Compute the ratio of the torque, Mechanical Engineering

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Compute the ratio of the torque:

Compute the ratio of the torque transmitted by a hollow & a solid shaft of the similar material, length & weight.

Solution

d_i = internal diameter of hollow shaft

d₀ = external diameter of hollow shaft

d = diameter of solid shaft

Similar material means modulus of rigidity and density is similar. The weight being equal means the cross-sectional areas of solid & hollow shafts are similar:

i.e.

1244_Compute the ratio of the torque.png

where

∴ n = d_i / d_o

d = do

550_Compute the ratio of the torque1.png

τs = 16Ts / π d ³ = 16Ts / π d ³(1 - n²) ^(3/2)

2362_Compute the ratio of the torque2.png

For same material τ_s = τ_h

∴ Ts /(1 - n² ) ^(3/2) =Th/(1 - n⁴)²

288_Compute the ratio of the torque3.png

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