How this calculator works
Circular-section stress equations provide a preliminary diameter under prescribed loads and allowables. Combined modes evaluate maximum shear and maximum principal tensile stress at the outer fibre, including an optional tensile axial force. The larger diameter governs. Supplied factors scale bending and torsion in the fluctuating-load mode; they do not constitute a fatigue-life calculation. Rigidity mode limits elastic twist. Bearings, keyways, shoulders, buckling, critical speed and fatigue detail remain separate design tasks.
Formula
sigma = 4F/[pi d²(1-k²)] + 32 Km M/[pi d³(1-k⁴)]; tau = 16 Kt T/[pi d³(1-k⁴)]. tau_max=sqrt((sigma/2)²+tau²); sigma1=sigma/2+tau_max. Twist=32TL/[pi G d⁴(1-k⁴)]. P=2 pi RPM T/60.
Worked example
A solid shaft carrying 314.159265 N m with allowable shear stress 1.6 MPa requires 100 mm diameter in pure torsion. Pure bending of the same moment with allowable normal stress 3.2 MPa also requires 100 mm.
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Frequently asked questions
What does a hollow ratio of 0.5 mean?
The inside diameter is half the outside diameter. Zero selects a solid shaft.
Are the fluctuating factors a fatigue check?
No. They are user-supplied load multipliers. A fatigue analysis needs alternating and mean stresses, material data and stress concentrations.
Which allowable stress should I use?
Use a value justified for the material, loading, temperature and design standard. The defaults are illustrative inputs.