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Diameter Combined Torsion and Bending Equation and Calculator

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Diameter of Solid Shaft subjected to Combined Torsion and Bending Equation and Calculator

Preview: Diameter Solid Shaft with Combined Torsion and Bending Calculator

According to maximum normal stress theory
Eq. 1
D = [ 16 / ( π σ_yd ) { M_b + ( M_b² + M_t² )^(1/2) } ] ^(1/3)

According to maximum shear stress theory
Eq. 2
D = { 16 / ( π τ_yd ) { M_b² + M_t² )^(1/2) } ^(1/3)

According to maximum shear energy theory
Eq. 3
D = { 16 / ( π τ_yd ) { M_b² + 3/4 M_t² )^(1/2) } ^(1/3)

where

D = diameter of shaft, m (in)
M_b = bending moment, Nm (lbf in)
M_t = twisting moment, Nm (lbf in)
τ_yd = shear stress, MPa (psi)
σ_yd = stress (tensile or compressive), MPa (psi)

Related:

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• Shaft Torsional Deflection and Rigidity Formulae and Calculator
• ASME Shaft Design Allowable Stress and Diameter equations and calculators
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• Bolt Preload Torsion Stress Formulas and Calculator per. MIL-HDBH-60
• Torsional Stress Calculator and Equations for Hollow Cylinders

Source:

Machine Design Handbook 2nd Edition, 2001 
Prof. Dr. K. Lingaiah
Former Principal, Professor and Head, Department of Mechanical Engineering
University Visvesvaraya College of Engineering, Bangalore University, Bangalore