194 3. THE DIMENSION OF A COMPONENT WITH REQUIRED RELIABILITY
(2) e cyclic bending stress and the component fatigue damage index.
e mean bending stress
m
, the bending stress amplitude
a
and its corresponding equiv-
alent bending stress amplitude
eq
of the beam due to the model #3 cyclic bending loading listed
in the above table are
m
D K
f
M
m
d=2
I
D K
f
M
m
d=2
d
4
=64
D K
f
32M
m
d
3
(c)
a
D K
f
M
a
d=2
I
D K
f
M
a
d=2
d
4
=64
D K
f
32M
a
d
3
(d)
eq
D K
f
a
S
u
S
u
m
D
32M
a
S
u
K
f
d
3
S
u
32K
f
M
m
: (e)
e component fatigue damage index of this shaft under model #3 cyclic bending stress per
Equation (2.84) is:
D D n
L
32M
a
S
u
K
f
d
3
S
u
32K
f
M
m
m
: (f)
(3) e limit state function.
e component fatigue strength index K can be calculated per Equation (2.79):
K D
.
k
a
k
b
k
c
/
m
K
0
: (g)
e surface finish modification factor k
a
follows a normal distribution. Its mean and standard
deviation can be determined per Equations (2.14), (2.15), and (2.16). k
b
is treated as a determin-
istic value and can be calculated per Equation (2.17). Its value will be updated in each iterative
step by using the newly available diameter of the beam. Since this is cyclic bending stress the
load modification factor k
c
will be 1.
e limit state function of the beam in this example per Equation (2.87) is:
g
K
0
; k
a
; K
f
; M
a
; d
D
.
k
a
k
b
/
m
K
0
n
L
32M
a
S
u
K
f
d
3
S
u
32K
f
M
m
m
(3.37)
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(h)
ere are five random variables in the limit state function (h). K
0
is a lognormal distribution. e
rests are normal distributions. e dimensions d can be treated as normal distributions, and its
mean and standard deviation can be calculated per Equation (1.1). e distribution parameters
in the limit state function (h) are listed in Table 3.64. K
f
and k
b
will be updated in each iterative
step by newly available diameter
d
.