Page 470 - Shigley's Mechanical Engineering Design

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Screws, Fasteners, and the Design of Nonpermanent Joints 445
Table 8–17 Grade or Class Size Range Endurance Strength

Fully Corrected SAE 5 1 –1 in 18.6 kpsi
4
Endurance Strengths for 1 –1 1 in 16.3 kpsi
1
Bolts and Screws with 1 8 1 2
Rolled Threads* SAE 7 4 –1 2 in 20.6 kpsi
SAE 8 1 –1 1 in 23.2 kpsi
4 2
ISO 8.8 M16–M36 129 MPa
ISO 9.8 M1.6–M16 140 MPa
ISO 10.9 M5–M36 162 MPa
ISO 12.9 M1.6–M36 190 MPa

*Repeatedly applied, axial loading, fully corrected.

For a general case with a constant preload, and an external load on a per bolt
basis fluctuating between P min and P max, a bolt will experience fluctuating forces such
that
(a)
F bmin = CP min + F i
(b)
F bmax = CP max + F i
The alternating stress experienced by a bolt is
(F bmax − F bmin )/2 (CP max + F i ) − (CP min + F i )
σ a = =
A t 2A t
C(P max − P min )
σ a = (8–35)
2A t
The midrange stress experienced by a bolt is
(F bmax + F bmin )/2 (CP max + F i ) + (CP min + F i )
σ m = =
A t 2A t
C(P max + P min ) F i
σ m = + (8–36)
2A t A t
A load line typically experienced by a bolt is shown in Fig. 8–20, where the stress
starts from the preload stress and increases with a constant slope of σ a /(σ m − σ i ).
The Goodman failure line is also shown in Fig. 8–20. The fatigue factor of safety can
be found by intersecting the load line and the Goodman line to find the intersection
point (S m, S a). The load line is given by
σ a
Load line: S a = (S m − σ i ) (a)
σ m − σ i
The Goodman line, rearranging Eq. (6–40), p. 306, is
S e
Goodman line: S a = S e − S m (b)
S ut
Equating Eqs. (a) and (b), solving for S m , then substituting S m back into Eq. (b) yields
S e σ a (S ut − σ i )
S a = (c)
S ut σ a + S e (σ m − σ i )