ACI 318 Concrete Beam Flexural Strength Calculator
This professional-grade calculator computes the flexural capacity of rectangular, singly reinforced concrete beams per ACI 318. It is designed for structural engineers and advanced students who need fast, accurate estimates of nominal moment Mn and design strength φMn, alongside strain classification and key intermediate values.
Calculator
Enable to compute d = h − cover − stirrup dia − 0.5 × bar dia
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Results
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Moments shown in kip·ft and kN·m. Dimensions in selected units.
Data Source and Methodology
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.
The Formula Explained
Whitney factor:
β_1 = 0.85 for f'_c ≤ 4000 psi (28 MPa), and decreases by 0.05 per 1000 psi (7 MPa) above that to a minimum of 0.65.
Compression block depth and neutral axis:
$$ a = \frac{A_s f_y}{0.85\, f'_c\, b}, \qquad c = \frac{a}{\beta_1} $$
Tensile strain and strength reduction factor:
$$ \varepsilon_t = \varepsilon_{cu} \frac{d - c}{c}, \quad \varepsilon_{cu} = 0.003 $$
$$ \phi = \begin{cases} 0.65, & \varepsilon_t \le 0.002 \\ 0.65 + \dfrac{0.25}{0.003}(\varepsilon_t - 0.002), & 0.002 < \varepsilon_t < 0.005 \\ 0.90, & \varepsilon_t \ge 0.005 \end{cases} $$
Nominal and design flexural strength:
$$ M_n = A_s f_y \left(d - \frac{a}{2}\right), \qquad \phi M_n = \phi\, M_n $$
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: A 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.
- Compute β1. For f'c = 4000 psi, β1 = 0.85.
- Compression block: a = As·fy/(0.85·f'c·b) = 3.16·60000 / (0.85·4000·12) ≈ 4.65 in. Then c = a/β1 ≈ 5.47 in.
- Strain: εt = 0.003·(d−c)/c = 0.003·(22−5.47)/5.47 ≈ 0.0091 ≥ 0.005 ⇒ tension-controlled.
- φ = 0.90.
- Nominal strength: Mn = As·fy·(d − a/2) = 3.16·60000·(22 − 2.325) ≈ 3,717,000 lb·in ≈ 309.8 kip·ft.
- Design strength: φMn = 0.90·309.8 ≈ 278.8 kip·ft (≈ 378.1 kN·m).
Frequently Asked Questions (FAQ)
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 (tension/transition/compression-controlled)?
Based on εt at nominal strength: εt ≥ 0.005 (tension-controlled), εt ≤ 0.002 (compression-controlled), otherwise transition (interpolated φ).
Do you use Whitney’s stress block?
Yes. Equivalent stress block with 0.85·f'c and β1 per ACI 318 is used to compute a and c.
What modulus of elasticity for steel is assumed?
Es = 29,000,000 psi (US) or 200,000 MPa (SI). It is only used implicitly for the εt boundaries defined by the code.
Can I compute the effective depth 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 any time; values convert automatically.
Is this sufficient for final design approval?
No. Use this tool for preliminary checks and education. Perform full code checks (shear, serviceability, detailing, development length, minimum/maximum steel) for final design.