RC Beam Flexure Check Calculator
Check the bending (flexural) moment capacity of a singly-reinforced rectangular concrete beam. Enter the tensile steel area, section size and material strengths and the tool returns the equivalent stress-block depth, the nominal moment Mn and the design capacity φMn using the AS 3600 rectangular stress block. Add your applied design moment M* to get the flexural utilisation and a pass/over check.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the tensile steel area As (mm²), the beam width b (mm) and the effective depth d (mm) — the distance from the extreme compression fibre to the centroid of the tension steel.
- Optionally override the steel yield fy (default 500 MPa), the concrete strength f'c (default 32 MPa) and the capacity factor φ (default 0.85). Leave them blank to use the defaults.
- Optionally enter your applied design moment M* (kNm) to see the utilisation as a percentage of φMn, with an OK / OVER-capacity flag.
How it works
The tension steel force As·fy is balanced by a uniform concrete compression stress of 0.85·f'c acting over a rectangular block of depth a, so a = As·fy / (0.85·f'c·b). The nominal moment is that force times the lever arm to the centre of the block: Mn = As·fy·(d − a/2). Dividing by 1e6 converts N·mm to kNm. The design capacity is φMn with φ ≈ 0.85 for a ductile, tension-controlled section. When you supply M*, utilisation = M* / φMn × 100.
Worked example
Worked example. As = 1500 mm², b = 300 mm, d = 450 mm, fy = 500 MPa, f'c = 32 MPa. a = 1500×500 / (0.85×32×300) = 91.912 mm. Mn = 1500×500×(450 − 45.956) / 1e6 = 303.033 kNm. φMn = 0.85 × 303.033 = 257.578 kNm. With M* = 200 kNm the utilisation is 200 / 257.578 × 100 = 77.6% (OK).
Common mistakes
- Using the overall beam depth instead of the effective depth d. Use the distance from the compression face to the centroid of the tension bars, not the full section depth.
- Assuming the result is valid for an over-reinforced or doubly-reinforced section. This tool assumes the steel yields and ignores compression steel; a high-As section needs a ductility (kuo) check and a reduced φ.
- Forgetting the minimum-steel and serviceability checks. A section can pass strength yet fail minimum reinforcement, deflection or crack-width limits.
Frequently asked questions
Why is φ taken as 0.85?
AS 3600 assigns φ ≈ 0.85 to bending in a tension-controlled (ductile) section where the steel yields well before the concrete crushes. Sections that are over-reinforced or in transition use a lower φ, so confirm the neutral-axis parameter kuo before relying on 0.85.
Does this handle T-beams or compression steel?
No. It models a singly-reinforced rectangular section only. Flanged (T/L) beams, compression reinforcement and axial load change the internal force balance and need a fuller analysis.
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