Eurocode 2 Concrete Slab Punching Shear Calculator

This professional-grade calculator evaluates punching shear around internal columns in reinforced concrete slabs according to Eurocode 2 (EN 1992-1-1). It is designed for structural engineers and advanced practitioners who need a fast, transparent check of v_Ed against v_Rd,c and v_Rd,max with full traceability, accessibility, and SEO-rich content.

Interactive Calculator

Column shape
mm
Short side of the rectangular column (measured on plan).
mm
Long side of the rectangular column (measured on plan).
mm
d is the distance from extreme compression fiber to centroid of tension reinforcement. For slabs, approximate as h − cover − 0.5·bar diameter.
mm
MPa
Characteristic 28‑day cylinder strength class (e.g., C30/37 ⇒ f_ck = 30 MPa). Limited to ≤ 90 MPa as per EC2.
%
Average of orthogonal tensile reinforcement ratios within a width equal to the control perimeter. EC2 limits ρ_l ≤ 2% for this check. Enter as percent.
kN
Use the design shear force crossing the first control perimeter. Often approximated as column reaction minus distributed load within the control area.
β accounts for non-uniform shear due to moment transfer. For concentric loading use β = 1.0. For significant eccentricity consider higher β per national guidance.
MPa
mm
EC2 allows subtracting lengths where the control perimeter crosses openings within 3d of the column face. Enter the total deducted length.

Results

Control perimeter u₁ — mm (— m)
Reduction for openings Σbo —
k factor —
ρl (used) —
vEd —
vRd,c —
vRd,max —
Utilization vEd/vRd,c —
Enter values to compute punching shear.

Notes: MPa = N/mm². If v_Ed ≤ v_Rd,c, no shear reinforcement is required. If v_Rd,c < v_Ed ≤ v_Rd,max, shear reinforcement is required. If v_Ed > v_Rd,max, increase slab depth, column size, or reduce load.

Data Source and Methodology

Primary reference: EN 1992-1-1:2004 Eurocode 2 – Design of concrete structures – Part 1-1: General rules and rules for buildings (including A1:2014). See Clause 6.4 (Punching Shear). Direct references:

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Control perimeter at 2d (internal column):

Rectangular: $$u_1 = 2\,(b + c + 8d)$$ Circular: $$u_1 = \pi\,(D + 4d)$$

k factor (d in mm): $$k = 1 + \sqrt{\frac{200}{d}} \le 2.0$$

Concrete shear resistance without shear reinforcement: $$v_{Rd,c} = \max\!\Bigl(C_{Rd,c}\,k\,(100\,\rho_l\,f_{ck})^{1/3},\; v_{\min}\Bigr) + k_1\,\sigma_{cp}$$ with $$C_{Rd,c} = \frac{0.18}{\gamma_c},\quad v_{\min} = 0.035\,k^{3/2}\,f_{ck}^{1/2},\quad k_1 = 0.1$$

Design shear stress at the control perimeter: $$v_{Ed} = \frac{\beta\,V_{Ed}}{u_1\,d}$$ with VEd in N, u1 and d in mm.

Maximum punching capacity: $$v_{Rd,\max} = 0.5\,v_1\,f_{cd}, \quad v_1 = 0.6\Bigl(1 - \frac{f_{ck}}{250}\Bigr), \quad f_{cd} = \frac{\alpha_{cc}\,f_{ck}}{\gamma_c}$$

Assumptions: internal column, first control perimeter at 2d, no torsion, β provided by user, and openings accounted as a deduction Σbo where permitted by EC2.

Glossary of Variables

b, c
Column side dimensions (mm) for rectangular columns.
D
Column diameter (mm) for circular columns.
d
Effective depth of slab (mm).
h
Overall slab thickness (mm).
fck
Characteristic concrete cylinder strength (MPa).
γc
Concrete partial safety factor (typically 1.5).
αcc
Coefficient for long-term effects on the compressive strength (1.0 if not stated otherwise).
ρl
Average longitudinal tensile reinforcement ratio (fraction, limited to 0.02).
σcp
Average compressive stress at the control perimeter due to axial force (MPa).
β
Eccentricity factor for non-uniform shear distribution (≥ 1.0).
Σbo
Total length deducted from u1 due to openings within 3d (mm).
u1
Control perimeter at distance 2d from the column face (mm).
vEd
Design shear stress at u1 (MPa).
vRd,c
Design shear resistance without shear reinforcement (MPa).
vRd,max
Maximum punching shear capacity (MPa).

How It Works: A Step-by-Step Example

Given: rectangular internal column: b = 300 mm, c = 300 mm; d = 200 mm; fck = 30 MPa; ρl = 1.0%; VEd = 900 kN; β = 1.0; γc = 1.5; σcp = 0; Σbo = 0.

  1. k = 1 + √(200/200) = 2.0 (limited to 2.0).
  2. u1 = 2(b + c + 8d) = 2(300 + 300 + 1600) = 4400 mm.
  3. CRd,c = 0.18/1.5 = 0.12; (100·ρl·fck)^(1/3) = (30)^(1/3) = 3.107.
  4. vRd,c = 0.12·2·3.107 = 0.746 MPa, which is greater than vmin = 0.543 MPa.
  5. vEd = 900 kN / (4400·200 mm²) = 1.02 MPa.
  6. v1 = 0.6(1 − 30/250) = 0.528; fcd = 30/1.5 = 20 MPa; vRd,max = 0.5·0.528·20 = 5.28 MPa.

Result: vEd (1.02 MPa) > vRd,c (0.746 MPa) but < vRd,max (5.28 MPa). Therefore, shear reinforcement is required to satisfy EC2.

Frequently Asked Questions (FAQ)

Does this tool handle edge or corner columns?

This version focuses on internal columns with the first control perimeter at 2d. Edge and corner cases involve different perimeter geometry and load redistribution and will be included in future updates.

How should I estimate VEd at the control perimeter?

As a simplification, use the design column reaction minus the fraction of distributed load acting within the control area. For accuracy, follow your national annex or project-specific load models.

What limits apply to ρl?

EC2 limits the reinforcement ratio used in the vRd,c expression to ρl ≤ 0.02 (2%). The calculator automatically caps the value if a higher percentage is entered.

Can compressive membrane action be included?

Yes. Enter σcp (MPa). The tool adds k1·σcp (with k1 = 0.1) to vRd,c per EC2.

When is vRd,max governing?

vRd,max caps the punching capacity regardless of provided shear reinforcement. If vEd exceeds vRd,max, increasing studs or links alone will not make the section safe.

How accurate is the perimeter deduction for openings?

EC2 allows subtracting lengths where the control perimeter crosses openings within 3d of the column. This tool applies a direct deduction Σbo. Complex opening layouts may require manual verification.

What units does the calculator use?

Consistent SI units: mm for geometry, MPa for stresses, and kN for forces. Internally, stresses are computed in N/mm² (MPa) to avoid unit errors.

Tool developed by Ugo Candido. Content verified by Senior Structural Engineer (PE).
Last reviewed for accuracy on: .