Concept explainers
A uniformly tapered aluminum-alloy tube AB with a circular cross section and length L is shown in the figure. The outside diameters at the ends arc dAand dB= 2dA. A hollow section of length LB and constant thickness t = dA/10 is cast into the tube and extends from B halfway toward A. (a)
Find the angle of twist é of the tube
when it is subjected to torques T acting at the ends. Use numerical values: dA= 2.5 in., L = 48 in., G = 3.9 × 106 psi, and T =40,000 in.-lb.
(b)
Repeat part (a) if the hollow section has con stant diameter rfj (see figure part b)
(a)
The angle of twist of the tube when it is subjected to torques at it ends.
Answer to Problem 3.4.15P
The angle of twist of the tube when it is subjected to torques at it end
The angle of twist of the tube when it is subjected to torques at it end
Explanation of Solution
Given information:
The diameter of the smaller section of the tube is
Write the expression for outer diameter.
Here, the elemental area of the tube is
Write the expression for inner diameter.
Write the expression for angle of twist of side
Substitute
Here, the torque at the ends of the tube is
Write the expression for angle of twist of side
Calculation:
Substitute
Substitute
Conclusion:
The angle of twist of the tube when it is subjected to torques at it end
The angle of twist of the tube when it is subjected to torques at it end
(b)
The angle of twist when the tapered shaft is hollow.
Answer to Problem 3.4.15P
The angle of twist of the tube when it is subjected to torques at it end
The angle of twist of the tube when it is subjected to torques at it end
Explanation of Solution
Write the expression for angle of twist on side
The figure below shows the torque acting on the tube.
Figure-(1)
Write the expression for angle of twist on side
Write the expression for equation of compatibility.
Substitute
Write the expression for the total torque
Here, the torque acting on the side
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The angle of twist of the tube when it is subjected to torques at it end
The angle of twist of the tube when it is subjected to torques at it end
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Chapter 3 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning