AE 322
Homework #2
Due Monday, February 8, 2010
NOTE:
If you use MATLAB
®
, show command sequence and output.
1.
Find the components of the traction
n
T
on planes defined by
n
1
=
1
2
,
n
2
=
1
2
,
n
3
=
0
and
n
1
=
1
2
,
n
2
= −
1
2
,
n
3
=
0
for the following states
of stress:
(a)
σ
11
=
σ
σ
12
=
σ
21
=
0
σ
13
=
σ
31
=
0
σ
22
=
σ
σ
23
=
σ
32
=
0
σ
33
=
σ
(b)
σ
11
=
σ
σ
12
=
σ
21
=
σ
σ
13
=
σ
31
=
0
σ
22
=
σ
σ
23
=
σ
32
=
0
σ
33
=
0
2.
The state of stress at a point P in a material is given by:
σ
ij
[ ]
=
20
2
1
2
−
15
2
1
2
3
KPa
(a) Compute the components of traction
n
T
on the plane passing through P whose
outward normal vector
n
makes equal angles with the coordinate axes.
Note:
this is the
octahedral plane,
1
2
3
1
3,
1
3,
1/
3
n
n
n
=
=
.
(b) Compute the normal
nn
σ
and tangential
ns
σ
components of traction on this plane.
(c) Repeat the above exercise for the stress state:
10
2
1
2
15
5
1
5
3
ij
KPa
σ
=
−
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3.
Determine the body forces for which the following stress field describes a state of
equilibrium:
σ
ij
[ ]
=
yz
+
4
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 Spring '08
 Voulgaris,P
 Force, Stress, Tn, traction Tn, 3 KPa

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