1000
cycles
at
Sa
30,000
psi
1000
cycles
at
Sa
26,000
psi
500
cycles
at
Sa
21,000
psi
500
cycles
at
Sa
15,000
psi.
Each of these cycles has used up a certain amount of the fatigue life of the
vessel. In order to determine the adequacy of the vessel to carry out its
mission over 20 years, the procedure is as follows: For each of the Sa's
shown, go to the appropriate fatigue design curve and find the number of
cycles, Ni, permitted at this amplitude level. Designate the actual number
of cycles of operation at this Si level as Ni. The cumulative usage
factor, component Ui, is then simply n1/N1. The total usage factor U
then equals the summation of all the Ui's and this figure must be less than
or equal to 1.0. In this case,
for S1 = 30,000 psi, N1 = 20,000 cycles, n1 = 1000 cycles
for S2 = 30,000 psi, N2 = 20,000 cycles, n2 = 1000 cycles
for S3 = 30,000 psi, N3 = 20,000 cycles, n3 =
500 cycles
for S4 = 30,000 psi, N4 = 20,000 cycles, n4 =
500 cycles
Thus
1000
U1 = = 0.05
20,000
1000
U2 = = 0.033
30,000
1000
U3 = = 0.005
100,000
1000
U4 = = 0.001
500,000
and
U = U1 + U2 + U3 + U4 = 0.089
1.0
and the vessel is quite adequate.
In most cases, the designer may design right up to the Code allowable
stresses. This is possible because in the generation of the Design Fatigue
Curves, a safety factor of 2.0 on stress and/or 20.0 on cyclic life,
whichever is greater, has been employed.
The designer is urged to read
Reference 1 (ASME Boiler and Pressure Vessel Code, 1980) for a fuller
understanding of the origin and methods of employment of the concept of
design by fatigue analysis.
NOTE:
In reading Article 5-1, the designer should take particular note of
Paragraphs 5-111, 5-112, and 5-140, which deal with the limitation
on fatigue strength reduction factors and progressive distortion of
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