A shaft of circular section is said to be in pure torsion when it is ...
Torsion is about the polar centroidal axis i.e., along the axis of shaft
A shaft of circular section is said to be in pure torsion when it is ...
In pure torsion, a shaft of circular section is subjected to equal and opposite end couples. These end couples produce twisting moments along the axis of the shaft, causing the shaft to twist. The correct answer to the given question is option 'D', which states that the axes of the end couples coincide with the axis of the shaft.
Explanation:
- Torsion is a type of mechanical loading in which a structural element is subjected to twisting forces, causing it to twist about its longitudinal axis. It commonly occurs in shafts, rods, and other cylindrical components.
- When a shaft is in pure torsion, it means that it is subjected to torsional loading only, without any other types of loads such as bending or axial forces.
- In pure torsion, the applied loads are in the form of equal and opposite couples or moments, which are applied at the ends of the shaft.
- The axes of these end couples coincide with the axis of the shaft. This means that the moments are applied along the same line as the longitudinal axis of the shaft.
- When the end couples act along the axis of the shaft, the resulting twisting moment is distributed uniformly across the cross-section of the shaft. This ensures that the shaft experiences pure torsion and there are no additional bending moments or axial forces.
- The axis of the shaft is the line passing through the center of the shaft along its length. It is the axis about which the shaft rotates when subjected to torsional forces.
- Therefore, in pure torsion, the end couples must have axes that coincide with the axis of the shaft in order to produce the desired twisting effect without any additional bending or axial forces.
In conclusion, when a shaft of circular section is subjected to equal and opposite end couples in pure torsion, the axes of these end couples coincide with the axis of the shaft. This ensures that the shaft experiences pure torsion without any additional bending or axial forces.