Find the inner diameter of the tubular steel shaft, Mechanical Engineering

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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.

Solution

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          

110_Find the inner diameter of the tubular steel shaft.png

We know,

T/J  = G θ/l or θ = T l/JG

Therefore,

θA  = (TA lA   /  ((625 π/32) × 0.28 × 10) ) radian

1423_Find the inner diameter of the tubular steel shaft1.png

 

Since θA = θs and also TA  = Ts , lA  = ls

1200_Find the inner diameter of the tubular steel shaft2.png

    dsi  = 45. 243 mm


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