ACI 318 Concrete Beam Shear Strength Calculator
This concrete shear design calculator helps structural engineers compute beam shear strength per ACI 318. It determines the concrete contribution Vc, shear reinforcement contribution Vs, the nominal shear strength Vn, and the design strength φVn, then checks whether the factored shear demand Vu is satisfied. The tool supports US (in, psi, kips) and SI (mm, MPa, kN) units.
Calculator
Results
Outputs shown in kips (US) or kN (SI).
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.