ACI 318 Concrete Beam Shear Strength Calculator

Professional concrete shear design calculator based on ACI 318. Compute nominal and design shear strength (Vc, Vs, φVn) for reinforced concrete beams, verify Vu ≤ φVn, and optimize shear reinforcement.

Full original guide (expanded)

ACI 318 Concrete Beam Shear Strength Calculator

Compute Vc, Vs, Vn, and φVn per ACI 318 and verify Vu ≤ φVn in US or SI units.

Calculator

Units
Shear reinforcement (stirrups)

Results

Outputs shown in kips (US) or kN (SI).

Concrete shear Vc
Stirrup shear Vs
Nominal shear Vn = Vc + Vs
Design shear φVn
Demand/capacity Vu / (φVn)
Vu: —
Status:

Note: Detailing limits (e.g., minimum shear reinforcement, maximum spacing, and special members) are not checked by this tool and must be verified per ACI 318.

Data Source and Methodology

Authoritative Source: ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary,” 2019. Direct link: ACI 318-19 Product Page.

All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

Concrete contribution (US customary):

$$V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}$$

Concrete contribution (SI):

$$V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}$$

Shear reinforcement contribution (vertical stirrups):

$$V_s = A_v\,\frac{f_{yv}\,d}{s}$$

Nominal and design strength:

$$V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)$$

Design check:

$$\phi V_n \ge V_u$$

Glossary of Variables

  • b_w: Beam web width (in or mm).
  • d: Effective depth to centroid of tensile reinforcement (in or mm).
  • f'c: Specified compressive strength of concrete (psi or MPa).
  • λ: Lightweight concrete modification factor (dimensionless; 1.0 for normalweight).
  • V_u: Factored design shear at the section (kips or kN).
  • A_v: Total stirrup area within spacing s that crosses a potential shear crack (in² or mm²).
  • f_yv: Yield strength of shear reinforcement (psi or MPa).
  • s: Longitudinal spacing of stirrups (in or mm).
  • V_c: Concrete contribution to shear strength (kips or kN after unit conversion).
  • V_s: Shear reinforcement contribution (kips or kN after unit conversion).
  • V_n: Nominal shear strength (kips or kN).
  • φV_n: Design shear strength (kips or kN).
  • φ: Strength reduction factor (dimensionless).

How It Works: A Step-by-Step Example

Scenario: US units, normalweight concrete, stirrups provided.

  • b_w = 12 in, d = 22 in
  • f'c = 4,000 psi, λ = 1.0
  • V_u = 85 kips
  • A_v = 0.31 in² (two-legged #5 stirrup), s = 8 in, f_yv = 60,000 psi
  • φ = 0.75

Compute:

V_c = 2 × 1.0 × √4000 × 12 × 22 = 2 × 63.25 × 264 ≈ 33,364 lb ≈ 33.36 kips

V_s = (0.31 × 60,000 × 22 / 8) = 51,150 lb ≈ 51.15 kips

V_n = V_c + V_s ≈ 33.36 + 51.15 = 84.51 kips

φV_n = 0.75 × 84.51 ≈ 63.38 kips

Check: φV_n (63.38) < V_u (85) → NG (increase stirrups or adjust design)

By decreasing s (closer spacing) or increasing A_v (larger bar/legs), Vs increases and the design may pass.

Frequently Asked Questions (FAQ)

Does this calculator automatically enforce all ACI 318 detailing provisions?

No. It focuses on strength equations (Vc, Vs, Vn, φVn) and the Vu ≤ φVn check. Verify minimum shear reinforcement, maximum spacing, member geometry limits, and any special provisions separately.

What λ value should I use?

Use λ = 1.0 for normalweight concrete. For lightweight concrete, use the value specified by ACI 318 per concrete type.

What φ factor should I select?

For shear in nonprestressed members, φ is commonly 0.75. Confirm with the latest ACI edition and the specific member classification.

Can I enter Av as “per leg” area?

Enter the total area within spacing s of all vertical legs crossing a potential shear crack. If your stirrup has multiple legs, multiply the area per leg by the number of legs.

Are deep beams or transfer girders covered?

