3.3. DIMENSION OF A COMPONENT UNDER STATIC LOADING 157
erefore, the diameter d of the double-shear pins at the points B and C with the required
reliability 0.99 under the specified loading is
d D 0:243
00
˙ 0:005
00
: (f)
3.3.4 SHAFT UNDER STATIC TORSION LOADING
e limit state function of a component and its reliability calculation under torsion for strength
issue and deformation issue have been discussed in detail in Section 4.8 of Volume 1 [1]. After
the limit state function of a component under static torsion loading is established, we can run
the dimension design with the required reliability. Now we will use examples to show how to
conduct component dimension design.
Example 3.11
e solid shaft is subjected to a torque T which follows a uniform distribution between 8.5
(klb.in) and 12.50 (klb.in). e shear yield strength of the shaft material follows a normal dis-
tribution with a mean
S
sy
D 32:2 (ksi) and the standard deviation
S
sy
D 3:63 (ksi). Use the
modified R-F method to design the diameter of the shaft with the required reliability 0.99 when
shaft diameter tolerance is ˙0:005.
Solution:
In this example, there is no dimension-dependent parameter.
(1) Limit state function.
e shear stress induced by the torque T is
D
Td=2
J
D
Td=2
d
4
=32
D
16T
d
3
: (a)
e limit state function of the shaft for this problem is
g
T; S
sy
; d
D S
sy
16T
d
3
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(b)
In the limit state function (b), there are three random variables. T follows a uniform distribu-
tion. e standard deviation of the shaft diameter
d
can be calculated per Equation (1.1). eir
distribution parameters are listed in Table 3.25.
(2) Use the modified R-F method to determine the dimension.