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LECTURE # 39LECTURE # 39
FATIGUE LOADING OF TENSION FATIGUE LOADING OF TENSION JOINTSJOINTS
Table 8-16 lists average fatigue Table 8-16 lists average fatigue stress-concentration factors for the stress-concentration factors for the fillet under the bolt head and also at fillet under the bolt head and also at the beginning of the threads on the the beginning of the threads on the bolt shankbolt shank
These are already corrected for notch These are already corrected for notch sensitivity and for surface finishsensitivity and for surface finish
Use of rolled threads is the Use of rolled threads is the predominant method of thread-forming predominant method of thread-forming in screw fasteners, where Table 8-16 in screw fasteners, where Table 8-16 appliesapplies
In thread-rolling the amount of cold-In thread-rolling the amount of cold-work and strain strengthening is work and strain strengthening is unknown to the designer; therefore, unknown to the designer; therefore, fully corrected (including Kfully corrected (including Kff) axial ) axial endurance strength is reported in Table endurance strength is reported in Table 8-178-17
Fatigue loading is the one in which Fatigue loading is the one in which the externally applied load fluctuates the externally applied load fluctuates between zero and some maximum between zero and some maximum force Pforce P
FFmaxmax = F = Fb b and Fand Fminmin = F = Fii
FFaa = (F = (Fmax max – F– Fminmin)/2 = (F)/2 = (Fbb – F – Fii)/2)/2
aa = F = Faa/A/Att
Fig. 8.20Fig. 8.20
tt
ii
t
iba A
CP
A
FFCP
A
FF
222
t
i
tm
A
F
A
CP
2
iam
Strength Components SStrength Components Saa and and SSmm of the Fatigue Failure Locus of the Fatigue Failure Locus
Goodman :Goodman :
GerberGerber
1ut
m
e
a
S
S
S
S
12
ut
m
e
a
S
S
S
S
ASME-ellipticASME-elliptic
1
22
p
m
e
a
S
S
S
S
Goodman :Goodman :
eut
iutea
SS
SSS
iam SS
GerberGerber
eiutieeutut
e
a SSSSSSS
S 242
1 22
iam SS
ASME-ellipticASME-elliptic
eiiepp
ep
ea SSSS
SS
SS 222
22
iam SS
Be sure to use KBe sure to use Kff for both for both aa and and mm, , otherwise slope of the load line will otherwise slope of the load line will not remain 1 to 1not remain 1 to 1
The factor of safety guarding against The factor of safety guarding against fatigue is fatigue is
a
af
Sn
Applying this to Goodman criterion, Applying this to Goodman criterion, with with
ii = F = Fii/A/Att
When preload FWhen preload Fii is present is present
eut
itutef SSCP
FASSn
2
With no preload, C = 1, FWith no preload, C = 1, Fii = 0 = 0
Preload is beneficial for resisting Preload is beneficial for resisting fatigue when nfatigue when nf f / n/ nf0 f0 > 1> 1
eut
tutef SSP
ASSn
2
0
For Goodman, last two equations For Goodman, last two equations with nwith nf f / n/ nf0 f0 > 1 puts an upper bound > 1 puts an upper bound on the preload Fon the preload Fii
FFii << (1-C) S (1-C) Sut ut AAtt
If this can not be achieved, and nf isIf this can not be achieved, and nf is
unsatisfactory, use Gerber or ASME-ellipticunsatisfactory, use Gerber or ASME-elliptic
Criterion or additional bolts or different Criterion or additional bolts or different size boltsize bolt
may be usedmay be used
The higher the preload, the betterThe higher the preload, the better
Preloads of 60 percent of proof load Preloads of 60 percent of proof load rarely loosenrarely loosen
Check the possibility of yielding, Check the possibility of yielding, using the proof strengthusing the proof strength
am
pp
Sn
Fig. 8.21Fig. 8.21
Fig. 8.22Fig. 8.22