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Difficulty: MediumTypes of Stress and Strain

A solid drive shaft transmits rotational power to a heavy gear. To lock them together and prevent the gear from slipping, a rectangular steel key is fitted into a shared horizontal slot between the shaft and the gear's inner hub. When the motor engages and the shaft forcefully rotates while the heavy gear resists, the shaft pushes against one side of the key's bottom half, while the gear's hub pushes back against the opposite side of the key's top half. What primary type of mechanical stress does the steel key experience in this scenario?

  1. Shear stressAnswer
  2. B
    Torsional stress
  3. C
    Tensile stress
  4. D
    Compressive stress

Answer

Shear stress
The correct answer accurately identifies that the key experiences two opposing forces acting on parallel, offset planes. The shaft pushes one half, and the gear pushes the other. This creates a cutting or sliding effect along the horizontal plane between the two halves, which is the exact definition of shear stress.

Step-by-Step Solution

1
Analyze the forces acting on the specific component in question (the steel key).
The shaft pushes the bottom half of the key in the direction of rotation, while the gear hub resists, pushing the top half of the key in the opposite direction.
Accurate force identification is the first step in determining internal stress.
2
Evaluate the alignment of these opposing forces.
The forces act parallel to each other but on slightly offset planes (top half vs. bottom half).
The alignment of the load dictates how the material will tend to deform.
3
Match the observed force pattern to standard mechanical stress definitions.
Opposing forces acting on offset, parallel planes attempt to slide one portion of the material over another, which defines shear stress.
This confirms the correct classification of the mechanical load.

Key Concept

Identifying Shear Stress in Fasteners and Load-Bearing Joints
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Topics

Types of Stress and Strain

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