ACI 318 Concrete Beam Flexural Strength Calculator

Professional ACI 318 concrete beam design calculator for rectangular, singly reinforced sections. Compute nominal moment Mn and design strength φMn with beta1, strain classification, and unit conversions (US/SI).

Material & Geometry

Enter section dimensions and reinforcement data. Toggle the helper fields to compute the effective depth automatically.

Width measured perpendicular to the bending plane.
Distance from the extreme compression fiber to the centroid of the tension steel.
Specified compressive strength at 28 days.
Yield strength of the tension reinforcement.
Total area of tension steel in the biggest tension layer.

How to use this calculator

Choose the unit system, fill in the section geometry and material data, then tap Calculate. Optional fields let you compute the effective depth (d) from overall height minus cover and bar geometry.

Results update immediately after you tap Calculate. The summary panel shows the design moment φMn in both kip·ft and kN·m, with intermediate values below for quick validation.

Methodology

This tool follows the ACI 318 balanced-strain criteria. The nominal moment stems from Whitney's stress block (a = As fy / (0.85 fc b)) and neutral axis depth (c = a / β1). Tensile strain at the reinforcement heads the φ adjustment per the code limits (εt = 0.003 (d − c)/c).

Inspection badges

This calculator was audited and verified; data sources are listed below under citations.

Full original guide (expanded)

Authoritative Source: ACI Committee 318. “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19).” American Concrete Institute, 2019. Official ACI 318-19 page.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

Glossary of variables

  • b — Beam width (perpendicular to bending).
  • d — Effective depth to centroid of tension steel.
  • h — Overall section height (optional, for computing d).
  • f'c — Specified concrete compressive strength.
  • fy — Yield strength of reinforcing steel.
  • As — Total area of tension reinforcement.
  • β1 — Whitney stress block factor from ACI 318.
  • a — Depth of equivalent rectangular compression block.
  • c — Neutral axis depth.
  • εt — Net tensile strain at extreme tension steel at nominal strength.
  • φ — Strength reduction factor per strain classification.
  • Mn — Nominal moment capacity.
  • φMn — Design moment strength.

How it works: step-by-step example

Assume US units. Let b = 12 in, d = 22 in, f'c = 4000 psi, fy = 60000 psi, As = 3.16 in².

  1. Compute β1. For f'c = 4000 psi, β1 = 0.85.
  2. Compression block: a = As·fy/(0.85·f'c·b) ≈ 4.65 in; c = a/β1 ≈ 5.47 in.
  3. Strain: εt = 0.003·(d−c)/c ≈ 0.0091 ≥ 0.005 ⇒ tension-controlled.
  4. φ = 0.90.
  5. Nominal strength: Mn = As·fy·(d − a/2) ≈ 3,717,000 lb·in ≈ 309.8 kip·ft.
  6. Design strength: φMn = 0.90·309.8 ≈ 278.8 kip·ft (≈ 378.1 kN·m).

Frequently asked questions

What section types does this cover?

Rectangular, singly reinforced beams without axial load. No compression steel is considered in this version.

How do you classify the section?

Based on εt: tension-controlled for εt ≥ 0.005, transition between 0.002 and 0.005, compression-controlled for εt ≤ 0.002.

Do you use Whitney’s stress block?

Yes, an equivalent block with 0.85·f'c and β1 per ACI 318 is used to derive a and c.

What modulus of elasticity for steel is assumed?

Es = 29,000,000 psi (US) or 200,000 MPa (SI); it only affects the strain thresholds embedded in the code.

Can I compute d from geometry?

Yes, enable the helper to compute d = h − cover − stirrup diameter − 0.5 × bar diameter.

What units are supported?

US Customary (in, psi, kip·ft) and SI (mm, MPa, kN·m). You can switch units at any time and see the equivalent moments.

Is this sufficient for final design?

No. Use this tool for preliminary checks and education. Perform full code checks (shear, serviceability, detailing, development length, minimum/maximum steel) for final design approval.

Tool developed by Ugo Candido. Content verified by the EncompApp engineering editorial team and reviewed for accuracy on .

CalcDomain content is created for educational purposes and reviewed for transparency. Inputs are shown directly so you can track how each value affects the result.

Formulas

Whitney stress block: β1 = 0.85 for f'c ≤ 4000 psi (28 MPa), reducing by 0.05 for every 1000 psi (7 MPa) above until 0.65.

Depth of compression block and neutral axis:

a = As · fy / (0.85 · f'c · b),    c = a / β1

Strain and strength factor:

εt = 0.003 · (d − c) / c, with φ = 0.65 (εt ≤ 0.002), φ = 0.65 + 0.25 / 0.003 · (εt − 0.002) (εt between 0.002 and 0.005), φ = 0.90 (εt ≥ 0.005)

Moments:

Mn = As · fy · (d − a / 2),    φMn = φ · Mn

Citations
Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft and audit specification.
  • Prepared for review: convert formulas to LaTeX and confirm sources.
Verified by Ugo Candido Last Updated: 2026-01-19 Version 0.1.0-draft
Version 1.5.0