Answer :
The formula to calculate the radius of a solid circular shaft with a twist angle can be obtained using the following steps:The maximum shear stress τmax = T .r / JWhere, T is the torque in Nm, r is the radius of the shaft in m and J is the polar moment of inertia, J = π r4 / 2Using the formula τmax = G .θ .r / L,
the polar moment of inertia can be obtained as J = π r4 / 2 = T . L / (G . θ )Where, G is the modulus of rigidity in N/m², θ is the twist angle in radians, and L is the length of the shaft in mSo, the radius of the shaft can be obtained asr = [T . L / (G . θ π / 2)]^(1/4)Given, torsional moment, T = 724.5 NmLength, L = 4.7 mTwist angle, θ = 21.5°
= 21.5° x π / 180° = 0.375 radModulus of rigidity, G = 98.5 GPa = 98.5 x 10^9 N/m²Substituting these values in the above equation,r = [724.5 x 4.7 / (98.5 x 10^9 x 0.375 x π / 2)]^(1/4)≈ 1.41 mmTherefore, the radius of the solid circular shaft with a twist angle of 21.5 degrees between the two ends, length 4.7 m and applied torsional moment of 724.5 Nm is approximately 1.41 mm.
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