Question

A propeller shaft 100 mm in diameter, is 45 m long, transmits 10 MW at 80 rpm. Determine the maximum shearing stress in shaft. Also calculate the stress at 20 mm, 40 mm, 60 mm and 80 mm diameters. Show the stress variation.

Answer 1

d = 100 mm 

L = 45 m 

P = 10 MW = 10 × 10⁶ W 

N = 80RPM 

ι_max = ? 

ι₂₀ = ?, ι₄₀ = ?, ι₆₀ = ?, ι₈₀ = ? 

Using the relation, P = 2π.N.T_max/60 watts 

10 × 10⁶ = 2π.80.T_max/60 

T_max = 1193662.073 N ...(i) 

For solid shaft ι = 16T_max/πd³ 

ι = 16(1193662.073) / [π(100)³] 

ι = 6.079 N/mm² 

This is shear stress at outer surface i.e.; ι₁₀₀ = 6.079 N/mm²  

Now the stress is varies linearly along the diameter of the shaft, the shear stress at inner diameter of the shaft i.e.; 

ι₂₀ = ι₁₀₀ × d₂₀/d₁₀₀ = 6.079 × 20/100 = 1.22 N/mm² 

ι₂₀ = 1.22 N/mm²

ι₄₀ = ι₁₀₀ × d₄₀/d₁₀₀ = 6.079 × 40/100 = 2.44 N/mm² 

ι₄₀ = 2.44 N/mm² 

ι₆₀ = ι₁₀₀ × d₆₀/d₁₀₀ = 6.079 × 60/100 = 3.66 N/mm² 

ι₆₀ = 3.66 N/mm²  

ι₈₀ = ι₁₀₀ × d₈₀/d₁₀₀ = 6.079 × 80/100 = 4.88 N/mm² 

ι₈₀ = 4.88 N/mm²