88 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
e component fatigue damage index of this pin under model #3 cyclic shear loading spectrum
per Equation (2.84) is:
D D n
L
2V
a
S
u
.
d
2
S
u
2V
m
/
8:21
: (d)
(2) e limit state function.
e limit state function of the pin under model #3 cyclic shearing loading spectrum per
Equation (2.87) is:
g
.
K; V
a
; d
/
D K n
L
2V
a
S
u
.
d
2
S
u
2V
m
/
8:21
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(e)
ere are three random variables in the limit state function (e). e dimension d can be treated as
a normal distribution, and its mean and standard deviation can be calculated per Equation (1.1).
e distribution parameters in the limit state function (e) are listed in Table 2.44.
(3) e reliability of the double-shear pin.
We will use the Monte Carlo method to calculate the reliability of this example. We
can follow the Monte Carlo method and the program flowchart in Appendix A.3 to create a
MATLAB program. Since the limit state function is not too complicated, we will use the trial
number N D 1;598;400. e reliability of this component R by the Monte Carlo method is
R D
1;581;583
1;598;400
D 0:9895:
Table 2.44: e distribution parameters of random variables in Equation (e)
K (lognormal) V
a
(klb) d (in)
μ
lnK
σ
lnK
μ
Va
σ
Va
μ
d
σ
d
37.308 0.518 4.815 0.6 0.5 0.00125
2.9.8 RELIABILITY OF A SHAFT UNDER CYCLIC TORSION LOADING
Per Equation (2.87) or Equation (2.88), we can establish the limit state function of a shaft under
any type of cyclic torsion loading spectrum and then calculate its reliability by using the H-L
method, or the R-F method and the Monte Carlo method. In this section, we will use two