- The maximum shearing stress in hollow shaft is 66.125 MPa.
- The magnitude of angle of twist is 0.0279 rad.
- The power generated by the shaft is 157 kW.
<h3>What is power ?</h3>
Power in a rotating body like shaft is the product of Torque and the angular speed of that shaft.
P = Tω
The Torque is related to the shearing stress is
T = π/16 xτ(Do³ -Di³)
* Given is the Torque T= 7.5 kN.m, the inner diameter Di = 0.075m, outer diameter Do= 0.1m
Then, the maximum shearing stress will be
7.5 x 10³ = π/16 xτ x (0.1³ - 0.075³)
τ = 66.125 MPa
Thus, the shearing stress is 66.125 MPa.
* From the Torque equation
T/J = Gθ/l
Where, J = π/32 (Do⁴ -Di⁴) = 0.00000671 m⁴
l = length of shaft = 2m, modulus of rigidity G = 80GPa = 80x 10⁹ Pa.
Substitute the values, we get the angle of twist
7.5 x10³ /0.00000671 = 80x 10⁹xθ/2
θ = 0.0279 rad.
Thus, the angle of twist is0.0279 rad.
* Power generated by the shaft is
P = 2πNT/60
where N = revolution/ minute = 200
Put the values, we get
P = 2π x 200 x 7500/60
P = 157 kW.
Thus, the power generated is 157 kW.
Learn more about power.
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