3.4. DIMENSION OF A COMPONENT UNDER CYCLIC LOADING SPECTRUM 177
erefore, the diameter of the shaft with the required reliability 0.99 under the specified cycle
bending loading is
d D 1:091 ˙ 0:005
00
:
3.4.3 ROD UNDER CYCLIC AXIAL LOADING SPECTRUM
e limit state function of a rod under any type of cyclic axial loading spectrum can be expressed
per Equations (2.87) or (2.88), which have been discussed in Section 2.9.6. After the limit state
function of a component under cyclic axial loading is established, we can run the dimension
design with the required reliability. In this section, we will show how to determine the dimension
of a rod with the required reliability under cyclic axial loading spectrum.
Example 3.20
A machined constant circular bar is subjected to model #2 cyclic axial loading spectrum as listed
in Table 3.46. e ultimate material strength S
u
is 75 (ksi). e three distribution parameters of
material fatigue strength index K
0
for the standard specimen under fully-reversed bending stress
are m D 8:21;
ln K
0
D 41:738, and
ln K
0
D 0:357. For the material fatigue strength index K
0
,
the stress unit is ksi. Determine the diameter of the bar with a reliability 0.95 when its dimension
tolerance is ˙0:005
00
.
Table 3.46: e model #2 cyclic axial loading spectrum for Example 3.20
Mean of the Cyclic
Axial Loading F
m
(klb)
Amplitude of Cyclic
Axial Loading F
a
(klb)
Number of Cycles n
L
(normal
distribution)
μ
n
L
σ
n
L
16.78 10.39 1.13 × 10
5
4.52 × 10
3
Solution:
For this example, there is no stress concentration area. Because the loading is an axial loading,
the size modification factor k
b
D 1. erefore, there are no dimension-dependant parameters.
(1) e cyclic axial stress and the component fatigue damage index.
e mean stress
m
and the stress amplitude
a
of the bar due to the cyclic axial loading
are:
m
D
F
m
d
2
=4
D
4F
m
d
2
;
a
D
F
a
d
2
=4
D
4F
a
d
2
: (a)
Since the cyclic stress is a no-zero mean cyclic stress, we need to convert it into a fully reversed
cyclic stress per Equation (2.83). e equivalent stress amplitude of this converted fully reversed