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Problem 3.12.
Imagine that stresses in the
xy
plane are reported to be:
σ
x
6
−
a
1
⋅
x
2
⋅
=
y
12
a
1
⋅
x
2
⋅
=
τ
xy
12
a
1
⋅
y
2
⋅
=
where
a
1
is a constant.
Consider the square region 0<=
x
<=
b
,
0<=
y
<=
b
.
Find: a) expressions for the tractions
Φ
x
and
Φ
y
on each side of this square, in terms of
x, y
,
b
, and
a
1
.
b) If body forces are zero, is this state of stress in fact possible?
Explain.
Solution:
1
2
3
4
x
y
b
b
a)
Apply Eq. 3.114, adapted for 2dimensions,
n
=0
Φ
x
l
x
⋅
m
xy
⋅
+
=
y
l
xy
⋅
m
y
⋅
+
=
For Side 12
l
1
=
m
0
=
xb
=
x
x
=
6
−
a
1
⋅
b
2
⋅
=
y
xy
=
12
a
1
⋅
y
2
⋅
=
For Side 23
l
0
=
m
1
=
yb
=
x
xy
=
12
a
1
⋅
b
2
⋅
=
y
y
=
12
a
1
⋅
x
2
⋅
=
For Side 34
l
1
−
=
m
0
=
x
0
=
x
x
−
=
0
=
y
xy
−
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.
 Fall '10
 Folkman
 Stress

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