238 4. RELIABILITY OF A COMPONENT UNDER STATIC LOAD
yield strength S
y
of the beam’s material follows a normal distribution with a mean
S
y
D 34,500 (psi) and a standard deviation
S
y
D 3120 (psi).
(a) Calculate the reliability of the shaft by using the MSS stress theory.
(b) Calculate the reliability of the shaft by using DE theory.
4.31. A plane stress element of a component of a ductile material at the critical point is shown
in Figure 4.29. e normal compressive stress
x
(ksi), the normal tensile stress
y
, and
the shear stress
xy
follows normal distributions. eir distribution parameters are listed
in Table 4.50.
Figure 4.29: Schematic of a plane stress element at the critical point.
Table 4.50: e stresses in a plane stress element
σ
x
(ksi) σ
y
(ksi) τ
xy
(ksi)
μ
σ
x
σ
σ
x
μ
σ
y
σ
σ
y
μ
τ
xy
σ
τ
xy
16,200 1,550 6,800 540 13,000 1100
e column is made of a ductile material. e yield strength S
y
of the beam’s material
follows a normal distribution with a mean
S
y
D 34,500 (psi) and a standard deviation
S
y
D 3120 (psi). Calculate the reliability of the shaft by using the DE theory.
4.32. Schematic of a critical cross-section of a column is shown in Figure 4.30. It is subjected
to a compression force F
x
D 4000 ˙ 180 (lb) and a bending moment M
z
D 28;000 ˙
300 (lb/in). e geometric dimensions of the critical cross-section of the column are
h D 2:25 ˙ 0:010
00
and b D 1:00 ˙ 0:010
00
. Its ultimate tensile strength S
ut
follows a
normal distribution with a mean
S
ut
D 22:00 (ksi) and a standard deviation
S
ut
D 1:80
(ksi). e ultimate compression strength S
uc
follows a normal distribution with a mean
S
uc
D 82:00 (ksi) and a standard deviation
S
uc
D 10:50 (ksi). Calculate the reliability
of the column by using the MNS theory.
4.33. A plane stress element of a component of a brittle material at the critical point is shown
in Figure 4.31. e normal tensile stress
x
(ksi), the normal compression stress
y
and