Data Source and Methodology
Authoritative Data Source: ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19 and ACI 318-22) and Commentary.” American Concrete Institute, 2019/2022. Official ACI link.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
This tool implements standard two-way (punching) shear checks at a critical section located at d/2 from the column face. The concrete shear strength vc coefficients for Interior, Edge, and Corner columns follow widely used ACI expressions. The critical perimeter b0 is computed using common rectangular approximations consistent with ACI practice. Unbalanced moment transfer and openings are not included in this quick check.
The Formula Explained
Glossary of Variables
- c1, c2 — Column plan dimensions (face-to-face) in directions 1 and 2.
- h — Slab thickness.
- d — Effective depth to tensile reinforcement. Auto mode uses d = h − cover − db/2.
- b0 — Critical punching shear perimeter at a distance d/2 from the column face.
- f'c — Concrete compressive strength (MPa or psi).
- λ — Lightweight concrete modification factor (use 1.0 for normal weight).
- φ — Strength reduction factor for shear (commonly 0.75 for slabs without shear reinforcement).
- Vu — Factored shear at the column-slab connection (kN or kips).
- vu — Demand shear stress at the critical section.
- vc — Nominal concrete shear strength per ACI expressions.
- φVc — Design punching shear strength (capacity) to compare against Vu.
How It Works: A Step-by-Step Example
Given: SI units; Interior column; c1 = 400 mm, c2 = 400 mm; h = 200 mm; auto d with cover = 25 mm and db = 16 mm; f'c = 30 MPa; λ = 1.0; φ = 0.75; Vu = 1200 kN.
- Compute d = h − cover − db/2 = 200 − 25 − 8 = 167 mm.
- Critical perimeter: b0 = 2(c1 + c2) + 4d = 2(400 + 400) + 4(167) = 1600 + 668 = 2268 mm.
- Demand stress: vu = Vu / (b0 d). Convert Vu to N: 1200 kN = 1,200,000 N. vu = 1,200,000 / (2268 × 167) = 3.15 N/mm² = 3.15 MPa.
- Strength: vc = 0.33 λ √f'c = 0.33 × 1.0 × √30 = 0.33 × 5.477 = 1.81 MPa.
- Capacity: Vc = vc b0 d = 1.81 × 2268 × 167 = 685,000 N = 685 kN; φVc = 0.75 × 685 = 513.8 kN.
- Check: Vu = 1200 kN > φVc = 513.8 kN → Not OK; utilization = 1200 / 513.8 = 2.34.
Result indicates that either slab thickness, column dimensions, drop panels, or shear reinforcement detailing must be revised. Also evaluate unbalanced moment per ACI when applicable.
Frequently Asked Questions (FAQ)
Which ACI edition does this tool follow?
ACI 318-19/22 principles for two-way punching shear without shear reinforcement. The stress coefficients (Interior, Edge, Corner) match common ACI practice.
How is the critical section defined?
At a perimeter located d/2 from the column or loaded area, measured within the slab. This tool uses standard rectangular approximations for b0.
Do you consider unbalanced moment transfer?
No. This is a concentric punching check. For frame action or lateral load effects, include unbalanced moment per ACI and re-evaluate.
What if I have a drop panel or column capital?
Drop panels primarily increase d (and may affect detailing). Update geometry accordingly and re-run. Column capitals reduce stress by increasing the loaded area; consider ACI provisions if present.
What λ value should I use?
Use 1.0 for normal-weight concrete. For lightweight, select λ per ACI 318 (e.g., 0.85–0.75 depending on type and if splitting tensile is known).
What φ should I use?
Typical φ for shear in slabs without shear reinforcement is 0.75. Always verify against your jurisdiction and project code edition.
Are openings or column eccentricity included?
No. Openings near the column and eccentric loading significantly affect b0 and demand. Include them in a detailed design per ACI 318.
Formula (LaTeX) + variables + units
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b_0 = \begin{cases} 2(c_1 + c_2) + 4d, & \text{Interior} \\\\ c_1 + 2c_2 + 3d \;(\text{edge} \parallel c_1) \;\text{ or }\; 2c_1 + c_2 + 3d \;(\text{edge} \parallel c_2), & \text{Edge} \\\\ c_1 + c_2 + 2d, & \text{Corner} \end{cases}
v_u = \frac{V_u}{b_0 \, d}
v_c = \begin{cases} 0.33\,\lambda\,\sqrt{f'_c} \ \text{(MPa)}, & \text{SI} \\\\ 4.0\,\lambda\,\sqrt{f'_c} \ \text{(psi)}, & \text{US} \end{cases}
V_c = v_c \, b_0 \, d \quad,\quad \phi V_c = \phi \, V_c
\text{Check: } \; V_u \le \phi V_c \quad\Rightarrow\quad \text{Utilization} = \frac{V_u}{\phi V_c}
$ b_0 = \begin{cases} 2(c_1 + c_2) + 4d, & \text{Interior} \\\\ c_1 + 2c_2 + 3d \;(\text{edge} \parallel c_1) \;\text{ or }\; 2c_1 + c_2 + 3d \;(\text{edge} \parallel c_2), & \text{Edge} \\\\ c_1 + c_2 + 2d, & \text{Corner} \end{cases} $ $ v_u = \frac{V_u}{b_0 \, d} $ $ v_c = \begin{cases} 0.33\,\lambda\,\sqrt{f'_c} \ \text{(MPa)}, & \text{SI} \\\\ 4.0\,\lambda\,\sqrt{f'_c} \ \text{(psi)}, & \text{US} \end{cases} $ $ V_c = v_c \, b_0 \, d \quad,\quad \phi V_c = \phi \, V_c $ $ \text{Check: } \; V_u \le \phi V_c \quad\Rightarrow\quad \text{Utilization} = \frac{V_u}{\phi V_c} $
- No variables provided in audit spec.
- Official ACI link — concrete.org · Accessed 2026-01-19
https://www.concrete.org/store/productdetail.aspx?ItemID=31822
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
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