discover the suitable diameter of the shafta

Question

Discover the suitable diameter of the shaft:

A shaft is required to fail while the torque on the shaft is 20 kN-m. Discover the suitable diameter of the shaft of the modulus of rupture of torsion is 200 mN/m².

 Solution

T = 200 kN-m = 20 × 10³ N-m

τ_max = 200 MN/m2 = 200 × 10⁶ N/m²

d = ?

τ_max      = 16T /πd₃

⇒200 × 10⁶  = 16 × 20 × 10/ πd ³

∴ d = 7.99 × 10^{- 2} m = 80 mm