No. Those members are governed by special provisions and strut-and-tie methods not covered by these equations.

What units are used in the results?

Results are shown in kips for US and kN for SI. A secondary line shows the alternate unit for quick reference.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}\]
V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}
Formula (extracted LaTeX)
\[V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}\]
V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}
Formula (extracted LaTeX)
\[V_s = A_v\,\frac{f_{yv}\,d}{s}\]
V_s = A_v\,\frac{f_{yv}\,d}{s}
Formula (extracted LaTeX)
\[V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)\]
V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)
Formula (extracted LaTeX)
\[\phi V_n \ge V_u\]
\phi V_n \ge V_u
Formula (extracted text)
Concrete contribution (US customary): $V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}$ Concrete contribution (SI): $V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}$ Shear reinforcement contribution (vertical stirrups): $V_s = A_v\,\frac{f_{yv}\,d}{s}$ Nominal and design strength: $V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)$ Design check: $\phi V_n \ge V_u$
Formula (extracted text)
V_c = 2 × 1.0 × √4000 × 12 × 22 = 2 × 63.25 × 264 ≈ 33,364 lb ≈ 33.36 kips V_s = (0.31 × 60,000 × 22 / 8) = 51,150 lb ≈ 51.15 kips V_n = V_c + V_s ≈ 33.36 + 51.15 = 84.51 kips φV_n = 0.75 × 84.51 ≈ 63.38 kips Check: φV_n (63.38) < V_u (85) → NG (increase stirrups or adjust design)
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

ACI 318 Concrete Beam Shear Strength Calculator

Compute Vc, Vs, Vn, and φVn per ACI 318 and verify Vu ≤ φVn in US or SI units.

Calculator

Units
Shear reinforcement (stirrups)

Results

Outputs shown in kips (US) or kN (SI).

Concrete shear Vc
Stirrup shear Vs
Nominal shear Vn = Vc + Vs
Design shear φVn
Demand/capacity Vu / (φVn)
Vu: —
Status:

Note: Detailing limits (e.g., minimum shear reinforcement, maximum spacing, and special members) are not checked by this tool and must be verified per ACI 318.

Data Source and Methodology

Authoritative Source: ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary,” 2019. Direct link: ACI 318-19 Product Page.

All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

Concrete contribution (US customary):

$$V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}$$

Concrete contribution (SI):

$$V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}$$

Shear reinforcement contribution (vertical stirrups):

$$V_s = A_v\,\frac{f_{yv}\,d}{s}$$

Nominal and design strength:

$$V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)$$

Design check:

$$\phi V_n \ge V_u$$

Glossary of Variables

  • b_w: Beam web width (in or mm).
  • d: Effective depth to centroid of tensile reinforcement (in or mm).
  • f'c: Specified compressive strength of concrete (psi or MPa).
  • λ: Lightweight concrete modification factor (dimensionless; 1.0 for normalweight).
  • V_u: Factored design shear at the section (kips or kN).
  • A_v: Total stirrup area within spacing s that crosses a potential shear crack (in² or mm²).
  • f_yv: Yield strength of shear reinforcement (psi or MPa).
  • s: Longitudinal spacing of stirrups (in or mm).
  • V_c: Concrete contribution to shear strength (kips or kN after unit conversion).
  • V_s: Shear reinforcement contribution (kips or kN after unit conversion).
  • V_n: Nominal shear strength (kips or kN).
  • φV_n: Design shear strength (kips or kN).
  • φ: Strength reduction factor (dimensionless).

How It Works: A Step-by-Step Example

Scenario: US units, normalweight concrete, stirrups provided.

  • b_w = 12 in, d = 22 in
  • f'c = 4,000 psi, λ = 1.0
  • V_u = 85 kips
  • A_v = 0.31 in² (two-legged #5 stirrup), s = 8 in, f_yv = 60,000 psi
  • φ = 0.75

Compute:

V_c = 2 × 1.0 × √4000 × 12 × 22 = 2 × 63.25 × 264 ≈ 33,364 lb ≈ 33.36 kips

V_s = (0.31 × 60,000 × 22 / 8) = 51,150 lb ≈ 51.15 kips

V_n = V_c + V_s ≈ 33.36 + 51.15 = 84.51 kips

φV_n = 0.75 × 84.51 ≈ 63.38 kips

Check: φV_n (63.38) < V_u (85) → NG (increase stirrups or adjust design)

By decreasing s (closer spacing) or increasing A_v (larger bar/legs), Vs increases and the design may pass.

