NAME:
(EM 319)
QUIZ #2 Summer 2000
Wednesday July 12 from 7-9 p.m. WRW 113
Closed Book
8.5" x 1 I" equation sheet
Points for each question are shown in ()

1. A cylindrical tube and a circular rod are supported rigidly at opposite ends. The diameter of the rod fits exactly the inside diameter of the tube at their common ends.
Each component has a hole drilled through its center at the common ends. The holes match in every way except that the hole in the rod is rotated by an angle
P from that in the tube. The hole in the rod is brought into alignment with that in the tube by twisting it until a rigid pin can be slipped through both holes. The torque on the rod is then released. If the rod and tube are made of the same material and have the same lengths, show that the optimum wall thickness of the tube should be 0.36 in. if its outside diameter is 2.00 in. Find the residual torque in this case. (10)

, ,'
!
2. The assembly shown below consists of a thin walled tube and a solid rod inside. They are supported by a rigid support at one end and a torque T = 15k -in. is applied at the other end through a rigid disk that is welded to the tube and rod. The wall thickness of the tube is t = t , ( 2 - cos 8) with to = 0.1" andits median radius is a = 1.5". The rod has a radius b = I" and a length L = 30". The shear modulus of the tube and rod is 15
*
106psi. Find the location and value of the maximum shear stress in each component and the rotation of the rigid disk. (15)
Note
2"
CLX
- 277 o a + b c o s x - m
Tube
,-
"'
.
+ :
-7
-.
,
- - -
-
7
.
..

3. The initially horizontal rigid bar BCD is supported at C by a pinned support. The threaded rods AB and ED are rigidly supported at one end and connect to the rigid bar at the other. The nuts at B and D are tightened so as to remove any slack in the assembly, but not so much that any preload is imparted to the structure. The temperature of both rods drops by an amount AT.
The material properties and geometry of the rods are:
Rod
AB
ED
Modulus
(lo6 psi)
15
30
CTE
(10-'inlin/"~)
20
15
Area
(in?
1.5
0.75
Length
(in)
40
30 and BC=25inandCD=lOin
(a) Determine the rotation of the rigid bar for AT = 50 C . (6)
(b) Determine the stress in the rod ED. (6)
(c) How much load does the support at C have to provide? (3)