3.4. DIMENSION OF A COMPONENT UNDER CYCLIC LOADING SPECTRUM 197
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 height h 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 under model #4 cyclic bending moment spectrum
per Equation (2.88) is:
g
.
K
0
; k
a
; b; h
/
D
.
k
a
k
b
/
m
K
0
n
L1
6M
a1
S
u
bh
2
S
u
6M
m1
m
n
L2
6M
a2
S
u
bh
2
S
u
6M
m2
m
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(h)
ere are four random variables in the limit state function (h). K
0
is a lognormal distribution.
e rests are normal distributions. e dimensions
b
and
h
can be treated as normal distributions.
eir means and standard deviations can be calculated per Equation (1.1). e distribution
parameters in the limit state function (h) are listed in Table 3.67.
Table 3.67: e distribution parameters of random variables in Equation (h)
K
0
(lognormal) k
a
b (in) h (in)
μ
lnK
0
σ
lnK
0
μ
k
a
σ
k
a
μ
b
σ
b
μ
h
σ
h
32.476 0.279 0.9053 0.05432 2.000 0.0025
μ
h
0.0025
(5) Use the modified R-F method to determine the height h of the beam.
We will use the modified R-F to conduct this component dimension design, which has
been discussed in Section 3.2.4. We can follow the procedure discussed in Section 3.2.4 and the
program flowchart shown in Figure 3.3 to compile a MATLAB program. e iterative results
are listed in Table 3.68.
According to the result obtained from the program, the mean of the height of the beam
with a reliability 0.99 is
h
D 2:904
00
: (i)
erefore, the height of the beam with the required reliability 0.99 under the specified loading
will be
h D 2:904 ˙ 0:010
00
:
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