AE 321 – Practice Problems
Chapter 7: Failure and Fatigue
1.
(Exam question) A linear, elastic, isotropic and homogeneous solid circular cylinder of length
L
and radius
R
(no restriction on
L
and
R
), Young’s modulus
E
, Poisson’s ratio
ν
and uniaxial
yield strength
σ
y
, is subjected to an applied pressure
P
on its lateral surface. The end faces are
traction free
(a) Find the stress and strain state in the bar. Hint:
Inplane, i.e. looking down the cylinder axis,
the loading appears hydrostatic.
(b) What is the maximum value of pressure before yield occurs if the material subscribes to a
Von Mises yield condition?
(c) What would the Von Mises criterion predict if the pressure
P
were applied on the end faces as
well as the lateral surface?
x
3
P
P
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(Exam question) Bending moments
M
y
and
M
z
are applied to the rectangular bar shown below.
The bar is made up of a brittle
linear elastic isotropic and homogeneous material with elastic
properties
E
,
ν
and failure strength
σ
f
..
(a) At what value of
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 Spring '09
 Lambros
 Yield surface, MZ, Von Mises yield criterion

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