Bending Stress Calculator computes linear-elastic bending stress from bending moment and cross-section geometry. Use it in “Custom (I & c)” mode or “Rectangle (b × h)” mode.
About bending stress. In the elastic range, normal stress varies linearly across the depth: maximum compression at one extreme fiber and maximum tension at the other. The neutral axis passes through zero stress. Peak stress at the extreme fiber is obtained by the flexure formula.
About units. Typical inputs are M (kN·m or ft·lbf), I (cm⁴ or in⁴), and dimensions (cm or in). Results are shown in engineering stress units (MPa and psi).
About section modes. Choose Custom (I & c) when I and c are known from section tables or analysis. Choose Rectangle (b × h) to let the tool determine I = b·h³/12 and c = h/2 for a solid rectangular section; irrelevant inputs are greyed out.
Conversion / Calculation. Bending stress is evaluated by applying the flexure formula σ = M·c / I. For rectangles, the method first determines the geometric terms I = b·h³/12 and c = h/2 from the entered dimensions; for custom sections, it uses the provided I and c directly in the same stress relation.
Formulas.
- σ = M·c / I (bending stress at the extreme fiber)
- I = b·h³ / 12 (second moment of area for a solid rectangle)
- c = h / 2 (distance from neutral axis to extreme fiber for a solid rectangle)
- S = I / c (section modulus; alternative form σ = M / S)
Examples.
- Custom. M = 50 kN·m, I = 8,000 cm⁴, c = 15 cm → σ = 93.75 MPa (≈ 13,600 psi).
- Rectangle. b = 30 cm, h = 60 cm, M = 50 kN·m → I = 0.0054 m⁴, c = 0.30 m → σ = 2.78 MPa (≈ 403 psi).
- Custom. M = 40,000 ft·lbf, I = 250 in⁴, c = 4 in → σ ≈ 52.9 MPa (≈ 7,670 psi).
Corresponding tools. For geometric properties, see the Structural Steel Section Properties Calculator. For plate self-weight when checking load effects, use the Plate Weight Calculator. For broader beam checks (deflection/shear), consult your code-based beam calculators or section tables.
