A 250-mm-long aluminum tube (E = 70 GPa) of 36-mm outer diameter and 28-mm inner diameter can be closed at both ends by means of single-threaded screw-on covers of 1.5-mm pitch. With one cover screwed on tight, a solid brass rod (E = 105 GPa) of 25-mm diameter is placed inside the tube and the second cover is screwed on. Since the rod is slightly longer than the tube, it is observed that the cover must be forced against the rod by rotating it one-quarter of a turn before it can be tightly closed. Determine (a) the average normal stress in the tube and in the rod, (b) the deformations of the tube and of the rod.
Fig. P2.16
a)
The average normal stress in the tube
Answer to Problem 16P
The average normal stress in the tube
Explanation of Solution
Given information:
The length of the tube (L) is
The outer diameter of the tube
The inner diameter of the tube
The Young’s modulus of the aluminium
The diameter of the rod
The Young’s modulus of the brass
The pitch of the single-threaded screw-on cover (p) is
The load act in the tube is P.
Calculation:
Calculate the cross sectional area of the tube
Substitute
Calculate the cross sectional area of the rod
Substitute
Calculate the deformation of the tube
Substitute
Calculate the deformation of the rod
Substitute
Calculate the deformation of the screw
Substitute
Calculate the load (P) act in the tube using the formula:
Substitute
Calculate the average normal stress in the tube
Substitute
Calculate the average normal stress in the rod
Substitute
Hence, the average normal stress in the tube
b)
The deformations of the tube
Answer to Problem 16P
The deformations of the tube
Explanation of Solution
Given information:
The length of the tube (L) is
The outer diameter of the tube
The inner diameter of the tube
The Young’s modulus of the aluminium
The diameter of the rod
The Young’s modulus of the brass
The pitch of the single-threaded screw-on cover (p) is
The load act in the tube is P.
Calculation:
Calculate the cross sectional area of the tube
Substitute
Calculate the cross sectional area of the rod
Substitute
Calculate the deformation of the tube
Substitute
Calculate the deformation of the rod
Substitute
Calculate the deformation of the screw
Substitute
Calculate the load (P) act in the tube using the formula:
Substitute
Calculate the deformations of the tube
Substitute
Calculate the deformations of the rod
Substitute
Hence, the deformations of the tube
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Chapter 2 Solutions
Mechanics of Materials, 7th Edition
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