PUNCHING SHEAR CHECK

What this calculator checks

The calculator verifies a reinforced-concrete slab for punching shear around a column, according to EN 1992-1-1 §6.4 — the local failure by which the column "punches" through the slab over a truncated-cone surface. Interior, edge and corner columns are treated, through three checks:

• \(v_{Rd,c}\) — the slab resistance without punching reinforcement, on the control perimeter (§6.4.4)
• \(v_{Rd,max}\) — crushing of the concrete at the column face, on perimeter \(u_0\) (§6.4.5)
• \(v_{Rd,cs}\) — design of the punching reinforcement, when the slab alone is not enough (§6.4.5, expr. 6.52)

The control perimeter

The central idea of the method: shear is not checked at the column face but on a control perimeter \(u_1\) drawn at a distance \(2d\) from the column, where \(d\) is the average effective depth of the slab. The shear stress is distributed over this perimeter:

\(v_{Ed} = \frac{\beta \, V_{Ed}}{u_1 \, d}\)

The factor \(\beta \ge 1\) magnifies the force to account for the moment transferred to the column: at an edge or corner column, or when a moment is present, the shear distribution is not uniform, and \(\beta\) corrects it. It may be taken simplified (tabulated values by position) or computed from the moments.

The three checks, in order

1. At the column face (\(u_0\)): \(v_{Ed} \le v_{Rd,max}\). If the concrete crushes here, no reinforcement helps — the column, slab or concrete class must be increased.
2. On the control perimeter (\(u_1\)): if \(v_{Ed} \le v_{Rd,c}\), the slab resists without special reinforcement.
3. Punching reinforcement: if \(v_{Rd,c} < v_{Ed} \le v_{Rd,max}\), the reinforcement is designed (\(v_{Rd,cs}\)) and the perimeter beyond which it is no longer needed is determined.

Input data

• Column position — interior, edge or corner; sets the shape of the control perimeter and the values of \(\beta\).
• Column geometry — \(c_1\) (side perpendicular to the edge) and \(c_2\) (parallel to the edge).
• The slab — thickness, effective depth \(d\), concrete class.
• Longitudinal reinforcement of the slab — through the ratio \(\rho_l\) (capped at 0.02).
• \(V_{Ed}\) and, if needed, the moments for computing \(\beta\).

Deliberate deviations from common models

The calculation corrects a few frequent errors in the Calcpad model sheets:

• \(v_{Rd,max}\) uses the coefficient \(k_{max} = 0.4\) (EC2 corrigendum AC2:2010), not 0.5 (UK National Annex).
• The reinforcement ratio \(\rho_l\) is capped at 0.02 (expr. 6.47).
• The interpolation of coefficient \(k\) (Table 6.1) is corrected over the range \(0.5 < c_1/c_2 < 1\).

Assumptions and limitations

• Flat slab without column heads; drop panels require the additional check of multiple perimeters (§6.4.2).
• Foundations as a slab on ground with reaction inside the perimeter are treated only in the dedicated mode (§6.4.4(2)).
• Symmetric longitudinal reinforcement in the two directions is assumed for the average \(\rho_l\).

Related calculations

• Reinforced section — the "linear" shear of beams, by comparison with the "point" shear here
• Concrete cover — for the effective depth \(d\) of the slab
• Crack-width verification — SLS for slabs
• Isolated footing — where punching is checked in foundation mode