A torque T is applied at the free end of a stepped rod of

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist θ at the free end is

Angular twist at the free end

θ = ∑		TL
		GL

₂

=		TL			+		TL
		GL		₁			GL

₁

₂

=	TL		32	+	32
	πGD⁴		16		2

⇒ d =		18TL		^1/₄
		πGθ

	32TL		^1/₄
	πθG

	16TL		^1/₄
	πθG

	2TL		^1/₄
	πθG