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

_{lRd,c}

## Eurocode 2 part 1-1: Design of concrete structures 11.6.4.1 (1) & 6.4.4 (1)

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

v = _{lRd,c}C _{lRd,c}k η(100 _{1}ρ _{l}f)_{lck}^{1/3} + k _{2}σ ≥ (_{cp}η _{1}v + _{l,min}k _{2}σ) _{cp} | (11.6.47) |

where:

`η`_{1}- is a coefficient for determining tensile strength of lightweight concrete
`f`_{lck}- is the characteristic compressive strength of lightweight concrete, see Table 11.3.1
`k`- = 1 + √200/
`d`≤ 2,0

where`d`is the effective depth, in [mm] `ρ`_{l}- is the reinforcement ratio for longitudinal reinforcement
`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`_{lRd,c}- is a Nationally Determined Parameter, see § 11.6.1 (1)
`v`_{l,min}- is a Nationally Determined Parameter, see § 11.6.1 (1), or the application for the calculation of
`v`following the Eurocode recommendation_{l,min} `k`_{2}- is a Nationally Determined Parameter, see § 11.6.4.1 (1).

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