3.2. DIMENSION DESIGN WITH REQUIRED RELIABILITY 143
erefore, the diameter of the shaft with the required reliability 0.99 under the specified loading
will be
d D 1:957 ˙ 0:005
00
:
Example 3.6
A machined double-shear pin is under a cyclic shearing loading spectrum. e mean shearing
loading can be treated as a constant V
m
D 10:125 (klb). e shearing loading amplitude V
a
can
be treated as a normal distribution with a mean
V
a
D 8:72 (klb) and a standard deviation
V
a
D
0:357 (klb). e number of cycles n
L
of this cyclic shearing loading is treated as a constant n
L
D
500000 (cycles). e ultimate material strength S
u
of the pin is 75 (ksi). e three parameters of
the material fatigue strength index K
0
on the critical section for a fully reversed bending loading
on the standard fatigue specimen are m D 8:21,
ln K
0
D 41:738, and
ln K
0
D 0:357. For the
material fatigue strength index K
0
, the stress unit is ksi. Determine the diameter of the pin with
a reliability 0.99 when the dimension tolerance is ˙0:005.
Solution
(1) Preliminary design for determining k
b
for fatigue design.
is problem does not have any stress concentration. However, it is a fatigue issue; the
size modification factor is a dimension-dependent parameter. e preliminary size modification
factor per Equation (3.3) will be
k
b
D 0:87: (a)
(2) e cyclic stress and the component fatigue damage index.
e mean shear stress
m
and the shear stress amplitude
a
of the pin due to this cyclic
shearing loading are:
m
D
V
m
=2
A
D
V
m
=2
d
2
=4
D
2V
m
d
2
(b)
a
D
V
a
=2
A
D
V
a
=2
d
2
=4
D
2V
a
d
2
: (c)
Since this is non-zero-mean cyclic shear stress, the equivalent stress amplitude of a fully reversed
cyclic shear stress is:
aeq
D
a
S
u
.
S
u
m
/
D
2V
a
d
2
S
u
.
S
u
2V
m
=d
2
/
D
2V
a
S
u
.
d
2
S
u
2V
m
/
: (d)
e component fatigue damage index of this pin under this model #3 cyclic shear loading per
Equation (2.84) is:
D D n
L
2V
a
S
u
.
d
2
S
u
2V
m
/
8:21
: (e)