1.
The principal stresses at a point are
1
2
3
10
,
2
,
12
MPa
MPa
MPa
σ
σ
σ
=
=
= −
.
Without calculating their principal stresses, indicate which of the following stress
tensors are NOT consistent with these principal stresses.
[
]
[
]
[
]
[
]
10
0
0
10
0
0
( ) :
0
5
7
( ) :
0
7
5
0
7
5
0
5
7
12
0
0
10
0
12
( ) :
0
6
46
( ) :
0
5
7
12
7
5
0
46
6
a
b
c
d
σ
σ
σ
σ
⎡
⎤
⎡
⎢
⎥
⎢
=
−
=
−
⎢
⎥
⎢
⎢
⎥
⎢
−
−
⎣
⎦
⎣
⎡
⎤
⎤
⎥
⎥
⎥
⎦
⎡
⎤
⎢
⎥
⎢
⎥
=
−
=
−
⎢
⎥
⎢
⎥
⎢
⎥
⎢
⎥
−
−
⎣
⎦
⎣
⎦
2.
The principal stresses at a point are
1
2
3
10
,
5
,
5
MPa
MPa
MPa
σ
σ
σ
=
=
=
. The
yield stress is 10MPa. Compare the safety factor using the Tresca, Von Mises, and
Rankine criteria. It would help to change the principal stresses some for some of
these criteria.
3.
Why are there multiple stress tensors, and which one are we using in this course?
4.
When do we have more than three principal directions (+ and – do
not count)?
5.
In the equations of equilibrium, why is it reasonable that we have derivatives of
stresses but not of body forces?
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 Spring '08
 Staff
 Stress, Tensile strength, Yield surface

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