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Torsion Members under Loading

Typical axial members with applied torque, T (double headed arrow). Point the thumb

on your right hand in the direction of the double-headed arrow. Your fingers show the

direction of the applied torque, T.

In a Nut Shell: Shear Strain in an Torsion Member, γ

The “twist” is such that the original line along the axis rotates thru the angle γ. The key

assumptions are that each circular cross-section remains plane and perpendicular to its axis

so that L γ = ρ φ . The result is:

γ = ρ φ / L

γ_max = c φ / L

where γ is the shear strain, ρ is the radial distance from the centroidal axis to the “fiber”

where the shear strain is calculated, φ is the angle of twist, and L is the length of the rod.

Note that the shear strain is zero on the axis of the member, varies linearly with the radial

distance, ρ, and is maximum at the outer fiber (outer radius, c) .

The common unit for shear strain is radians.

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