Understanding Shear Stress in Shaft Mechanics

What is shear stress and how is it developed in a shaft subjected to torque?

When a shaft is subjected to a torque, how can we determine the shear stress at different points along the shaft?

Answer:

In a shaft subjected to a torque, shear stress is maximized at the outer surface of the shaft and is zero at the center. So, the shear stress at point A is 0. The exact value at B however requires additional information which is not provided.

Shear stress is a type of stress that acts parallel to the surface of an object or material. In the context of a shaft subjected to torque, shear stress is developed due to the applied twisting force.

The shear stress developed at points A and B on a shaft can be calculated based on the applied torque and the geometry of the shaft. Considering the shaft in our question with a torque of 50 kip∙inch at C and fully fixed at D, shear stress is maximized at the outer surface of the shaft (point B) and decreases linearly to zero at the center of the shaft (point A).

The shear stress at point B can be determined from the formula for shear stress in a circular shaft: τ = Tr/J, where T is the applied torque, r is the radius at the location of interest, and J is the polar moment of inertia. However, we cannot accurately provide a numeric answer for point B without information about the radius of the shaft and the material properties.

Therefore, in response to the multiple-choice aspect of our question, option (c) Shear stress at A = 0, Shear stress at B = 50 kip/in^2 only provides a correct stress at point A, but an inaccurate/assumed value at point B.

For further details and in-depth understanding of shear stress in shaft mechanics, it's essential to consider the geometric and material properties of the shaft in question. Without this information, it's challenging to accurately determine the shear stress at all points along the shaft.