Page 356 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
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APPLICATION TO MACHINES
Substitute the total bolt load (F bolt ) from Eq. (8.39) in Eq. (8.52) to give
(CP + F preload ) − F preload CP
F a = = (8.53)
2 2
Dividing the mean force on the bolt (F m ) given in Eq. (8.51) by the tensile-stress area
(A T ) gives the mean stress on the bolt (σ m ) as
F m CP F preload
σ m = = + (8.54)
A T 2 A T A T
Similarly, dividing the alternating force on the bolt (F a ) given in Eq. (8.53) by the
tensile-stress area (A T ) gives the alternating stress on the bolt (σ a ) as
F a CP
σ a = = (8.55)
A T 2 A T
Comparing Eqs. (8.54) and (8.55), the mean stress on the bolt (σ m ) can be expressed as
the sum of two terms
F preload
σ m = σ a + (8.56)
A T
where the first term (σ a ) varies with the external load (P) and the second term is constant.
If the Goodman theory is used to determine if the design is safe, then a fatigue factor-of-
safety (n fatigue ) can be defined as
S a
n fatigue = (8.57)
σ a
where (S a ) is the alternating strength of the bolt.
An expression for the mean strength of the bolt (S m ) can be found from Eq. (8.56) as
F preload
S m = S a + (8.58)
A T
AsdiscussedinChap.7onfluctuatingloading,agraphicalapproachtousingtheGoodman
theory is useful. A Goodman diagram, similar to Fig. 7.12, is shown in Fig. 8.5.

1
Alternating stress (s a ) S e a Calculated stresses 1 Goodman line
Load line

S
s a
0 d
F )
0 preload s m S m S ut Mean stress (s m
A T
S a

FIGURE 8.5 Graphical approach using the Goodman theory.