MECHANICS OF SOLIDS
(EM 319)
LiL?C h f <
QUIZ #2
Spring 2004
Friday Marchl2, 8-9am WEL 3.502
Closed book, notes, homework
Both questions should be attempted, they are each worth 20 points.
SECTION (Circle one)
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1. The structure shown below consists of a steel bar symmetrically placed between
two aluminum bars. The holes in the aluminum bars are placed a distance, L ,
from the fixed end. The hole in the steel bar is closer to the fixed end by an
amount, b . The temperature in the aluminum bars is raised by AT and held
while the steel bar is stretched in order to line up the holes at the right hand end.
A rigid rod is slipped into the aligned holes and the load on the steel bar is
released (the temperature is still the same). Find the stress in the steel bar if ths
temperature increase in the aluminum bars is 100°F.
Material
I
Modulus E
CTE cu
(10-"in/in/"~)
Hole location
(in2)
2. A hollow casing from a pile driver is stuck in some mud. One
--scheme being
proposed to extract it is to weld a rod and base plate to the bottom of the casing
and twist the rod, thereby freeing the casing from the mud. The rod and base
plate would be made of the same material. The mud provides a resistive torque
I/?
intensity f(xj = lo
[ z ) to the casing, where
x is measured from the top
LC,
surface o i the casing ~ludLC is iis length. Tne length of the rod is twice that of
the casing.
(a) If the torque applied to the rod is To. show that
3T" .
to = -
2Lc
(b) The inner diameter of the casing is
90%
oi
the
outer
diameter.
Derel-mine what I'raciion of rile
d - order. to
casing oute;- diameie thc d~ameter
of the roc s i ~ ~ n lhe
d
ii?
ensure that the rod and casing fail
at the same time.
(c) Under the conditions (b). determine
the relative twist between the top of
the casing and the end of the rod
where
the
torque
is
applied.
(Assume that the base plate is
rigid). The torque is 200 in-k. the
casing length is 200 in, the casing
outer diameter is 2 0 in and the
shear modulus is 16 msi.
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