Free Tool · EN 1992-1-1 §6.4

Punching Shear Calculator

Check punching shear for flat slabs and pad foundations to EN 1992-1-1 §6.4. Computes control perimeters u0/u1, eccentricity factor β, design stress vEd, concrete resistance vRd,c (§6.4.4), maximum stress vRd,max (§6.4.5), and required shear reinforcement Asw per ring.

flat slab / foundation column c₁ × c₂ u₀ u₁ (at 2d) u_out 2d u₀ (§6.4.5) u₁ = 2d (§6.4.2) u_out (no reinf.) studs

Inputs


d = (h − cover − ½φ), typically slab h − 40mm for top steel


a = distance from column face to resultant soil pressure (mm)
Computing…
Overall result PASS
1. Control perimeters u₀, u₁ (§6.4.2)
u₀ at column face1200 mm
u₁ at 2d from face3838.9 mm
2d420 mm
Rectangular 300×300mm internal
2. Eccentricity factor β (§6.4.3)
Eccentricity factor β1.15
Methodsimplified §6.4.3(6)
β = 1.15 (internal column, no moment)
3. Design shear stress v_Ed
v_Ed at u₁0.856 N/mm²
v_Ed,0 at u₀2.738 N/mm²
vEd = β·VEd / (u·d)
4. Concrete resistance v_Rd,c (§6.4.4 eq.6.47)
k (size effect)1.976 (= 1+√(200/d) ≤ 2.0)
ρ_l = √(ρ_lx · ρ_ly)0.005
C_Rd,c0.12
v_min floor0.532 N/mm²
v_Rd,c0.585 N/mm²
Governs: main formula · §6.4.4 eq.6.47
5. Maximum stress v_Rd,max at u₀ (§6.4.5 eq.6.53)
ν = 0.6(1 − fck/250)0.528
fcd = fckC20 N/mm²
v_Rd,max5.28 N/mm²
6. Utilisation checks
v_Ed / v_Rd,c at u₁ 1.464 FAIL
v_Ed,0 / v_Rd,max at u₀ 0.519 PASS
7. Shear reinforcement (§6.4.5 eq.6.52)
A_sw per ring1230.9 mm²
fywd,ef273.3 MPa
s_r max (≤ 0.75d)157.5 mm
u_out (no-reinf. perimeter)5618.9 mm
§6.4.5 eq.6.52 — vertical studs (α=90°), f_ywd,ef = min(435, 250+d/9) = 273.3 MPa
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  • Opening / hole reduction in control perimeter (§6.4.2(3))
  • Prestress contribution σ_cp (§6.4.4 eq.6.47)
  • Post-installed shear stud layout optimisation
  • Batch check all columns from IFC model
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Frequently asked questions

What control perimeter u_1 does EN 1992-1-1 use for punching shear?
The basic control perimeter u_1 is located at a distance 2d from the column face (§6.4.2), where d is the effective depth of the slab. For a 300×300mm internal column on a 250mm slab with d=210mm: u_1 = 2(300+300) + 4π×210 ≈ 3837mm. A second perimeter u_0 at the column face is used to check v_Rd,max (crushing limit §6.4.5).
What is the eccentricity factor β?
β accounts for moment transfer at the column-slab joint. For simplified design (§6.4.3(6)): β=1.15 for internal columns, β=1.4 for edge, β=1.5 for corner. When moments M_Ed are provided, the detailed method (eq.6.39 with k from Table 6.1) gives a more accurate β. This tool calculates both; if no moment is supplied the simplified value is used.
When is shear reinforcement (punching studs) required?
Shear reinforcement is required when v_Ed > v_Rd,c at the u_1 perimeter. The required area per ring is A_sw = (v_Ed − 0.75·v_Rd,c)·u_1·d / (f_ywd,ef·sin α) per §6.4.5 eq.6.52. Reinforcement must extend to the outer perimeter u_out where shear stress drops below v_Rd,c.
How does the foundation enhanced resistance work?
For pad foundations (§6.4.4(2)), v_Rd,c is enhanced by the factor 2d/a ≥ 1, where a is the distance from the column face to the resultant of the applied soil pressure. This accounts for the direct strut mechanism. Select "Pad foundation" and enter a (mm) to apply this enhancement.