Frequently Asked Questions (FAQ)

Does this calculator automatically enforce all ACI 318 detailing provisions?

No. It focuses on strength equations (Vc, Vs, Vn, φVn) and the Vu ≤ φVn check. Verify minimum shear reinforcement, maximum spacing, member geometry limits, and any special provisions separately.

What λ value should I use?

Use λ = 1.0 for normalweight concrete. For lightweight concrete, use the value specified by ACI 318 per concrete type.

What φ factor should I select?

For shear in nonprestressed members, φ is commonly 0.75. Confirm with the latest ACI edition and the specific member classification.

Can I enter Av as “per leg” area?

Enter the total area within spacing s of all vertical legs crossing a potential shear crack. If your stirrup has multiple legs, multiply the area per leg by the number of legs.

Are deep beams or transfer girders covered?

No. Those members are governed by special provisions and strut-and-tie methods not covered by these equations.

What units are used in the results?

Results are shown in kips for US and kN for SI. A secondary line shows the alternate unit for quick reference.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}\]
V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}
Formula (extracted LaTeX)
\[V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}\]
V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}
Formula (extracted LaTeX)
\[V_s = A_v\,\frac{f_{yv}\,d}{s}\]
V_s = A_v\,\frac{f_{yv}\,d}{s}
Formula (extracted LaTeX)
\[V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)\]
V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)
Formula (extracted LaTeX)
\[\phi V_n \ge V_u\]
\phi V_n \ge V_u
Formula (extracted text)
Concrete contribution (US customary): $V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}$ Concrete contribution (SI): $V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}$ Shear reinforcement contribution (vertical stirrups): $V_s = A_v\,\frac{f_{yv}\,d}{s}$ Nominal and design strength: $V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)$ Design check: $\phi V_n \ge V_u$
Formula (extracted text)
V_c = 2 × 1.0 × √4000 × 12 × 22 = 2 × 63.25 × 264 ≈ 33,364 lb ≈ 33.36 kips V_s = (0.31 × 60,000 × 22 / 8) = 51,150 lb ≈ 51.15 kips V_n = V_c + V_s ≈ 33.36 + 51.15 = 84.51 kips φV_n = 0.75 × 84.51 ≈ 63.38 kips Check: φV_n (63.38) < V_u (85) → NG (increase stirrups or adjust design)
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

ACI 318 Concrete Beam Shear Strength Calculator

Compute Vc, Vs, Vn, and φVn per ACI 318 and verify Vu ≤ φVn in US or SI units.

Calculator

Units
Shear reinforcement (stirrups)

Results

Outputs shown in kips (US) or kN (SI).

Concrete shear Vc
Stirrup shear Vs
Nominal shear Vn = Vc + Vs
Design shear φVn
Demand/capacity Vu / (φVn)
Vu: —
Status:

Note: Detailing limits (e.g., minimum shear reinforcement, maximum spacing, and special members) are not checked by this tool and must be verified per ACI 318.

Data Source and Methodology

Authoritative Source: ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary,” 2019. Direct link: ACI 318-19 Product Page.

All calculations are strictly based on the formulas and data provided by this source.

The Formula Explained

Concrete contribution (US customary):

$$V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}$$

Concrete contribution (SI):

$$V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}$$

Shear reinforcement contribution (vertical stirrups):

$$V_s = A_v\,\frac{f_{yv}\,d}{s}$$

Nominal and design strength:

$$V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)$$

Design check:

$$\phi V_n \ge V_u$$

Glossary of Variables

  • b_w: Beam web width (in or mm).
  • d: Effective depth to centroid of tensile reinforcement (in or mm).
  • f'c: Specified compressive strength of concrete (psi or MPa).
  • λ: Lightweight concrete modification factor (dimensionless; 1.0 for normalweight).
  • V_u: Factored design shear at the section (kips or kN).
  • A_v: Total stirrup area within spacing s that crosses a potential shear crack (in² or mm²).
  • f_yv: Yield strength of shear reinforcement (psi or MPa).
  • s: Longitudinal spacing of stirrups (in or mm).
  • V_c: Concrete contribution to shear strength (kips or kN after unit conversion).
  • V_s: Shear reinforcement contribution (kips or kN after unit conversion).
  • V_n: Nominal shear strength (kips or kN).
  • φV_n: Design shear strength (kips or kN).
  • φ: Strength reduction factor (dimensionless).

