AE304_spring10_HW2

AE304_spring10_HW2 - H omework 2 


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Unformatted text preview: H omework 2 
 AE304
–
Aircraft
Structures
I
–
Spring
2010
 Due:
Monday,
February
1,
2010
 Exercise
1:

 The
 state
 of
 stress
 at
 a
 point
 in
 a
 cast‐iron
 structure
 (σut
 =
 290
 MPa
 and
 σuc
 =
 650
 MPa,
 and
 ν
 =
 0.23)
 is
 described
by
 σy
 =
 ‐
180
MPa
and

 τxy
=
200
MPa.
Determine
whether
the
failure
occurs
at
the
point,
according
 to
 the
 (a)
 maximum
 principal
 stress
 criterion,
 (b)
 strain
 energy
 density
 criterion
 and
 (c)
 Coulomb‐Mohr
 criterion.
 Exercise
2:
 A
thin‐walled
cylindrical
pressure
vessel
having
radius
r
=
300
mm
and
a
wall
thickness
t
=
12
mm
is
subjected
 to
an
internal
pressure
of
p
=
2.5
MPa.
In
addition,
a
torque
T
=
120
kN.m
acts
at
each
end
of
the
cylinder
(see
 figure
below).

 1. Determine
the
maximum
tensile
stress
σmax
and
the
maximum
shear
stress
τmax
in
the
cylindrical
wall
 2. If
the
allowable
in‐plane
shear
stress
is
30
MPa,
what
is
the
maximum
allowable
torque
T?
 
 
 
 Figure
2
 
 Figure
3
 Exercise
3:
 A
structural
member
is
 subjected
to
combined
loading
such
that
the
 state
of
 stress
 given
in
Figure
3
 occurs
at
 the
 critical
 point.
 
 The
 tensile
 yield
 strength
 of
 the
 material
 is
 300
 MPa.
 Determine
 the
 factor
 of
 safety
 n
 according
to
(a)
maximum
shearing
stress
theory
and
(b)
maximum
energy
distortion
theory
 Exercise
4:
 A
100‐mm
diameter
bar
shown
in
Figure
4
is
made
of
steel
 with
a
yield
stress
 σY
=
420
MPa.
The
free
end
 of
 the
 bar
 is
 subjected
 to
 loads
 5
 P
 in
 x‐direction
 and
 2
 P
 in
 z‐direction.
 If
 the
 bar
 was
 design
 with
 a
 factor
 of
 safety
 of
 2.0,
 determine
 the
 magnitude
 of
 P
 that
 initiates
 yielding
 at
 point
 A,
 based
 on
 (a)
 the
 distortional
 energy
density
criterion
and
(b)
maximum
shearing
stress
criterion.
 Figure
4
 
 ...
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This note was uploaded on 04/12/2011 for the course AE 304 taught by Professor Lestari during the Fall '10 term at Prescott College.

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