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Conditions of symmetry in torsional problem ensures that: (i) Plane sections originally normal to the plane of twist remain plane after twist. (ii) There is no lengthening or shortening of the shaft. (iii) Straight diameters are carried into straight diameters by the twisting deformation Which of the above statements are correct?

Conditions of symmetry in torsional problem ensures that: (i) Plane sections originally normal to the plane of twist remain plane after twist. (ii) There is no lengthening or shortening of the shaft. (iii) Straight diameters are carried into straight diameters by the twisting deformation Which of the above statements are correct? Correct Answer All (i), (ii) and (iii)

Explanation:

In the development of a torsion formula for a circular shaft, the following assumptions are made:

(i) During the deformation, the cross-sections are not distorted in any manner they remain plane, and the radius r does not change. In addition, the length L of the shaft remains constant

(ii) Based on these observations, we make the following assumptions:

  • Circular cross-sections remain plane (do not warp) and perpendicular to the axis of the shaft.
  • Cross-sections deform (there is no strain in the plane of the cross-section).
  • The distances between cross-sections do not change (the axial normal strain is zero).

(iii) Each cross-section rotates as a rigid entity about the axis of the shaft. Although this conclusion is based on the observed deformation of a cylindrical shaft carrying a constant internal torque, we assume that the result remains valid even if the diameter of the shaft or the internal torque varies along the length of the shaft.

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