Circle one: Mikkelson Suresh Name: ______________________________

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University of Wisconsin Madison; ME 306

Midterm; March 14th

2012, 7:30 9:00 pm

Problem 1 (4 points): For the problem below, if 4d a= , find the stress at point A

Solution:

Circle one: Mikkelson Suresh Name: ______________________________

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Problem 2 (6 points): Three solid shafts, each of 20 mm diameter, are connected by the gears

as shown. The torque is applied in the direction shown with magnitudes given by TA = 15 Nm

and TE = 30 Nm. The radii of the gears are rB = 35 mm, rC = 150 mm and rF = 50 mm. The shaft

lengths are LAB = 1.5 m and LCD = 1 m. Knowing that G = 64 GPa, find the total angle of twist at A

in degrees.

rB

rC

rF

TA

TE

LCD

LAB

rB

rC

rF

TA

TE

LCD

LAB

Solution:

Circle one: Mikkelson Suresh Name: ______________________________

Write on reverse if needed

Problem (10 points): A hollow circular tube T of length L = 15 in is uniformly compressed by a

force P acting through a rigid plate. The outside and inside diameters of the tube are 3.0 and

2.75 in respectively. A concentric solid circular bar B of 1.5 diameter is mounted inside the tube.

When no load is present, there is a clearance of c = 0.010 in. between the bar and the rigid

plate. Both the bar and the tube are made of steel with E = 29x103 ksi and y = 36 ksi.

A load P is applied till the total deflection is 0.025 in.

(a) Draw the force-displacement curve for the tube (disregarding the bar), where

displacement is the rigid plate displacement.

(b) Draw the force-displacement curve for the bar (disregarding the tube), where

displacement is again the rigid plate displacement.

(c) Using the above two plots, find the load P.

Solution:

Circle one: Mikkelson Suresh Name: ______________________________

Write on reverse if needed