1
AE 321
Homework 3
Due in class on September 20
1. Find the components of the traction on planes whose normal vector have components
n
1
=
12
,
n
2
=
n
3
=
0
,
and
n
1
=
n
2
=−
n
3
=
0
for the following states
of stress:
(a)
σ
11
=
12
=
21
=
0
13
=
31
=
0
22
=
σσ
23
=
32
=
0
33
=
(b)
11
=
12
=
21
=
13
=
31
=
0
22
=
23
=
32
=
0
33
=
0
2. The state of stress at a point P in a material is given by:
20
2
1
21
5
2
3
ij
kPa
(a) Compute the components of traction on the plane passing through P whose outward normal
vector
±
n
makes equal angles with the coordinate axes.
(b) Compute the normal and tangential components of traction on this plane.
3. The state of stress at a point is given by
ij
. A plane is defined by the direction cosines of the
normal (1/2, 1/2, 1/
√
2). Under what conditions will the traction vector on this plane be parallel to
the
x
2
axis and have a unit magnitude?
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 Fall '07
 waller
 Force, 1 Pa, 5 Pa, 0 PA, 7 Pa, 6 Pa

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