page 148
3. ATOMIC MATERIAL DATA
Element |
Atomic # |
Atomic weight density g/cm3 |
Valances H |
|
copper |
29 |
63.57 |
8.96 |
w |
1/2 |
||||
iron |
26 |
55.85 |
7.86 |
2/3 |
aluminum |
13 |
26.97 |
2.67 |
3 |
tungsten |
74 |
183.85 |
19.3 |
6/8 |
zinc |
30 |
65.37 |
7.13 |
2 |
silicon |
14 |
28.09 |
2.33 |
4 |
carbon |
6 |
12.01 |
2.1 |
2/4 |
titanium |
22 |
47.9 |
4.51 |
3/4 |
F = 96,500 coulombs
4. MECHANICAL MATERIAL PROPERTIES
Table 1:
Material |
Type |
Density |
E |
G |
poisson |
ten - yield stress |
ten - ult. stress |
ten - yield strain |
yield stress - comp. |
ult. stress - comp. |
ult. stress - shear |
thermal expansion |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(Mg/m3) |
(GPa) |
(GPa) |
|
(MPa) |
|
(%) |
(MPa) |
|
|
10-6/deg C |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
aluminum |
typical |
2.6-2.8 |
70-79 |
26-30 |
0.33 |
35-500 |
100-550 |
1-45 |
|
|
|
23 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1100-h14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2024-T6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5456-h116 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2014-T6 |
2.8 |
73 |
36-41 |
0.33 |
410 |
480 |
13 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6061-T6 |
2.8 |
70 |
26 |
0.33 |
270 |
310 |
17 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
7075-T6 |
2.7 |
72 |
26 |
0.33 |
480 |
550 |
11 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
page 149
Table 1:
Material |
Type |
Density |
E |
G |
poisson |
ten - yield stress |
ten - ult. stress |
ten - yield strain |
yield stress - comp. |
ult. stress - comp. |
ult. stress - shear |
thermal expansion |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(Mg/m3) |
(GPa) |
(GPa) |
|
(MPa) |
|
(%) |
(MPa) |
|
|
10-6/deg C |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Brass |
typical |
8.4-8.6 |
96-110 |
36-41 |
0.34 |
70-550 |
200-620 |
4-60 |
|
|
|
19.1- |
|
|
|
|
|
|
|
|
|
|
|
|
21.2 |
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
Yellow Brass |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
cold rolled |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
annealed |
|
|
|
|
|
|
|
|
|
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|
Red Brass |
|
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|
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cold rolled |
|
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annealed |
|
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|
|
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|
|
|
|
|
|
|
|
|
|
Bronze |
typical |
8.2-8.8 |
96-120 |
36-44 |
0.34 |
82-690 |
200-830 |
5-60 |
|
|
|
18-21 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Cast Iron |
typical |
7.0-7.4 |
83-170 |
32-69 |
0.2-0.3 |
120 |
69-480 |
0-1 |
|
340- |
|
9.9-12 |
|
|
|
|
|
|
|
|
|
|
1400 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Concrete |
typical |
2.3 |
17-31 |
na |
0.1-0.2 |
|
|
|
|
10-70 |
|
7-14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
reinforced |
2.4 |
17-31 |
na |
0.1-0.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
lightweight |
1.1-1.8 |
17-31 |
na |
0.1-0.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Copper |
typical |
8.9 |
110-120 |
40-47 |
0.33- |
55-760 |
230-830 |
4-50 |
|
|
|
16.6- |
|
|
|
|
|
0.36 |
|
|
|
|
|
|
17.6 |
|
|
|
|
|
|
|
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|
|
|
|
|
|
annealed |
|
|
|
|
|
|
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|
|
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|
|
|
|
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|
|
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|
hard drawn |
|
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|
|
|
|
|
Glass |
typical |
2.4-2.8 |
48-83 |
19-35 |
0.17- |
|
30-1000 |
0 |
|
|
|
5-11 |
|
|
|
|
|
0.27 |
|
|
|
|
|
|
|
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|
|
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|
Plate |
|
|
|
|
|
70 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Fibers |
|
|
|
|
|
7000- |
|
|
|
|
|
|
|
|
|
|
|
|
20000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Magnesium |
typ. alloys |
1.76- |
41-45 |
15-17 |
0.35 |
80-280 |
140-340 |
2-20 |
|
|
|
26.1- |
|
|
1.83 |
|
|
|
|
|
|
|
|
|
28.8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Monel |
67%Ni,30% |
8.8 |
170 |
66 |
0.32 |
170- |
450- |
2-50 |
|
|
|
14 |
|
Cu |
|
|
|
|
1100 |
1200 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Nickel |
|
8.8 |
210 |
80 |
0.31 |
100-620 |
310-760 |
2-50 |
|
|
|
13 |
|
|
|
|
|
|
|
|
|
|
|
|
|
page 150
Table 1:
Material |
Type |
Density |
E |
G |
poisson |
ten - yield stress |
ten - ult. stress |
ten - yield strain |
yield stress - comp. |
ult. stress - comp. |
ult. stress - shear |
thermal expansion |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(Mg/m3) |
(GPa) |
(GPa) |
|
(MPa) |
|
(%) |
(MPa) |
|
|
10-6/deg C |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Plastics |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Nylon |
.88-1.1 |
2.1-3.4 |
na |
0.4 |
