How to use this calculator
Choose the cross-section and the point (top, bottom or side), then enter the internal forces and moments at that section from your free-body diagram. Add the yield strength for a factor of safety.
Formulas
Normal stressσ = N/A − Mzy/Iz + Myz/Iy
Shear stressτ = Tc/J + VQ/(It)
Principalσ1,2 = σ/2 ± √((σ/2)² + τ²)
von Misesσ′ = √(σ² + 3τ²)
Worked example
50 mm solid shaft with 20 kN tension, 1.2 kN·m bending and 1.5 kN·m torque, top point (the default)
- A = 1963 mm², I = 306 800 mm⁴, J = 613 600 mm⁴.
- σ = 20 000/1963 − 1.2×10⁶(25)/306 800 = 10.19 − 97.78 = −87.6 MPa; τ = 1.5×10⁶(25)/613 600 = 61.1 MPa.
- σ1,2 = 31.4 and −119.0 MPa; von Mises 137.4 MPa.
Frequently asked questions
Where is the critical point?
Usually on the outer surface where bending stress is largest, but check the neutral axis too when transverse shear is large.
Which failure theory should I use?
von Mises (distortion energy) for ductile metals is the most accurate; Tresca (maximum shear) is slightly more conservative.