228 4. RELIABILITY OF A COMPONENT UNDER STATIC LOAD
Table 4.49: e distribution parameters of random variables in Equations (b)
S
ut
(ksi) S
uc
(ksi) σ
x
(ksi) σ
y
(ksi) τ
xy
(ksi)
μ
S
ut
σ
S
ut
μ
S
uc
σ
S
uc
μ
σ
x
σ
σ
x
μ
σ
y
σ
σ
y
μ
τ
xy
σ
τ
xy
22.00 1.80 82.00 10.50 31.2 2.51 1.80 0.085 15.0 2.31
the program flowchart in Figure 3.8 to create a MATLAB program. Since this problem is
no very big and complicated, we will use the trial number N D 1,598,400 from Table 3.2
in Section 3.8. e estimated reliability R of this component at the critical point is:
R D 0:9417:
4.11 SUMMARY
In reliability-based mechanical design, all design parameters, including geometric dimensions,
loadings, and material strengths, are treated as random variables. ese statements are true in
reality but require most information for their descriptions. Reliability links all design parameters
through a limit state function and is a measure of components’ safety status. e physical mean-
ing of reliability is a relative percentage of safe components in the sample space of the whole
same component.
When loading conditions, geometric dimensions, and the type of material are fully speci-
fied, we can calculate its reliability. Failure theories under static loadings in mechanics of mate-
rials and the reliability-based design are the same. ese failure theories discussed in the tradi-
tional design theory can be used to build the limit state function. After the limit state function is
established, the methods discussed in Chapter 3 including the H-L method, R-F method, and
Monte Carlo method can be used to calculate the reliability of a component under any design
case. e following is the summary of typical limit state functions.
For a strength issue, the typical limit state functions of a component under simple typical
loading are summarized as follows.
• For a rod of brittle material under axial loading,
g
.
S
u
; K
t
; A; F
a
/
D S
u
K
t
F
a
A
D
8
ˆ
<
ˆ
:
> 0 Safe
D 0 Limit state
< 0 Failure:
(4.12)