Size beams confidently using bending moment and stress limits. Compare ASD and LRFD with adjustable safety factors. Export results and reports for every job.
| Case | Moment (kN·m) | Factor | Fy (MPa) | ϕ | Required S (cm³) |
|---|---|---|---|---|---|
| A | 180 | 1.50 | 250 | 0.90 | 1,200.000 |
| B | 260 | 1.40 | 345 | 0.90 | 1,172.303 |
| C | 120 | 1.60 | 275 | 0.90 | 775.758 |
These examples assume LRFD with stress capacity = ϕ·Fy.
Md = Mmax × kF = Fb,allowF = Fy / ΩF = ϕ × FyS = Md / FSadj = S / U, where U is the utilization limit.
Notes: Units are internally converted to N·mm and N/mm², giving mm³.
Convert to cm³ by dividing by 1000, and to in³ by dividing by 16387.064.
Section modulus (S) links beam geometry to bending strength. For a given bending moment, a larger S reduces extreme‑fiber stress. In practice, designers select shapes so the computed stress stays below the chosen capacity model, then verify deflection, stability, and connection detailing.
Jobsite moments may be reported in kN·m, kip·ft, or N·mm depending on drawings and software. This calculator converts all inputs to N·mm internally so the stress units N/mm² remain consistent. Keeping one coherent unit chain prevents order‑of‑magnitude errors during rapid checks.
The moment factor (k) lets you apply load factors or construction stage amplification. For example, temporary erection loads, eccentric lifting points, or equipment surcharges can raise demand above a simple service case. When in doubt, use the governing combination from your load model and document the factor used.
Some projects specify an explicit allowable bending stress based on material, code limits, or client criteria. With this method, required S is computed from the factored moment divided by the allowable stress. It is straightforward for quick screening, but still requires confirming the chosen allowable reflects buckling and lateral restraint conditions.
Allowable stress design often derives bending capacity by dividing yield stress by a safety factor Ω. Typical values vary by standard and limit state, so this tool keeps Ω editable. After computing S, compare to available shapes, then verify flange local buckling, web slenderness, and lateral‑torsional buckling separately.
Load and resistance factor design uses a resistance factor ϕ applied to yield stress for a simplified bending capacity model. Many workflows pair factored loads with ϕ‑reduced strengths to control reliability. Use this calculator to estimate the minimum S, then confirm the governing code limit state and detailing requirements.
Field conditions are rarely perfect: tolerances, residual stresses, corrosion allowance, and uncertain load paths can increase risk. A utilization limit (for example 0.90) intentionally sizes the beam larger by dividing S by U. This provides reserve without changing the underlying capacity model.
If you enter a provided section modulus from a selected shape, the calculator reports utilization and PASS/FAIL. A PASS indicates the provided S meets the adjusted requirement under the chosen assumptions. Always follow up with checks for deflection, shear, bearing, stability, and connection capacity before approval.
Use the governing maximum bending moment for the critical load case or combination, including construction stages. If multiple cases exist, run the calculator for each and design for the largest adjusted requirement.
No. It estimates required section modulus from bending demand and a chosen stress capacity model. You must still check lateral‑torsional buckling, local buckling, shear, deflection, bearing, and connection requirements.
Set it to 1.0 for a direct service check, or use the factor from your load combination rules or construction method statement. Document the source so reviewers can reproduce the calculation.
Use it when your project specifies an allowable bending stress directly, such as for temporary works or proprietary criteria. Ensure the allowable stress already accounts for relevant stability limits.
Utilization intentionally adds margin by sizing up: Sadj = S/U. For example, U = 0.90 increases the requirement by about 11%. It helps accommodate uncertainty and variability.
PASS means the provided section modulus is at least the adjusted required value under your chosen inputs. FAIL means it is smaller. It does not confirm other limit states or serviceability checks.
Compare the adjusted requirement to the elastic section modulus listed for the bending axis you are designing about (Sx or Sy). Confirm the table’s units match the calculator output you select.
Accurate section modulus checks help prevent costly failures today.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.