Introduction to Elasticity Part 4 ppt
Introduction to Elasticity Part 4 ppt
... force vector F:
T = r × F (6)
This vector is in a direction given by the right hand rule, and is normal to the plane containing
the point O and the force vector. The torque tending to loosen ... the
component of this moment vector along the plug axis:
4
Normal stresses act to pull parallel planes within the material apart or push them closer
together, while shear stresses act to sli...
Introduction to Elasticity Part 8 pptx
... matrix:
0.1185E+12 0.1653E+10 0.2 942 E+ 04 -0.2798D+11 0.0000D+00 0.7354D+03
0.1653E+10 0.1185E+12 0.1389E+06 0.0000D+00 0.2798D+11 0. 347 3D+05
0.2 942 E+ 04 0.1389E+06 0 .48 00E+10 0.7354D+03 0. 347 3D+05 0.0000D+00
-0.2798E+11 ... from zero to C
v
x,0
=5×10
4
as time progresses
through the relaxation time.
15
Now substituting these into Eqn. 9, we have
∂
4
φ
∂x
4
+2
∂
4
φ
∂x...
Introduction to Elasticity Part 9 pptx
... is:
k
(1)
=
25.00 43 .30 −25.00 43 .30
43 .30 75.00 43 .30 −75.00
−25.00 43 .30 25.00 43 .30
43 .30 −75.00 43 .30 75.00
× 10
3
and for element 2:
k
(2)
=
25.00 43 .30 −25.00 43 .30
43 .30 75.00 43 .30 ... k
(2)
22
k
(2)
23
k
(2)
24
00 k
(2)
31
k
(2)
32
k
(2)
33
k
(2)
34
00 k
(2)
41
k
(2)
42
k
(2)
43
k
(2)
44
This matrix premultipl...
Introduction to Elasticity Part 14 ppt
...
1 .4
1.5
0.6
0 .42
53
60
50
0. 54
75
Silicon
ceramic
2.35
2.3
110
44
0. 24
3200
35
0.0
1.5
6
Silicon Carbide (SiC)
ceramic
36.00
2.8
45 0
190
0.15
9800
35
0.0
4. 2
4. 2
Spruce (parallel to ...
0.60
9
0.8
0.30
48
50
10
2.5
4
Steel, high strength 43 40
metal
0.25
7.8
210
76
0.29
1 240
1550
2.5
100
14
Steel, mild 1020
metal
0.50
7.8
210
76
0.29
200
380
25
14...
Elasticity Part 4 ppt
... 89.6 0. 34 33 .4 71 93.3 18
Glass 68.9 0.25 27.6 27.6 45 .9 8.8
Nylon 28.3 0 .40 10.1 4. 04 47.2 102
Rubber 0.0019 0 .49 9 0:6 54 Â10
À3
0.326 0.326 200
Steel 207 0.29 80.2 111 1 64 13.5
Sadd / Elasticity ... temperature change. By using (4. 4.1), this result can be
combined with the mechanical relation (4. 2.10) to give
e
ij
¼
1 þ n
E
s
ij
À
n
E
s
kk
d
ij
þ a(T À T
o
)d
ij
(4: 4...
Introduction to Elasticity Part 1 docx
... convert the MPa to psi rather
than convert the pounds to Newtons. Also using A = πd
2
/4 to compute the diameter rather than the
area, we have
d =
4A
π
=
4P
f
πσ
f
=
4 × 10000(lb)
π × ... ×10
−6
,
◦
C
−1
Pb 14 (2) 327 5 .4 29
Al 69 (10) 660 10.5 22
Cu 117 (17) 10 84 13.5 17
Fe 207 (30) 1538 15.3 12
W 40 7 (59) 341 0 32 4. 2
The system will generally have sufficient therma...
Introduction to Elasticity Part 2 docx
... ($/kg)
E-glass 72 .4 2 .4 2.6 2. 54 28.5 0.95 1.1
S-glass 85.5 4. 5 2.0 2 .49 34. 3 1.8 22–33
aramid 1 24 3.6 2.3 1 .45 86 2.5 22–33
boron 40 0 3.5 1.0 2 .45 163 1 .43 330 44 0
HS graphite 253 4. 5 1.1 1.80 140 2.5 ... stretches to λ
d
, after which the engineering stress there
would have to rise to stretch it further. But this stress is greater than that needed to
stretch mate...
Introduction to Elasticity Part 5 pot
... planes to appear at 45
◦
to the chalk’s long axis. The crack will appear
transverse to the principal tensile stress, producing a spiral-like failure surface. (As the crack progresses
into the ... pseudovector form. This relation serves to define the stress concept as an
entity that relates the traction (a vector) acting on an arbitrary surface to the orientation of the
surface (anot...
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