crossing frequency determined from the data.
The long term stress range distribution may be represented by a two-parameter Weibull
distribution as follows:
S
F: = exp( -  EW
 q
q: =
S aw
In ( N w )
1
h
h

 )

(W-3)
(W-4)
Where,
F = probability for exceeding the stress range SEW
exp(x) = ex
The design fatigue curve is represented by a single equation of the form given by
eq. (W-1):
Allowable Fatigue Damage for variable Wave Loadings:
dw = 1-dt
(W-5)
Design Storm Wave height associated cycles:
Nw = 33.54·106·VoLw
(W-6)
Design number of pipe stress cycles
Nd = 33.54·106·VoLd
(W-7)
The maximum probable stress range shall be determined from the maximum probable
wave height based on a two parameter Weibull model. The maximum probable wave
height (or maximum probable stress range) will be exceeded on the average once every
Nw design wave cycles.
Allowable maximum probable stress range during Nw wave cycles:
1
1
Saw =
C ME
1
 d w  a  m In( N w ) h

 
1
N
 d  (1  mh ) m
(W-8)
Where,
f
a= I
fE
 f  CF 

  MT k
T
E


m
(W-9)
The computed maximum stress range, SEW is assumed to be proportional to the maximum
probable wave height (trough to peak). The stress range shall be computed in accordance
with 319 from the imposed displacements created by the maximum probable wave height
and shall not exceed the allowable maximum probable stress range, Saw.
W302.2.1 Design Parameters
This Appendix does not prescribe specific values for h, Vo, Lw, or Ld. These design
parameters shall be specified by the owner and/or regulatory authority as applicable. The
values for h and Vo are determined by statistical data based on the specific Sea
Environment. The design life of the piping, Ld, and the design maximum probable wave
height based on the design storm period of occurrence, Lw, shall be based on the intended
life of the piping and acceptable risk.
In the absence of more applicable data for the specific Sea site the following typical
values may be used.
h = 1.0
V0 = .159
Hz
LD = 20 years
Lw, = 100 years.
W302.3 Alternative Analysis Methods
The fatigue analysis method presented in W302.2 is based on a two parameter weibull
model for a design fatigue curve with a single linear slope on a log-log stress-cycles plot
and a single sea state. With the owner’s approval, the designer may apply more
applicable data or more rigorous analysis method for fatigue of piping. The applicable
parameters (eg. CF, m, etc.) for materials other than the materials covered in Table
W302.1 shall be as specified in the engineering design.
The fatigue analysis methodology of ASME BPV Section VIII Division 2 may be used
for piping as an alternative to the methodology of this Appendix.
W305 Fluid Service Requirements
If SE > .8 Sa or SEW > .8 Saw the requirements for severe cyclic service in Chapters I
through IX apply, in addition to the requirements of this Appendix, except that pipe
designed in accordance with this Appendix shall meet the requirements of 305.2.3 and
lap joint flanges are not permitted.
W323 Materials
The impact test exemptions of Fig. 323.2.2B are not permitted.
W328 Fabrication
All circumferential girth welds in piping greater than 1 1/2 NPS shall be full penetration
_
butt welds. If the offset at the circumferential butt weld exceeds the lesser of .1 T or 1/8
in (3mm) an additional stress concentration factor shall be applied.
W341 Examination
All longitudinal welds shall be full penetration butt welds and subjected to 100%
radiography per para. 344.5.1 and Table 341.3.2.
The extent of radiographic examination of circumferential butt welds shall be as follows:
1. ASME Class 150 through Class 600: 10% of the welds shall be subjected 100%
radiography and 20% of the welds shall be subjected to Liquid Penetrant (LP) or
Magnetic Particle (MP) examination.
2. ASME Class 900 through Class 1500: 20% of the welds shall be subjected 100%
radiography and 100% LP or MP
3. ASME Class 2500 through API 10K: 100% radiography and 100% LP or MP
4. The requirements of W305 apply when applicable.
In addition to the above requirements, 100% radiographic examination is required for the
following conditions, regardless of pressure rating:
1. All circumferential butt welds, in other than Category D Fluid Service, made in
the field.
2. All circumferential butt welds within 10 meters from personnel accommodations.
3. All circumferential butt welds requiring Post Weld Heat Treatment.
4. All circumferential butt welds, in other than Category D Fluid Service, not
accessible for in service inspection and examination.
W341 Pressure Testing
Pressure testing of the system shall be in accordance with the requirements of para. 347
except the test duration for hydrostatic testing, which shall be a minimum of one hour
after the test pressure has been adequately stabilized.
BACKGROUND
High cycle fatigue evaluation of offshore piping systems has been performed by the DNV
methodology. The stress – cycle S-N curve for welded construction used in the DNV
method has a slope of – 1/3 and agrees with approaches used in Europe. The slope of the
welded component fatigue curve also agrees with the Structural Stress Approach in
paragraph 5.5.5 of the 2007 Edition of the ASME BPV Code Section VIII Division 2.
However the Markl correlation used by the B31 Codes has a slope of – 1/5 and may be
non-conservative relative to the other approaches at high cycles. The problem is to bring
high cycle fatigue into B31.3, recognizing the long successful history of the Markl
approach for displacement stress analysis. The stress intensification factors in Appendix
D were also determined using Markl. Comparing fatigue curves shows that the Markl
correlation is conservative at low cycles, where the typical piping system operates.
The approach used in this appendix is to defer to the traditional B31.3 approach for the
conventional displacement stress analysis and the Structural Stress approach for high
cycle fatigue.
The coefficients and factors agree with the Div. 2 Structural Stress approach based on the
following definition of terms:
CF = I1/mss C
I1/mss = 1.221 (If the stress range is all membrane, Rb,k = 0, the most conservative
assumption. If it is all bending, Rb,k = 1 and I1/mss = 1.3308)
m = 1/h
Using the -3σ correlation for coefficient C
C (SI) (US)
11578 (818.3)
Ferritic and Stainless
Steels
Aluminum
1886 (133.3)
SI units include SEi (MPa) and TE (mm)
US units include SEi (Ksi) and TE (in)
CF (SI) (US)
14137 (999.1)
2303 (162.8)
The environmental factors, fE, are based on the DNV document.
The 100,000 cycle limit for the base code was based on discussion on the Paulin
Research report at the spring 2008 B31 MDC meeting. The concerns with the base code
are the construction details allowed and the known inaccuracies in the SIF’s.
A comparison of C.S. design curves DNV F3, Div. 2 Structural Stress (-3σ), and B31.3
for two assumptions on SL using SH = SC = 20 Ksi is shown in the figure below.
Design Curves: Div 2 Structural Stress, DNV, B31.3 Air Data, t = 32mm (1.26")
Stress Amplitude (ksi)
1000
100
Div 2 Str Stress
DNV F3
B31.3 SL=0
B31.3 SL=.5SH
10
1
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
Cycles, N
1.00E+07
1.00E+08
1.00E+09
1.00E+10