Calculate maximum bending stress using the flexure formula σ = My/I. Verify structural members against material yield strength.
Enter the maximum bending moment acting on the section and the distance from the neutral axis to the extreme fiber (y).
Input the Moment of Inertia (I). The tool uses the flexure formula: σ = My/I to calculate the maximum normal stress in the member.
Compare the resulting stress to the yield strength of your material (e.g., 250 MPa for A36 steel) and apply a safety factor (typically 1.5 to 2.0).
Principal stresses σ₁ and σ₂ are the maximum and minimum normal stresses, acting on planes with no shear. The calculator uses Mohr's circle: σ₁,₂ = (σx+σy)/2 ± √(((σx−σy)/2)² + τxy²). For σx = 120, σy = 40, τxy = 30 MPa, this gives σ₁ = 130 MPa and σ₂ = 30 MPa, oriented at θp ≈ 18.4°.
It equals the radius of Mohr's circle, τmax = √(((σx−σy)/2)² + τxy²), and acts 45° from the principal planes. For the same 120/40/30 MPa state, τmax = 50 MPa. Maximum-shear (Tresca) checks compare this directly against half the material's yield strength.
Von Mises σvm = √(σx² − σxσy + σy² + 3τxy²) collapses a multiaxial state into one equivalent value to compare against yield. The 120/40/30 MPa state gives σvm ≈ 117.9 MPa, so against A36 steel (σy = 250 MPa) the safety factor is 250/117.9 ≈ 2.1 — comfortably above the usual 1.5–2.0 target.
Yes. Under pure uniaxial tension the von Mises stress equals the applied stress (σvm = σx), so a 200 MPa pull reads 200 MPa. Under pure shear it becomes σvm = √3·τ, so 100 MPa of shear yields about 173 MPa — which is why a shear-dominated member yields sooner than its raw shear number suggests.