134 3. THE DIMENSION OF A COMPONENT WITH REQUIRED RELIABILITY
In the limit state function, there are four normally distributed variables. For the dimension, the
dimension standard deviation
d
can be determined per Equation (1.1). e mean and standard
deviation of the static stress concentration factor K
t
are determined per Equation (1.3). eir
distribution parameters in the limit state function (c) are listed in Table 3.7. e mean and
standard deviation of K
t
in the table will be updated in each iterative step. (Note: e user-
defined subroutine for updating the stress concentration factor is required for this example.)
Table 3.7: Distribution parameters for Example 3.3
S
y
(ksi) F (klb) K
t
d (in)
μ
S
y
σ
S
y
μ
F
σ
F
μ
K
t
σ
K
t
μ
d
σ
d
32.2 3.63 28.72 2.87 1.9 0.095
μ
d
0.00125
(3) e reliability index ˇ with the required reliability R.
e reliability index ˇ with the required reliability R D 0:99 per Equation (3.2) is
ˇ D ˆ
1
.
0:99
/
D 2:32635: (d)
(4) Use the modified H-L method to determine the dimension.
Following the procedure and the flowchart in Figure 3.2 discussed above, we can compile a
MATLAB program. e program is listed in Appendix B.4 as “M-H-L-program-Example 3.3.”
e iterative results are listed in Table 3.8.
Table 3.8: e iterative results of Example 3.3 by the modified H-L method
Iterative #
S
y
*
F
*
K
t
*
d
*
|∆d
*
|
1 32.2 28.72 1.9 1.468913
2 26.20276 32.92314 1.969613 1.775099 0.306186
3 25.437 32.08462 2.286689 1.916347 0.141248
4 25.3237 32.1278 2.286277 1.921748 0.005401
5 25.31118 32.11423 2.286569 1.92194 0.000192
6 25.31073 32.11421 2.286546 1.921946 6.79E-06
According to the result obtained from the program, the mean of the diameter with a
reliability 0.99 is
d
D 1:922
00
: (e)