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292 Mechanical Engineering Design
from Table 6–4 or Eq. (6–27) and proceed as usual. If the rotating-beam endurance limit
is not given, then compute it using Eq. (6–8) and the temperature-corrected tensile
strength obtained by using the factor from Table 6–4. Then use k d = 1.

EXAMPLE 6–5 A 1035 steel has a tensile strength of 70 kpsi and is to be used for a part that sees 450°F
in service. Estimate the Marin temperature modification factor and (S e ) 450 if
◦
(a) The room-temperature endurance limit by test is (S ) 70 = 39.0 kpsi.

◦
e
(b) Only the tensile strength at room temperature is known.
Solution (a) First, from Eq. (6–27),
−5
2
−3
k d = 0.975 + 0.432(10 )(450) − 0.115(10 )(450 )
−8
3
4
+ 0.104(10 )(450 ) − 0.595(10 −12 )(450 ) = 1.007
Thus,
Answer (S e ) 450 = k d (S ) 70 = 1.007(39.0) = 39.3 kpsi

◦
◦
e
(b) Interpolating from Table 6–4 gives
450 − 400
(S T /S RT ) 450 = 1.018 + (0.995 − 1.018) = 1.007
◦
500 − 400
Thus, the tensile strength at 450°F is estimated as
(S ut ) 450 = (S T /S RT ) 450 (S ut ) 70 = 1.007(70) = 70.5 kpsi
◦
◦
◦
From Eq. (6–8) then,
Answer (S e ) 450 = 0.5(S ut ) 450 = 0.5(70.5) = 35.2 kpsi
◦
◦
Part a gives the better estimate due to actual testing of the particular material.

Reliability Factor k e
The discussion presented here accounts for the scatter of data such as shown in
.
Fig. 6–17 where the mean endurance limit is shown to be S /S ut = 0.5, or as given by

e
Eq. (6–8). Most endurance strength data are reported as mean values. Data presented
19
by Haugen and Wirching show standard deviations of endurance strengths of less than
8 percent. Thus the reliability modification factor to account for this can be written as
(6–29)
k e = 1 − 0.08 z a
where z a is defined by Eq. (20–16) and values for any desired reliability can be deter-
mined from Table A–10. Table 6–5 gives reliability factors for some standard specified
reliabilities.
For a more comprehensive approach to reliability, see Sec. 6–17.

19 E. B. Haugen and P. H. Wirsching, “Probabilistic Design,” Machine Design, vol. 47, no. 12, 1975,
pp. 10–14.