Explain torsion of a cylinder.

1.	Explain torsion of a cylinder.
Answer» If one end of a cylinder of length l is clamped and other is given a twist ϕ by an application of a couple, then the relation between angle of ϕ and shear θ is θ = xϕ/1 (where x is distance from axis) Shear at surface (x = r) is maximum and given by θ_max = rϕ/l Torsional rigidity of hollow cylinder of internal and external radii r₁ and r₂. C_h = {πη(r₂⁴ - r₁⁴)}/{2l} Restoring couple of solid cylinder T_s = C_sϕ = πηr₄ϕ/2l and the restoring couple of hollow cylinder T_h = C_hϕ = {(πr₂⁴ - r₁⁴)ϕ}/{2l} For same mass, material and length, the hollow cylinder is stronger than the solid cylinder.

Answer»

If one end of a cylinder of length l is clamped and other is given a twist ϕ by an application of a couple, then the relation between angle of ϕ and shear θ is

θ = xϕ/1 (where x is distance from axis)

Shear at surface (x = r) is maximum and given by

θ_max = rϕ/l

Torsional rigidity of hollow cylinder of internal and external radii r₁ and r₂.

C_h = {πη(r₂⁴ - r₁⁴)}/{2l}

Restoring couple of solid cylinder

T_s = C_sϕ = πηr₄ϕ/2l

and the restoring couple of hollow cylinder

T_h = C_hϕ = {(πr₂⁴ - r₁⁴)ϕ}/{2l}

For same mass, material and length, the hollow cylinder is stronger than the solid cylinder.

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