4.5. ESTIMATION OF SOME DESIGN PARAMETERS 169
Table 4.4: Young’s modulus, shear modulus, and Poisson’s ratio of some materials
Mechanical
Properties
E (MPa) G (Mpa) ν (Poisson’s Ratio)
Materials
μ
E
σ
E
γ
E
μ
G
σ
G
γ
G
μ
v
σ
v
γ
v
Steel 206010 3269.7 0.0159 78970.5 163.5 0.0021 0.29 0.01333 0.046
Alloy steel 201105 4905 0.0244 79461 / / 0.285 0.015 0.0526
Grey iron 134888 7357.5 0.0545 44145 / / 0.25 0.00667 0.0267
Ductile
iron
142245 4905 0.0345 73084.5 538.7 0.006 / / /
Aluminum
and its
alloy
69651 3269.7 0.0469 25996.5 163.5 0.0063 0.3333 / /
Copper
and its
alloy
100062 9165 0.0916 42183 98.1 0.0023 0.365 0.01838 0.0502
Titanium
alloy
112315 1635.3 0.0145 40858.7 1336.7 0.0327 0.30667 0.01155 0.0377
material properties all follow a normal distribution. Table 4.5 lists distribution parameters of
ultimate strength and yield strength of some aluminum alloy. Table 4.6 displays distribution
parameters of ultimate strength and yield strength of some Magnesium alloys and titanium
alloys. Table 4.7 displays distribution parameters of ultimate strength and yield strength of some
steels. Table 4.8 displays distribution parameters of ultimate strength and yield strength of some
steel alloys. Table 4.9 displays distribution parameters of ultimate strength and yield strength of
some stainless steels. Table 4.10 displays distribution parameters of ultimate strength and yield
strength of some irons.
4.5 ESTIMATION OF SOME DESIGN PARAMETERS
In reliability-based mechanical design, reliability is the measure of a component safety status.
e reliability of a component is solely determined by and based on the statistical descriptions of
all design parameters, that is, the type of distributions and corresponding distribution parameters
of all design parameters. We should use the reliable distribution parameters based on reliable
statistical data to conduct the calculation of the reliability. However, for a rough estimation of the
reliability, when the statistical descriptions of material mechanical properties and some design
170 4. RELIABILITY OF A COMPONENT UNDER STATIC LOAD
Table 4.5: Ultimate strength and yield strength of some aluminum alloy
Ultimate Strength S
u
(ksi) Yield Strength S
y
(ksi)
Materials Remarks
μ
S
u
σ
S
u
γ
S
u
Sample
size
μ
S
y
σ
S
y
γ
S
y
Sample
size
2014
Plate, L-T,
0.50–1.5
˝
85.0 2.76 0.032 20 75.0 1.75 0.023 20
2014-T651
Plate L-T, Ambient
temperature
69.0 1.82 0.026 20 63.0 1.35 0.021 20
2024-T81
Clad sheet,
0.068–0.140 L-T
69.9 1.70 0.024 15 64.4 2.41 0.037 15
2219-T87
Plate,
0.50–1.5
˝ L-T
67.0 1.64 0.024 17 54.0 1.53 0.028 17
6061-T4 Sheet, 0.032–0.125
˝ 36.6 1.69 0.046 1461 20.1 2.30 0.114 1461
6061-T6 Sheet, 0.032–0.125˝ 45.6 1.91 0.042 1648 41.7 2.89 0.069 1648
2219-T87
Plate,
0.50–1.5
˝ T-L
67.0 1.64 0.024 17 54.0 1.53 0.028 17
