92 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
From the iterative results, the reliability index ˇ and corresponding reliability R of the shaft in
this example are:
ˇ D 2:278915 R D ˆ
.
2:278915
/
D 0:9887:
Table 2.48: e distribution parameters of random variables in Equation (e)
K (lognormal) T
a
(klb.in) d (in)
μ
lnK
σ
lnK
μ
T
a
σ
T
a
μ
d
σ
d
37.308 0.518 8.9 0.85 1.500 0.00125
Table 2.49: e iterative results of Example 2.27 by the R-F method
Iterative #
K
*
T
a
*
d
*
β
*
|∆β
*
|
1 1.82E+16 1.5 11.57999 2.220042
2 2.13E+15 1.499878 8.913915 2.158924 0.061117
3 5.11E+15 1.499899 9.915022 2.265797 0.106873
4 7.37E+15 1.499887 10.36785 2.278682 0.012884
5
7.76E+15 1.499883 10.43223 2.278909 0.000228
6
7.75E+15 1.499882 10.43026 2.278915 5.31E-06
2.9.9 RELIABILITY OF A BEAM UNDER CYCLIC BENDING LOADING
Per Equation (2.87) or Equation (2.88), we can establish the limit state function of a beam under
any type of cyclic bending loading spectrum and then calculate its reliability. In this section, we
will use two examples to demonstrate how to calculate the reliability of a beam under cyclic
bending loading spectrum.
Example 2.28
e critical section of a beam with a rectangular cross-section is subjected to model #5 cyclic
bending loading spectrum listed in Table 2.50. e height h and the width b of the critical
cross-section are h D 2:500 ˙ 0:010
00
and b D 4:00 ˙ 0:010
00
. e ultimate material strength S
u
of the beam is 61.5 (ksi). ree parameters of the component fatigue strength index K on the
critical section for the cyclic bending loading are m D 6:38,
ln K
D 32:476, and
ln K
D 0:279.
For the component fatigue strength index K, the stress unit is ksi. Calculate the reliability of
the beam.