Question about torsional shear stress

In summary, the discussion on torsional shear stress focuses on the internal resistance of materials to twisting forces. It highlights how shear stress is distributed across a cross-section when a torque is applied, with key factors including the material's properties, the shape of the cross-section, and the magnitude of the applied torque. Understanding these principles is crucial for engineering applications to ensure structural integrity and safety.
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rcw2004
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If a circular rod is allowed to rotate freely and a moment (M) is applied to one end of the rod. A moment acting in the opposite direction, with magnitude (M/3), is applied to the other end of the rod. What is the maximum moment in the rod that would be used to calculate the maximum torsional shear stress in the equation (T*c)/J?
 
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  • #2
Welcome to PF.

Because the rod is free to rotate, the unbalanced moment will result in an acceleration of the rotation of the rod. The rod will be subjected only to the moment (M), which will be balanced by (M/3) plus the moment causing acceleration.
 
  • #3
Welcome to PF.

rcw2004 said:
If a circular rod is allowed to rotate freely and a moment (M) is applied to one end of the rod. A moment acting in the opposite direction, with magnitude (M/3), is applied to the other end of the rod. What is the maximum moment in the rod that would be used to calculate the maximum torsional shear stress in the equation (T*c)/J?
Please show your work based on the hints given by Baluncore. Thank you.
 
  • #4
Baluncore said:
Welcome to PF.

Because the rod is free to rotate, the unbalanced moment will result in an acceleration of the rotation of the rod. The rod will be subjected only to the moment (M), which will be balanced by (M/3) plus the moment causing acceleration.
Thank you for the answer. I am still confused, is M not the moment that is causing the acceleration? My initial thought was that one third of M would go towards resisting the M/3 moment, and the other two thirds of M would accelerate the rod. Then the Moment that is actually twisting the rod and causing torsion would be M/3. Is this incorrect? and if so why?
 
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  • #5
rcw2004 said:
Is this incorrect? and if so why?
The moment, M, is applied to one end of the rod.
The rod must be able to transmit that M, along the rod, to where it will be countered by the 2M/3 that accelerates the rod, and the far end M/3.

There are multiple interpretations of your question. We need a diagram, or the original wording to determine the situation.
 
  • #6
Let's say you apply M/3 to both ends - then the stress is M/3 times c/J. Since one end applies M then there is no equilibrium and rod accelerates since free to rotate. So max twist moment is M/3
 

FAQ: Question about torsional shear stress

What is torsional shear stress?

Torsional shear stress is the internal shear stress that occurs in a material when it is subjected to a twisting or torsional load. It is defined as the force per unit area acting parallel to the surface of the material, resulting from the applied torque. This stress is critical in understanding how materials behave under torsional loads, particularly in shafts and beams.

How is torsional shear stress calculated?

Torsional shear stress can be calculated using the formula: τ = T*r/J, where τ is the torsional shear stress, T is the applied torque, r is the distance from the center of the shaft to the point where the stress is being calculated, and J is the polar moment of inertia of the cross-section. This formula allows engineers to determine the shear stress at different points along the shaft.

What factors affect torsional shear stress?

Several factors affect torsional shear stress, including the magnitude of the applied torque, the geometry of the object (such as its diameter and cross-sectional shape), the material properties (like yield strength and modulus of elasticity), and the length of the object. Changes in any of these factors can lead to variations in the torsional shear stress experienced by the material.

What are the consequences of excessive torsional shear stress?

Excessive torsional shear stress can lead to material failure, which may occur in the form of yielding, cracking, or complete fracture. In rotating shafts, this can result in torsional fatigue, where repeated loading and unloading cycles cause progressive damage. Understanding and managing torsional shear stress is essential to ensure the structural integrity and safety of mechanical components.

How can torsional shear stress be mitigated in design?

Torsional shear stress can be mitigated in design through several approaches, such as selecting materials with higher strength properties, increasing the diameter of shafts to enhance the polar moment of inertia, using appropriate cross-sectional shapes (like hollow shafts), and implementing torsional dampers or supports to distribute loads more evenly. Proper design considerations can significantly reduce the risk of failure due to torsional shear stress.

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