Determine maximum shearing stress in shaft:
A propeller shaft 100 mm in the diameter, is 45 m long, transmits 10 MW at 80 rotation per minute. Determine maximum shearing stress in shaft. Also compute the stress at 20 mm, 40 mm, 60 mm and 80 mm diameters. Demonstrate the stress variation.
Sol.:
d = 100mm
L = 45m
P = 10MW = 10 × 10^{6} W
N = 80RPM
Τ_{max} = ?
τ_{20} = ?, τ _{40} = ?, τ _{60} = ?, τ _{80} = ?
By using the relation
P = 2 .N.T_{max}/60 watts
10 × 10^{6} = 2 .80.T_{max}/60
T_{max} = 1193662.073 N ...(i)
For solid shaft τ = 16T_{max}/ d^{3}
τ = 16(1193662.073)/[ (100)^{3}]
τ= 6.079 N/mm^{2}
This is shear stress at outer surface that is; τ_{10}_{0} = 6.079 N/mm^{2} .......ANS
Now stress is varies linearly along diameter of shaft, the shear stress at inner diameter of
the shaft that is; τ_{20} = τ_{20} × d_{20}/d_{100} = 6.079 × 20/100 = 1.22 N/mm^{2}
τ_{100 }= 1.22 N/mm^{2} ......ANS
τ_{40} = τ100 × d_{40}/d_{100} = 6.079 × 40/100 = 2.44 N/mm^{2}
τ_{40} = 2.44 N/mm2 .......ANS
τ_{40} = τ100 × d_{60}/d_{100} = 6.079 × 60/100 = 3.66 N/mm^{2}
τ_{40} = 3.66 N/mm2 .......ANS
τ_{40}= τ100 × d_{80}/d_{100} = 6.079 × 80/100 = 4.88 N/mm^{2}
τ_{40}= 4.88 N/mm^{2} .......ANS