About this tool
The Beam Bending Stress Calculator is a free, in-browser tool that applies the flexure formula σ = M·c/I to find the maximum bending stress at the extreme fibre of a beam, and optionally the maximum transverse shear stress. Enter the bending moment M, the area moment of inertia I, and c, the distance from the neutral axis to the outermost fibre. It also reports the section modulus S = I/c, the property engineers use to size a beam directly against an allowable stress. All arithmetic runs locally in your browser.
Bending stress is σ = M·c/I, and equivalently σ = M/S. For transverse shear, enter the shear force V and cross-sectional area A and pick the section shape: the peak shear stress is τ = k·V/A, where the factor k is 1.5 for a solid rectangle, 4/3 for a solid circle, 2.0 for a thin-walled tube, or 1.0 for the simple average V/A. This form of the general τ = VQ/(Ib) relation captures the peak shear at the neutral axis for common shapes. Choose SI (N·m, mm⁴, mm, N, mm²) with results in MPa, or imperial (lbf·in, in⁴, in, lbf, in²) with results in psi.
As a worked example, a beam carrying M = 10,000 N·m with I = 10,000,000 mm⁴ and c = 100 mm has σ = (10,000 × 1000 × 100) / 10,000,000 = 100 MPa and a section modulus of 100,000 mm³. If it also carries V = 20,000 N over a rectangular area of 5,000 mm², the peak shear is 1.5 × 20,000 / 5,000 = 6 MPa. These are elastic stresses; compare them to the material's yield strength with an appropriate factor of safety.