A solid shaft of diameter d and length L is fixed at both

A solid shaft of diameter d and length L is fixed at both the ends. A torque, T0 is applied at a distance, L/4 from the left end as shown in the figure given below.

τ_max =	16	[√M² + T²]
	πd³

But M = 0

∴ τ_max =	16T₀
	πd³

Alternately

We know,	T	=	τ
	J		r

Where, J =	πd⁴
	32

∴ τ =	Tr	=	T₀ × R × 32	=	16T₀
	J		πd⁴		πd³