A long shaft of diameter d is subjected to twisting moment

A long shaft of diameter d is subjected to twisting moment T at its ends. The maximum normal stress acting at its cross-section is equal to

J =	π	d⁴
	32

b² + ω²

σ_n =	(σ₁ + σ₂)	+	(σ₁ - σ₂)	cos2θ = τsin2θ
	2		2

σ₁ = 0, σ₂ = 0, θ = 45°

σ_n(max) = 0 + 0 - τ_max × 1 =	16T
	πd³

	32T
	πd³

	64T
	πd³