How It Works: A Step-by-Step Example

Scenario: US units, normalweight concrete, stirrups provided.

  • b_w = 12 in, d = 22 in
  • f'c = 4,000 psi, λ = 1.0
  • V_u = 85 kips
  • A_v = 0.31 in² (two-legged #5 stirrup), s = 8 in, f_yv = 60,000 psi
  • φ = 0.75

Compute:

V_c = 2 × 1.0 × √4000 × 12 × 22 = 2 × 63.25 × 264 ≈ 33,364 lb ≈ 33.36 kips

V_s = (0.31 × 60,000 × 22 / 8) = 51,150 lb ≈ 51.15 kips

V_n = V_c + V_s ≈ 33.36 + 51.15 = 84.51 kips

φV_n = 0.75 × 84.51 ≈ 63.38 kips

Check: φV_n (63.38) < V_u (85) → NG (increase stirrups or adjust design)

By decreasing s (closer spacing) or increasing A_v (larger bar/legs), Vs increases and the design may pass.

Frequently Asked Questions (FAQ)

Does this calculator automatically enforce all ACI 318 detailing provisions?

No. It focuses on strength equations (Vc, Vs, Vn, φVn) and the Vu ≤ φVn check. Verify minimum shear reinforcement, maximum spacing, member geometry limits, and any special provisions separately.

What λ value should I use?

Use λ = 1.0 for normalweight concrete. For lightweight concrete, use the value specified by ACI 318 per concrete type.

What φ factor should I select?

For shear in nonprestressed members, φ is commonly 0.75. Confirm with the latest ACI edition and the specific member classification.

Can I enter Av as “per leg” area?

Enter the total area within spacing s of all vertical legs crossing a potential shear crack. If your stirrup has multiple legs, multiply the area per leg by the number of legs.

Are deep beams or transfer girders covered?

No. Those members are governed by special provisions and strut-and-tie methods not covered by these equations.

What units are used in the results?

Results are shown in kips for US and kN for SI. A secondary line shows the alternate unit for quick reference.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}\]
V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}
Formula (extracted LaTeX)
\[V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}\]
V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}
Formula (extracted LaTeX)
\[V_s = A_v\,\frac{f_{yv}\,d}{s}\]
V_s = A_v\,\frac{f_{yv}\,d}{s}
Formula (extracted LaTeX)
\[V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)\]
V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)
Formula (extracted LaTeX)
\[\phi V_n \ge V_u\]
\phi V_n \ge V_u
Formula (extracted text)
Concrete contribution (US customary): $V_c = 2\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(lb; f'c in psi, b_w and d in in)}$ Concrete contribution (SI): $V_c = 0.17\,\lambda\,\sqrt{f'_c}\,b_w\,d \quad \text{(N; f'c in MPa, b_w and d in mm)}$ Shear reinforcement contribution (vertical stirrups): $V_s = A_v\,\frac{f_{yv}\,d}{s}$ Nominal and design strength: $V_n = V_c + V_s \qquad \phi V_n = \phi\,(V_c + V_s)$ Design check: $\phi V_n \ge V_u$
Formula (extracted text)
V_c = 2 × 1.0 × √4000 × 12 × 22 = 2 × 63.25 × 264 ≈ 33,364 lb ≈ 33.36 kips V_s = (0.31 × 60,000 × 22 / 8) = 51,150 lb ≈ 51.15 kips V_n = V_c + V_s ≈ 33.36 + 51.15 = 84.51 kips φV_n = 0.75 × 84.51 ≈ 63.38 kips Check: φV_n (63.38) < V_u (85) → NG (increase stirrups or adjust design)
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).