Torsion in Shafts: Conceptual Doubt Explained

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SUMMARY

This discussion clarifies the concept of torsion in shafts, particularly addressing the confusion surrounding the fixed end in torque applications. It establishes that while one end of a shaft may be treated as fixed for simplification, it is not truly fixed in a physical sense, especially when the shaft is supported by bearings. The torque in the shaft is determined by the relative angle between the ends, not their absolute positions. The shear stress induced in the shaft is calculated using the formula T*c/J, where T is torque, c is the distance from the center, and J is the polar moment of inertia.

PREREQUISITES
  • Understanding of basic mechanics, specifically torsion in materials.
  • Familiarity with shear stress calculations in rotating shafts.
  • Knowledge of polar moment of inertia (J) and its significance in torsion.
  • Concept of torque and its role in power transmission systems.
NEXT STEPS
  • Study the derivation and application of the shear stress formula T*c/J in various shaft configurations.
  • Explore the effects of boundary conditions on torsion in shafts, particularly in practical engineering applications.
  • Learn about the design considerations for shafts supported by bearings and their implications on torque transmission.
  • Investigate the relationship between angular velocity and torque in rotating systems, particularly in machinery.
USEFUL FOR

Mechanical engineers, students studying Strength of Materials, and professionals involved in the design and analysis of rotating machinery will benefit from this discussion.

ramzerimar
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I have some conceptual doubts about shafts subjected to torsion. When studying Strenght of Materials, to find stress and strain in power transmission shafts, we consider that one of the ends of the shaft is fixed, with all degrees of freedom restricted, and the other one is receiving torque. I'm having trouble to understand this fixed end. If it's a rotating shaft, how can it be fixed? But if it's not fixed, we can't apply equilibrium equations to solve the problem.
 
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Suppose that the shaft is strain free (no twist) to begin. Make a mark on each end at the same angular position. Now, twist the shaft so that the angle between the marks is phi. There is now shear stress = T*c/J in the outer fibre, OK?

Now, suppose you roll both ends through an angle theta, maintaining the angular difference phi. The torque in the shaft is the same as it was before because it depends on the relative angle between the ends, not the absolute angle.

Where you choose the reference mark, at theta = 0, theta = pi/27, or something else, it is only the relative rotation, the twist, that matters as far as the induced torque. Treating one end as fixed may be convenient, but it is certainly not necessary.
 
Dr.D said:
Suppose that the shaft is strain free (no twist) to begin. Make a mark on each end at the same angular position. Now, twist the shaft so that the angle between the marks is phi. There is now shear stress = T*c/J in the outer fibre, OK?

Now, suppose you roll both ends through an angle theta, maintaining the angular difference phi. The torque in the shaft is the same as it was before because it depends on the relative angle between the ends, not the absolute angle.

Where you choose the reference mark, at theta = 0, theta = pi/27, or something else, it is only the relative rotation, the twist, that matters as far as the induced torque. Treating one end as fixed may be convenient, but it is certainly not necessary.

Suppose I have a shaft supported by a pair of bearings, one at each end, and there's a motor connected to the shaft. When we start the motor, the shaft will rotate with some angular velocity. Why would the shaft twist then, if it is free to rotate because of the bearings?
 
If it is truly free to rotate, there will be no torque in the shaft and no shear stress. Why would you do this?

The usual reason for turning a shaft with a motor is to enable the shaft to drive some machine, to do work, and that takes a torque in the shaft to transmit power to the driven machine.
 
Dr.D said:
Where you choose the reference mark, at theta = 0, theta = pi/27, or something else, it is only the relative rotation, the twist, that matters as far as the induced torque. Treating one end as fixed may be convenient, but it is certainly not necessary.

Okay. So when I treat one end as fixed is just a way of simplifying things. Actually, it's not really fixed, only in relation to the other end.
 
That's about the size of it.
 

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