|
40-80 |
20-100 |
|
|
|
70-140 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Polyethylene |
.96-1.4 |
0.7-1.4 |
na |
0.4 |
|
7-28 |
15-300 |
|
|
|
140-290 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Rock |
|
|
|
|
|
|
|
|
|
|
|
5-9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Granite |
2.6-2.9 |
40-100 |
na |
0.2-0.3 |
|
|
|
|
50- |
|
|
|
|
|
|
|
|
|
|
|
|
280 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Marble |
2.6-2.9 |
40-100 |
na |
0.2-0.3 |
|
|
|
|
50- |
|
|
|
|
|
|
|
|
|
|
|
|
280 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Quartz |
2.6-2.9 |
40-100 |
na |
0.2-0.3 |
|
|
|
|
50- |
|
|
|
|
|
|
|
|
|
|
|
|
280 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Limestone |
2.0-2.9 |
20-70 |
na |
0.2-0.3 |
|
|
|
|
20- |
|
|
|
|
|
|
|
|
|
|
|
|
200 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Sandstone |
2.0-2.9 |
20-70 |
na |
0.2-0.3 |
|
|
|
|
20- |
|
|
|
|
|
|
|
|
|
|
|
|
200 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Rubber |
typical |
.96-1.3 |
0.0007- |
0.0002- |
0.45- |
1-7 |
7-20 |
100-800 |
|
|
|
130-200 |
|
|
|
0.004 |
0.001 |
0.50 |
|
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|
Sand,soil,gra |
|
1.2-2.2 |
|
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|
vel |
|
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|
Steel |
|
7.85 |
190-210 |
75-80 |
0.27- |
|
|
|
|
|
|
10-18 |
|
|
|
|
|
0.30 |
|
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|
cold rolled |
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annealed |
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|
high strength |
|
|
|
|
340- |
550- |
5-25 |
|
|
|
14 |
|
|
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|
|
|
1000 |
1200 |
|
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|
machine |
|
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|
340-700 |
550-860 |
5-25 |
|
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|
spring |
|
|
|
|
400- |
700- |
3-15 |
|
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|
1600 |
1900 |
|
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|
|
|
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|
|
|
|
stainless |
|
|
|
|
280-700 |
400- |
5-40 |
|
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|
1000 |
|
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|
tool |
|
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|
520 |
900 |
8 |
|
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|
|
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|
structural |
|
|
|
|
200-700 |
340-830 |
10-40 |
|
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|
12 |
|
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|
astm-a48 |
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|
page 151
Table 1:
Material |
Type |
Density |
E |
G |
poisson |
ten - yield stress |
ten - ult. stress |
ten - yield strain |
yield stress - comp. |
ult. stress - comp. |
ult. stress - shear |
thermal expansion |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
(Mg/m3) |
(GPa) |
(GPa) |
|
(MPa) |
|
(%) |
(MPa) |
|
|
10-6/deg C |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
astm-a47 |
|
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|
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|
astm-a36 |
|
|
|
|
250 |
400 |
30 |
|
|
|
12 |
|
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|
|
|
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|
|
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|
|
astm-a5242 |
|
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|
astm-a441 |
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|
astm-a572 |
|
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|
340 |
500 |
20 |
|
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|
12 |
|
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|
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|
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|
|
astm-a514 |
|
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|
700 |
830 |
15 |
|
|
|
12 |
|
|
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|
wire |
|
|
|
|
280- |
550- |
5-40 |
|
|
|
|
|
|
|
|
|
|
1000 |
1400 |
|
|
|
|
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|
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|
Stainless |
aisi 302 |
|
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|
17 |
Steel |
|
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|
Titanium |
typ. alloys |
4.5 |
100-120 |
39-44 |
0.33 |
760- |
900- |
10 |
|
|
|
8.1-11 |
|
|
|
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|
1000 |
1200 |
|
|
|
|
|
|
|
|
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|
|
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|
|
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|
|
Tungsten |
|
1.9 |
340-380 |
140-160 |
0.2 |
|
1400- |
0-4 |
|
|
|
4.3 |
|
|
|
|
|
|
|
4000 |
|
|
|
|
|
|
|
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|
Water |
fresh |
1.0 |
|
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|
sea |
1.02 |
|
