Find the inner diameter of the tubular steel shaft:
A solid aluminium shaft having 1 m long & of 50 mm diameter is to be replaced by a tubular steel shaft of the similar length and similar outside diameter so that either shaft might carry the same torque and contain the similar angle of twist, over the overall length. What should be the inner diameter of the tubular steel shaft?
Modulus of rigidity of steel might be taken as 0.85 × 105 N/mm2 and that of aluminium as 0.28 × 105 N/mm2.
Solid Aluminium Shaft lA = 1000 mm
dA = 50 mm
GA = 0.28 × 105 N/mm2
Tabular Steel Shaft
Ls = 100 cm
Ds0 = 50 mm, dsi = ?
Gs = 0.85 × 105 N/mm2
Here, TA = Ts and θA = θs
J A= π (d A)4 = (π/32) × 504 = 6.25 π × 106 / 32 mm4
T/J = G θ/l or θ = T l/JG
θA = (TA lA / ((625 π/32) × 0.28 × 10) ) radian
Since θA = θs and also TA = Ts , lA = ls
dsi = 45. 243 mm