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Discover the angle of twist:
Discover the diameter of the shaft needed to transmit 60 kW at 150 r.p.m., if the maximum torque is possible to exceed the mean torque by 25% for a maximum permissible shear stress of 60 N/mm2. Discover also the angle of twist for a length of 2.5 metres.
Take G = 8 × 104 N/mm2.
Solution
Here, P = 60 kW = 60 × 103 W
N = 150 rpm, Tmax = 1.25 Tmean, τm = 60 N/mm2
l = 2.5 m = 2.5 × 103 mm2
We know,
P = 2πNT /60
60 ×103 = (2π ×150 × T)/60
T = 3819.7 N m = 3.82 ×106 N mm, T is the mean torque
Tmax = 1.25 Tmean = 1.25 × 3.8197 × 106 = 4.746 ×106 N mm
T max = (π/16 ) τm d 3
4.7746 × 106 = ( π /16 )× 60 × d 3
d 3 = 4.7746 × 106× 16 / π× 60
∴ d = 74 mm
T / J = Gθ/ l
4.7746 ×106 / (π/32) × (74)4 = (8 ×104/2500 )× θ
θ = 0.0507 radians
θ = 2° 54′
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