The permissible angle of twist=1.3 degree in length of 5.8 m and the shear stress is not exceed 60 MPa. Take Modulus of Rigidity G=90 MPa.

Noet

*Value of maximum Torque must satisfy the condition for strength and stiffness i.e always consider the lowest value of Torque so that shaft will not fail in strength and stiffness condition *

Data: Maximum Torque $(T_{max}) = \ ?$

Diameter of shaft (d) = 270 mm and $r = \frac{d}{2} = 135 \ mm$

Angle of twist $\theta = 1.3° = 1.3 \times \frac{\pi}{180} $ (radian)

Length (L) = 5.8 m = 5800 mm.

Shear stress $\zeta = 60 \ Mpa = 60 \ N/mm^2$

Modulus of Rigidity (G) = 90 Mpa.

$\rightarrow$ 1] Torque from strength:

$\frac{T}{J_p} = \frac{\zeta}{r}$

$\frac{T}{\frac{\pi}{32} \times 270^4} = \frac{60}{(\frac{270}{2})}$

$\therefore$ $T = 231.88 \times 10^6 \ Nmm$

2] Torque from stiffness:

$\frac{T}{J_p} = \frac{G \theta}{l}$

$\frac{T}{\frac{\pi}{32} \times 270^4} = \frac{90}{5800} \times (1.3 \times \frac{\pi}{180})$

$\therefore$ $T = 183.69 \times 10^3 \ Nmm$

Value of Torque be such that it must satisfies for strength and stiffness condition.

$\because$ $T = 231.88 \times 10^6 \ Nmm$ is greater than $T = 183.69 \times 10^3 \ Nmm$

Which is from stiffness condition.

i.e. Maximum Torque can be applied to shaft so that it doesn’t fail in stiffness condition is $183.69 \times 10^3 \ Nmm$