7075-T6
Clad sheet, 0.125
L-T
76.2 1.08 0.014 300 65.3 1.52 0.023 300
4.5. ESTIMATION OF SOME DESIGN PARAMETERS 171
Table 4.6: Ultimate strength and yield strength of some magnesium alloys and titanium alloys
Ultimate Strength S
u
(ksi) Yield Strength S
y
(ksi)
Materials Remarks
μ
S
u
σ
S
u
γ
S
u
Sample
size
μ
S
y
σ
S
y
γ
S
y
Sample
size
Magnesium Alloys
AZ 31-B-
H24
Sheet and plate
0.016–0.249 L-T
41.2 0.95 0.023 / 31.2 0.95 0.030 /
AZ 91-T4
Castings
QQ-M-56
38.5 2.26 0.059 30 14.2 0.67 0.047 30
AZ 318-
H24
Sheet and plate
0.0016–0.249
41.78 0.97 0.023 14800 31.54 1.34 0.042 14800
Titanium Alloys
Titanium
99%
Commercially pure,
L-T
101.9 6.98 0.068 1363 85.1 9.03 0.106 1354
T1-
6Al-4V
Sheet and bar
Annealed 75°F
135.5 6.7 0.049 2542 130.6 7.2 0.055 2611
T1-
6Al-4V
Sheet and bar
Temperature 572°F
99.1 4.49 0.045 462 81.0 5.25 0.065 556
T1-
6Al-4V
Sheet and bar
Forgings
143 4.98 0.035 89 135.3 4.75 0.035 89
T1-
6Al-4V
Sheet, heat treated
and aged
175.4 7.91 0.045 603 163.7 9.03 0.055 603
172 4. RELIABILITY OF A COMPONENT UNDER STATIC LOAD
Table 4.7: Ultimate strength and yield strength of some steels
Ultimate Strength S
u
(ksi) Yield Strength S
y
(ksi)
Materials Remarks
μ
S
u
σ
S
u
γ
S
u
Sample
size
μ
S
y
σ
S
y
γ
S
y
Sample
size
C1006 Sheet, hot rolled 48.3 0.52 0.011 5 35.7 0.8 0.022 5
C1018 Round bar, cold draw 87.6 5.74 0.066 50 78.4 5.9 0.075 50
C1035
Round bar, hot rolled,
1-9˝ diameter
86.2 3.92 0.045 913 49.5 5.36 0.108 899
C1045
Round bar, cold drawn
3/4–1 1/4˝ diameter
117.7 7.13 0.061 30 95.5 6.59 0.069 25
Low-carbon
steel
Sheet, drawing quality,
hot rolled, 0.075˝
44.7 1.26 0.028 140 34 2.25 0.066 140
Low-carbon
steel
Sheet, drawing quality,
cold rolled
44.7 1.12 0.025 140 25.6 1.87 0.073 140
Low-carbon
steel
Casting, as cast 66.7 2.01 0.030 200 34.8 0.84 0.024 200
4.5. ESTIMATION OF SOME DESIGN PARAMETERS 173
Table 4.8: Ultimate strength and yield strength of some steel alloys
Ultimate Strength S
u
(ksi) Yield Strength S
y
(ksi)
Materials Remarks
μ
S
u
σ
S
u
γ
S
u
Sample
size
μ
S
y
σ
S
y
γ
S
y
Sample
size
5Cr-Mo-V
alloy
5Cr-1.5Mo-0.4V-
0.35C
3/4
˝ dia bar aircraft
steel
296.5 1.84 0.006 25 240.8 3.1 0.013 25
Nickel steel
0.2C-2.25Ni casting,
normalized and tem-
pered
83.2 2.35 0.028 200 55.4 1.54 0.028 200
Ni-Cr-Mo
alloy
0.28C-2Mi-0.8Cr-
0.35Mo, normalized,
quenched and tem-
pered
161.1 4.97 0.031 44 148.1 4.98 0.034 44
High-
strength
structural
steel
0.22C-1.35Mn-
0.025O
0.50–1.50 in
76.9 2.06 0.027 109 49.6 3.69 0.074 113
High-
strength
structural
steel
0.25Si-0.25Cu
as rolled, 0.134-4˝
79.1 4.65 0.059 214 51 4.63 0.091 234
ASTM A7
Plate (heavy)
ambient temp.
64.8 2.93 0.045 141 39.8 4.15 0.104 141
ASTM A7
Structural steel
angles, channels,
beams
65.6 2.43 0.037 166 42.7 4.86 0.114 166
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