Bending Stress Calculator
Calculate bending stress or applied moment using the flexure formula for common cross-sections, with a utilization-ratio check.
Disclaimer
Estimate only — verify with a licensed engineer or your local building code before construction.
Bending Stress Calculator: Flexure Formula for Beams and Sections
This calculator applies the classic flexure formula, sigma = M×c/I, to find the maximum bending stress in a beam or section from an applied bending moment, or to back-solve the moment a section can carry at a given stress. It covers square, rectangular, rectangular tube, solid circle, hollow circle, and custom cross-sections. It is a mechanics-of-materials estimate, not a substitute for a licensed structural engineer's design check — always verify against your local building code before construction.
How to use the bending stress calculator
- Choose whether to solve for stress (from a known moment) or for moment (from a target stress), then pick the cross-section shape — square, rectangle, rectangular tube, solid circle, hollow circle, or custom.
- Enter the section's dimensions (or, for a custom section, its moment of inertia I and distance to the extreme fiber c directly).
- Enter the applied moment (or target stress), plus an optional allowable/yield stress to see the utilization ratio and a pass/fail check against that limit.
The bending stress formula
Maximum bending stress is sigma = M×c/I, equivalently sigma = M/S where S = I/c is the section modulus. M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the section's moment of inertia. For a rectangle, I = b×d³/12 and c = d/2; for a solid circle, I = π×r⁴/4 and c = r.
Example: a 200 mm × 300 mm rectangular section carrying a 10 kN·m moment has I = 0.2×0.3³/12 = 0.00045 m⁴ and c = 0.15 m, so sigma = 10,000×0.15/0.00045 ≈ 3.33 MPa. Compare that result against the material's yield or allowable stress (entered as the allowable stress input) to check whether the section is adequate — the calculator flags pass/fail once you enter that limit.
Tips
This is the maximum stress at the outer fiber only — it does not check shear, deflection, buckling, or combined loading, all of which a full structural design also requires.
For a custom or irregular shape (I-beam, tee, channel, angle), look up I and c from a section property table or manufacturer's catalog and enter them directly using the custom section option.
In Gibraltar, a licensed structural engineer typically charges around £170-£680 to review and sign off on a bending-stress check for a beam or structural member, depending on the complexity of the calculation.
