128 3. THE DIMENSION OF A COMPONENT WITH REQUIRED RELIABILITY
Table 3.5: e results of the interactive process for Example 3.1
Iterative #
K
t
μ
d
*
∆|μ
d
*
|
1 1.9 1.777084
2 2.203939 1.913948 0.136865
3 2.214874 1.918691 0.004742
4 2.21526 1.918858 0.000167
Solution:
For this example, we do not have a static stress concentration factor. So, we can directly
use Step 2 of the procedure discussed above to conduct the component dimension design with
the required reliability.
(1) e limit state function.
e normal stress of the beam caused by the bending moment
M
is
D
M h=2
bh
3
=12
D
6M
bh
2
: (a)
e limit state function of the beam is
g
S
y
; M; b ; h
D S
y
6M
bh
2
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(b)
e bending moment M can be treated as a normal distribution. Its mean and standard deviation
can be determined per Equation (1.2). For the dimension, the dimension standard deviation
d
can be determined per Equation (1.1). In the limit state function, there are four normally
distributed variables. eir distribution parameters in the limit state function (b) are listed in
Table 3.6.
Table 3.6: Distribution parameters for Example 3.2
S
y
(ksi) M (klb.in) b (in) h (in)
μ
S
y
σ
S
y
μ
M
σ
M
μ
b
σ
b
μ
h
σ
h
32.2 3.63 50.25 1.04 2.000 0.0025
μ
h
0.0025
(2) e mean and the standard deviation of the limit state function.
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