How does stress vary along the length of a key fitted in a shaft?

• A. Is uniformly constant
• B. Varies linearly
• C. Is of exponential shape, being more at the torque input end
• D. Is of exponential shape, being less at the torque input end

Answer: (C)

The correct choice indicates that the stress along the length of a key fitted in a shaft is characterized by an exponential variation, with more stress occurring at the torque input end. This phenomenon can be attributed to the nature of torque transmission and the mechanics involved in how the key engages with both the shaft and the hub.

When torque is applied to a shaft, the region closest to the input (the torque input end) experiences greater stress because it must overcome the most direct resistance due to the applied load. As you move away from the torque input end, the amount of torque and associated stress decreases because the load path and the angle of engagement change the distribution of forces acting on the key.

Understanding how stress varies this way is crucial in engineering design and analysis. By knowing that stress is more concentrated at the torque input end, engineers can appropriately address issues such as material selection, key dimensions, and potential failure points, leading to safer and more efficient designs in mechanical components.

The other options do not accurately reflect the stress distribution that occurs in this scenario. Uniformly constant stress would imply no variation at all, which is not the case in a keyed connection subject to torque. Option involving linear variation does not incorporate the exponential nature of stress response based on the mechanical