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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