Torsion

Torsion Equation

• Torsion means twisting a structural Member when it is loaded by a couple that Produces rotation about the longitudinal axis.
• Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F.d applied in a plane perpendicular to the axis of the bar such a shaft is said to be in torsion.
• Effects of Torsion: The effects of a torsional load applied to a bar are
• To impart an angular displacement of one end cross – section with respect to the other end.
• To setup, the shear stresses on any cross section of the bar perpendicular to its axis
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Assumptions made for the Equation

• Assumptions made for derivation of the Torsion equation-
• Pure twisting moment is applied to shaft and it acts in a plane perpendicular to axis of shaft
• Material of shaft is homogeneous and isotropic and load is applied within elastic limit
• Twisting moment is uniform for entire length of shaft
• Cross-section of shaft remains plane after twisting
• No changes occur in length of shaft

Torsion Equation

Important Formulae

Compounding of Shafts

• Series connection: Series connection of compound shaft as shown in the figure. Due to a series connection, the torque on shaft 1 will be equal to shaft 2 and the total angular deformation will be equal to the sum of deformation of the 1st shaft and 2nd shaft.
• Parallel Connection: Parallel connection of compound shaft as shown in the figure. Due to a parallel connection of compound shaft, the total torque will be equal to the sum of torque of shaft 1 and torque of shaft 2 and the deflection will be same in both the shafts.
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Strain Energy due to Torsion

Effect of Pure Bending and Pure Torsion

Combined Effect of Bending and Torsion

Shear Stress Distribution