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Unformatted text preview: EM 319
1St MIDTERM EXAM NAME: SESSION: October 9‘“, 2007, 6:308:30pm, FAC 21 Closed books and notes exam Exercise 1 (30 gointsl The piie ABC of length L is partially buried in the soil. Assuming that the friction
provided by the soil per unit length of the pile, f, is constant:
3) Find the force P needed to extract the pile from the soil.
b) Find the distribution of the internal force in the pile ABC (use the coordinate
system of the figure).
c) Find the internal stresses in the pile ABC.
d) Find the change in length 6M. Use your result from a) to provide an answer in terms only of P. é £9“: 3&4" 38c. Exercise 2 (30 points! A rigid bar is supported by a Spring and a rod, and carries a vertical load P, as in
the figure. Neglecting all weights, find: a) The distance d from the left support that the force P needs to be applied, so
that the bar remains horizontal. v D b) The stress that develops in them 0) If thejaris made of a material with yield stress equal to 500 MPa, what is
the safety factor?  Given: L=0.2m, H=0. 1m, A=0. 1m2, k=1010 N/m, 5:210 GPa, P=20kN /} Jrl/tc? Em Wweim LVD‘v'iiohiQé)“ a: 6?” F5 H 5:52, t . . N Links: c: 6 CD} it if“? m “‘7‘” "tr—i a I537; k {i A Q pm}, $5.: LEA! Exercise 3 (40 gointsl A problem that can arise in the design of front~wheel—drive cars is that of the
uneven distribution of the drivingltorque, To=190Nm, between the two'wheels,
because of the unequal lengths of the driving shafts (see top View of car hood at
Figure A). Asimple model of the system is given in Figure B. If the shafts 1 and 2
were exactly alike apart from their different lengths (i.e same I p ), then the driving torque from the engine would be distributed between the ieft and the right wheel
according to the equation TL 2 L2 /(L1 + L2)To, TR = L1 /(L1 +I.‘.,_)TO which for the lengths given (L1=15cm, L2=45cm) would result in TL=0.75Toand
TR=O.25TO. These unequal torques would cause steering and handling problems to the vehicle, in addition to uneven wear of the two tires etc. You are
asked to redesign the system (ﬁnd the shaft diameters) to solve this problem.
Using the model of Figure B,
a) Calculate the reaction torques TL and TR as a function of the input torque TO
and of the polar moments of inertia of the two shafts, IP] and 1'?2 (hint: the system is statically indeterminate). Then equate TL and TR (=To/2), and find
the reiation between ip1 and Iﬂthat results. b) Find the necessary diameter d1 of the left shaft (solid crosssection), based
on the maximum shear stress that develops (notice that each shaft now
carries half of the total torque To). The material’s yield stress in shear is
ryjem=400MPa and the required safety factor equals 3. 0) Calculate lip2 (holiow cross—section), using the relation from part a). For (1321.3 d2, find 0'2 and d3.
d) Calculate the maximum shear stress on the right shaft. What is the safety
factor for that shaft? e) Calculate the ratio of the weights of the two shafts. Gearbox r ...
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