A circular shaft shown in the figure is subjected to torsion

A circular shaft shown in the figure is subjected to torsion T at two points A and B. The torsional rigidity of portions CA and BD is GJ₁ and that of portion AB is GJ₂. The rotations of shaft at point A and B are θ₁ and θ₂. The rotation θ₁ is

Portion AB rotates without twisting

	T	=	Cθ
	J		l

∴ θ =	TJ
	C θ

Angle of twist at A,

θ_A =	TL
	GJ