Check whether a given beam section and reinforcement can carry a factored moment and shear. Enter the section dimensions, concrete and steel strengths, top and bottom longitudinal bars, stirrup size and spacing, and the factored demand Mu and Vu, and the calculator works out the flexural capacity φMn (with the ACI 318 21.2.2 variable φ and minimum-steel check) and the shear capacity φVn (concrete plus stirrups, with the code’s spacing limits) — and tells you immediately whether each governs OK or NG.
This is the companion check to the RCC Column & Beam Section Drawing Generator, which lays out and dimensions a beam section but doesn’t check its capacity — use this tool once you have a trial section to confirm it actually works.
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This is a capacity CHECK against demands you supply — it does not perform the structural analysis to get Mu/Vu, and it is not a substitute for a full design check by a licensed engineer.
What the calculator checks
- Flexural capacity. Whitney rectangular stress block analysis of the governing tension steel (top or bottom, whichever you’re checking), the net tensile strain εt, the ACI 318 21.2.2 variable strength-reduction factor φ (0.65–0.90 for beams, with a εt ≥ 0.004 ductility floor), and the ACI 318 9.6.1 minimum steel requirement.
- Shear capacity. Concrete shear capacity Vc, stirrup contribution Vs from your bar size and spacing, the ACI 318 maximum-Vs ceiling, and the code’s stirrup spacing limits.
What to have ready
- Beam width, overall depth and effective depth (or cover and bar size to derive it)
- Concrete strength and steel yield strength
- Longitudinal bar size and count (top and bottom)
- Stirrup bar size, number of legs, and spacing
- Factored moment Mu and factored shear Vu at the section you’re checking
Notes and limitations
This is a single-section capacity check, not a full beam design — it does not check deflection, torsion, development/splice lengths, or a moment envelope along the span. Run it at each critical section (supports and midspan) separately. Final acceptance of the design rests with the responsible engineer.
ACI 318 Beam Flexural & Shear Capacity Reference Table
| Parameter | Value / Formula | ACI 318-19 Section | Notes |
|---|---|---|---|
| Flexure strength reduction factor (φ) | 0.90 | 21.2.1 | Tension-controlled section (εt ≥ 0.005) |
| Shear strength reduction factor (φ) | 0.75 | 21.2.1 | For shear and torsion |
| Concrete shear capacity (Vc) — simplified | 2λ√f’c × b_w × d | 22.5.5.1 | Normal-weight concrete; λ = 1.0 |
| Steel shear capacity (Vs) — vertical stirrups | Av × fy × d / s | 22.5.10.5 | s = stirrup spacing; Av = stirrup area |
| Maximum stirrup spacing (s_max) | min(d/2, 24 in) | 9.7.6.2.2 | When Vs ≤ 4λ√f’c × b_w × d |
| Minimum flexural reinforcement (ρ_min) | max(3√f’c/fy, 200/fy) | 9.6.1.2 | As_min = ρ_min × b_w × d |
| Maximum steel ratio (ρ_max) | ≤ 0.75ρ_b (ASD) or εt ≥ 0.004 (LRFD) | 21.2.2 | Tension-controlled limit for φ = 0.90 |
| Equivalent stress block depth (a) | a = As × fy / (0.85 × f’c × b) | 22.2.2 | Whitney rectangular stress block |
| Nominal flexural capacity (Mn) | As × fy × (d − a/2) | 22.3.2 | Design moment capacity = φMn ≥ Mu |
| Concrete compressive strength (f’c) — typical | 3,000–5,000 psi | — | f’c = 4,000 psi most common for beams |
Source: ACI 318-19 (Building Code Requirements for Structural Concrete) Chapters 9, 21, and 22.
Beam Flexural & Shear Capacity Check (ACI 318) FAQ
How do I calculate the design flexural capacity (φMn) of a rectangular concrete beam?
Using the Whitney rectangular stress block (ACI 318-19 Section 22.2): (1) Compute the depth of the equivalent stress block: a = As × fy / (0.85 × f’c × b), where As is the area of tension steel, fy is the yield strength (psi), f’c is the concrete compressive strength (psi), and b is the beam width (in); (2) Compute nominal moment capacity: Mn = As × fy × (d − a/2), where d is the effective depth (distance from compression face to steel centroid); (3) Apply the strength reduction factor: φMn, where φ = 0.90 for tension-controlled sections (εt ≥ 0.005). The design is adequate when φMn ≥ Mu (factored moment demand per ASCE 7 load combinations).
How is the concrete shear capacity (Vc) calculated per ACI 318-19?
The simplified expression for the concrete shear contribution is: Vc = 2λ√f’c × bw × d (ACI 318-19 Equation 22.5.5.1), where λ = 1.0 for normal-weight concrete, f’c is in psi, bw is the beam web width (in), and d is the effective depth (in). This gives Vc in pounds. The 2019 edition also provides a more detailed Table 22.5.5.1 that accounts for Nᵤ (axial load), Vᵤ, Mᵤ, As, and ρw for a more precise value. The design shear capacity is φVc = 0.75 × Vc. If Vᵤ > φVc, stirrups are required; if Vᵤ > 0.5φVc, minimum stirrups per Section 9.6.3 apply.
What is the maximum stirrup spacing allowed by ACI 318?
Per ACI 318-19 Section 9.7.6.2.2, the maximum stirrup spacing is the lesser of d/2 or 24 inches when the required Vs ≤ 4λ√f’c × bw × d. When Vs exceeds this threshold (indicating high shear demand), the maximum spacing is reduced to d/4 or 12 inches (Section 9.7.6.2.2). Seismic detailing requirements (ACI 318-19 Chapter 18) apply in SDC B–F, imposing additional spacing limits within the plastic hinge region: for special moment frames, the maximum hoop spacing in the confinement zone is the smallest of d/4, 6 times the diameter of the smallest longitudinal bar, or 6 inches (Section 18.4.2.4).
What is the minimum flexural reinforcement ratio for a beam?
ACI 318-19 Section 9.6.1.2 requires the minimum area of flexural tension reinforcement to be: As,min = max(3√f’c/fy, 200/fy) × bw × d. For f’c = 4,000 psi and fy = 60,000 psi, ρ_min = max(3√4000/60000, 200/60000) = max(0.00316, 0.00333) = 0.00333. This minimum ensures the beam has enough steel that the cracking moment does not exceed the flexural capacity of the section — preventing sudden brittle failure at the onset of cracking. The minimum applies to each layer of reinforcement in positive and negative moment regions.
What is the difference between a tension-controlled and a compression-controlled section?
ACI 318-19 Section 21.2.2 classifies sections by the net tensile strain (εt) in the outermost tension steel at nominal strength: tension-controlled sections have εt ≥ 0.005, corresponding to ductile behavior with wide warning before collapse (φ = 0.90 for bending). Compression-controlled sections have εt ≤ ε_y (typically 0.002 for Grade 60 steel), with very little tensile deformation (φ = 0.65 for tied columns). Between εt = 0.002 and 0.005 is the “transition zone” where φ varies linearly between 0.65 and 0.90. Beams should always be designed as tension-controlled sections — the steel should yield before the concrete crushes, ensuring ductile flexural failure mode.