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|
Wood (dry) |
|
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|
Douglas fir |
.48-.56 |
11-13 |
|
|
30-50 |
50-80 |
|
30-50 |
40-70 |
|
|
|
|
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|
|
Oak |
.64-.72 |
11-12 |
|
|
40-60 |
50-100 |
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30-40 |
30-50 |
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Southern |
.56-.64 |
11-14 |
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40-60 |
50-100 |
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30-50 |
40-70 |
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pine |
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4.1 FORMULA SHEET
• A collection of the essential mechanics of materials formulas are given below
page 152
Axial/Normal Stress/Strain
Shear Stress/Strain
Poisson’s ratio
Torsion
Beams
σ |
= ε |
E = |
P |
δ |
= ε L = |
PL |
-- |
------ |
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A |
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AE |
τ = γ G |
γ xy |
τ xy |
= ------ |
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G |
νε lateral
=–---------------------------
εlongitudinal
ε |
x = |
σ x |
– ν |
σ |
y |
σ z |
----- |
----- – ν ---- |
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E |
E |
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τ max = |
Tc |
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----- |
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J |
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φTL
=------
JG
σ ten = –σ comp = τ
ε= --γ 2
σMy
=–-------
I
τVQ
=-------
Ib
L = ρθ
σMy
=–-------
I
E = 2G(1 + ν )
γ max |
= |
τ max |
---------- |
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G |
J = |
π |
r4 |
------- |
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2 |
J= π--(r4 – r4 )
2 o i
P = 2π fT
(cylinder)
(hollow tube)
I |
= |
bh3 |
(for rectangle) |
-------- |
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12 |
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I |
= |
π r4 |
(for circle) |
------- |
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2 |
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ε max = |
c |
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ρ |
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ρEI
=-----
M
page 153
Buckling |
π 2EI |
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P <----------- |
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k2L2 |
k=0.5 (both ends fixed)
k=0.7 (one end fixed, one pinned) k=1.0 (both ends pinned)
k=2.0 (one end pinned, one free)
K |
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d/2 |
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r |
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3.0 |
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2.5 |
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d/2 |
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2.0 |
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1.5 |
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r/d |
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0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
page 154
K |
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r |
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2.5 |
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P |
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D |
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d |
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P |
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2.0 |
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1.5 |
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D/d = 2.0 |
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D/d = 1.5 |
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D/d = 1.25 |
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D/d = 1.1 |
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1.0 |
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r/d |
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0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
page 155
K |
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T |
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r |
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T |
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D |
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d |
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2.5 |
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2.0 |
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1.5 |
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D/d = 2.0 |
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D/d = 1.33 |
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D/d = 1.2 |
1.0 |
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D/d = 1.1 |
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r/d |
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0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
0.1 |