9.1 INTRODUCTION

Torsion forms one of the basic structural actions besides axial force, bending, and shear. Rotating shafts, pulleys, and gears are the structural components, which are subjected to torsion/twisting moments. Torsion of circular shafts greatly differs from torsion of noncircular shafts. In this chapter, torsion of circular sections will be discussed. Torsion produces shearing stresses in the cross-section of the member. In case of circular cross-sections, the assumption that plane sections remain plane is valid, but the same is not valid in case of noncircular sections. However, solid noncircular sections are subjected to shearing stress alone. In case of open sections such as T, I, and C, the cross-section is subjected to shearing stresses and warping stresses. Warping stresses are normal stresses produced due to warping of the cross-section.

Assumption: The following assumptions were made to evaluate the shearing stress and tensional deformation (twist) in case of circular sections.

• 1. Material of the shaft is homogenous, elastic, and isotropic.

• 2. Plane sections remains plane, even after the application of the twisting moment.

Consider a circular shaft of length ‘L’, subjected to twisting moment ‘T’, as shown in Figure 9.1.

Let ‘D’ be the diameter of the shaft. Consider an angular portion of the shaft. Let its radius be ‘r’. Fixidity at one of the supports does not allow the cross-section to rotate but free rotation is possible at the free end. AB, a fi ber before the application of the twisting, takes the position AB' after the application of the twisting moment. The inclination of the line segment AB' with AB is same along the length of the shaft, as plane sections remain plane even after twisting.

The radial OB (shown in Figure 9.1) rotates by ‘θ’ and assumes the position OB'. ‘θ’ is called the angle of twist.

From geometrical considerations, assuming torsional deformations are very small.