# Punching shear resistance of a slab without shear reinforcement, `v`_{Rd,c}

_{Rd,c}

## Eurocode 2 part 1-1: Design of concrete structures 6.4.4 (1)

The punching shear resistance of a slab should be assessed for the basic control section (see Figure 6.12). The design punching shear resistance [MPa] may be calculated as follows:

v = _{Rd,c}C _{Rd,c}k (100 ρ _{l}f)_{ck}^{1/3} + k _{1}σ ≥ (_{cp}v + _{min}k _{1}σ) _{cp} | (6.47) |

where:

`f`_{ck}- is the characteristic compressive strength of concrete, see Table 3.1
`k`- = 1 + √200/
`d`≤ 2,0

where`d`is the effective depth, in [mm] `ρ`_{l}- = (
`ρ`⋅_{ly}`ρ`)_{lz}^{1/2}≤ 2%

`ρ`,_{ly}`ρ`are longitudinal reinforcement ratios in y- and z- directions respectively. Their values should be calculated as mean values taking into account a slab width equal to to column width plus 3_{lz}`d`each side `σ`_{cp}- = (
`σ`+_{cy}`σ`)/2,_{cz}

where`σ`,_{cy}`σ`are the normal concrete stresses in the critical section in y- and z- directions (in [MPa], positive if compression):_{cz}

`σ`=_{cy}`N`/_{Ed,y}`A`and_{cy}`σ`=_{cy}`N`/_{Ed,z}`A`_{cz}

`N`,_{Ed,y}`N`are the longitudinal forces across the full bay for internal columns and the longitudinal force across the control section for edge columns. The force may be from a load or prestressing action._{Ed,y}

`A`,_{cy}`A`are the areas of concrete according to the definition of_{cz}`N`,_{Ed,y}`N`respectively_{Ed,y} `C`_{Rd,c}- is a Nationally Determined Parameter, see § 6.4.4 (1)
`v`_{min}- is a Nationally Determined Parameter, see § 6.4.4 (1), or (6.3N) for the calculation of
`v`following the Eurocode recommendation_{min} `k`_{1}- is a Nationally Determined Parameter, see § 6.4.4 (1).

This application calculates
the punching shear resistance of a slab `v _{Rd,c}`
from your inputs.
Intermediate results will also be given.