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BE 110
CONTINUUM MECHANICS
Fall 2009
Homework Assignment #4
Due Thursday 10/12/09, 3:30 PM before class
No late submissions will be accepted.
Practice Problems
.
1. Find the resultant force and moment distribution in the foot of a diving athlete with weight W
standing upright on a platform just before the jump.
The athlete is standing on the edge of the
platform supported only by the toes without support on the heels.
The length of the foot from the
heel to the base of the toes is L.
2. Let
τ
ij
be the stress tensor.
What is the physical interpretation of the following quantities:
(a)
τ
33
(b)
τ
13
(c) (1/3)
τ
ij
δ
ij
(d)
τ
ij
i
where
δ
ij
is the Kronecker symbol and
i
is a unit vector.
3. The stress components
τ
ij
have been determined to be
3
x
2
+
4
xy

8
y
2
ax
2

6
xy
+
by
2
0
ax
2

6
xy
+
by
2
2
x
2
+
2
xy

3
y
2
0
0
0
0
The body force components are assumed to be zero.
Under what conditions is this stress field in
equilibrium?
Sketch in graphical form the stress components in the xy plane.
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 Winter '09
 MCCULLOCH

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