48 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
Example 2.12
A component is subjected to a fully reversed cyclic bending stress with a constant stress amplitude
a
D 26:6 (ksi). e number of cycles n
L
of this cyclic loading can be described by a normal dis-
tribution with a mean
n
L
D 4:25 10
4
(cycles) and a standard deviation
n
L
D 3253 (cycles).
e fatigue life of this component N
c
at the fatigue strength S
0
f
D
a
D 26:6 (ksi) follows a log-
normal distribution with a log-mean
ln N
c
D 11:01 and the standard deviation
ln N
c
D 0:158.
Calculate the reliability of the component.
Solution:
Since the component fatigue life N
c
of this component at the cyclic stress level
a
D 26:6 (ksi)
is given, we can use Equation (2.41) to build the limit state function:
g
.
N
c
; n
L
/
D N
c
n
L
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(a)
e distribution parameters of the limit state function (a) are listed in Table 2.17.
e limit state function (a) contains one normally distributed random variable and one
lognormal distribution. We can use the R-F method to calculate its reliability, which is presented
in Appendix A.2, to compile a MATLAB program for this example. e iterative results are
listed in Table 2.18. From the iterative results, the reliability index ˇ and corresponding reliability
R of the component in this example are:
ˇ D 2:02131 R D ˆ
.
2:02131
/
D 0:9784:
Table 2.17: e distribution parameters of random variables in Equation (a)
N
C
(lognormal distribution) n
L
(normal distribution)
μ
lnN
C
σ
lnN
C
μ
n
L
σ
n
L
11.01 0.158 42500 3253
2.8.5 RELIABILITY OF A COMPONENT UNDER MODEL #3 CYCLIC
LOADING SPECTRUM
Model #3 cyclic loading spectrum is one constant number of cycles n
L
with a distributed cyclic
stress amplitude
a
. When a component is subjected to model #3 cyclic loading and if the com-
ponent fatigue strength S
Cf
at the fatigue life N D n
L
is provided, we will have the following