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Torsional rigidity calculations for hollow and stepped shafts.
[Given Inputs] - Torque (T) = 500 Nm - Bending Moment (M) = 350 Nm - Allowable Shear Stress (τ_allow) = 50 MPa [Step 1: Calculate Equivalent Torque] T_e = √(M² + T²) T_e = √(350² + 500²) = 610.33 Nm [Step 2: Apply Torsion Formula for Diameter (d)] d = [ (16 * T_e) / (π * τ_allow) ]^(1/3) d = [ (16 * 610.33) / (π * 50 * 10^6) ]^(1/3) d ≈ 0.0396 meters or 39.6 mm [Conclusion] Specify a standard stock shaft diameter of 40 mm to ensure structural safety.
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