Find Max Torque Using Smaller Rad of Shaft

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Discussion Overview

The discussion revolves around the calculation of maximum torque in a shaft with varying radii. Participants are examining why the radius of the smaller part of the shaft is used in the torque calculation instead of the larger radius, considering the implications for shear stress and torque transmission.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the use of the smaller radius in the torque calculation, suggesting that the larger radius should be used since it is the maximum radius of the shaft.
  • Another participant proposes that the torque is applied to the thinner part of the shaft, which may justify the use of the smaller radius for calculating shear stress.
  • A different viewpoint suggests that the definition of shear force should be revisited, implying that the application of torque could affect the stress distribution differently depending on the shaft's geometry.
  • One participant acknowledges the oversight regarding the torque application point, indicating a realization that the torque is indeed applied to the smaller radius section.
  • It is stated that the smaller radius shaft must transmit the same torque as the larger radius part, implying a relationship between the two sections of the shaft.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using the smaller radius for torque calculations, with some acknowledging the reasoning behind it while others remain uncertain about the implications of the shaft's geometry on shear stress.

Contextual Notes

There is a lack of consensus on the interpretation of shear stress in relation to the torque application point, and the discussion highlights potential misunderstandings regarding the definitions and relationships involved in torque transmission through shafts of varying radii.

Who May Find This Useful

This discussion may be useful for students or professionals studying mechanics of materials, particularly those interested in torque transmission in shafts and the effects of geometry on stress calculations.

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Homework Statement


The question wants me to find the maximum torque.
I do not understand why the solution uses the radius of the smaller part of the shaft rather than the radius of the thicker part of the shaft. Please see the attached image.

Homework Equations



shear stress = (max torque)(maximum radius)/J where J = polar moment of inertia.

J = π/2c^4 where c = max radius of the rod

The Attempt at a Solution



I want to use 37.5mm as the radius (radius of larger part of the shaft), but it is not correct. The formula above directly relates torque T and c (radius), which is why I would assume it would be correct to use the largest c value possible. I would appreciate any insight. Thanks.
 

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I do not understand why the solution uses the radius of the smaller part of the shaft rather than the radius of the thicker part of the shaft.
Probably because the diagram shows the torque being applied to the thin part of the shaft.

It's shear stress you are calculating - the bigger part of the shaft may get a torsional (corkscrew) and a centrifugal stress - but to get a shear stress, something has to be pulling on the surface.
I suspect you are just taking your equation too literally - go back to the definition of a shear force and see how that applies to a torque. i.e. what if you applied the torque to the inner surface of a hollow shaft?
 
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Simon Bridge said:
Probably because the diagram shows the torque being applied to the thin part of the shaft.

Should have seen that, haha. Thank you.
 
The smaller radius shaft must transmit the same torque as the larger radius part.
 

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