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# Punching shear resistance of a slab without shear reinforcement, vRd,c

## Eurocode 2 part 1-1: Design of concrete structures \$(document).ready(function () { var freeExample = \$("#freeExample").length; \$("#mainMenu li#nav-appCate, #mainMenu li#nav-appEC211").addClass("active"); var proUser = false === true || false === true || freeExample !== 0; if (!proUser) { \$('#Input input').keyup(function(){ \$('#AlertSubscribe').modal(); }); \$('#Input select').change(function(){ \$('#AlertSubscribe').modal(); }); }; var tempInput = \$("#tempInput").text(); if (tempInput != "") { \$("#Input").parent("form").deserialize(tempInput); if (proUser) { \$("#acceptBtn").trigger("click"); } }; });  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:

 vRd,c = CRd,c k (100 ρl fck)1/3 + k1 σcp   ≥ (vmin + k1 σcp) (6.47)

where:

fck
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]
ρl
= (ρlyρlz)1/2   ≤ 2%
ρly, ρlz 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 3d each side
σcp
= (σcy + σcz)/2,
where σcy, σcz are the normal concrete stresses in the critical section in y- and z- directions (in [MPa], positive if compression):
σcy = NEd,y / Acy and σcy = NEd,z / Acz
NEd,y, NEd,y 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.
Acy, Acz are the areas of concrete according to the definition of NEd,y, NEd,y respectively
CRd,c
is a Nationally Determined Parameter, see § 6.4.4 (1)
vmin
is a Nationally Determined Parameter, see § 6.4.4 (1), or (6.3N) for the calculation of vmin following the Eurocode recommendation
k1
is a Nationally Determined Parameter, see § 6.4.4 (1).

This application calculates the punching shear resistance of a slab vRd,c from your inputs. Intermediate results will also be given.

Input
MPa
mm
MPa
%
%
kN
kN
mm2
mm2

Output
k
ρl
%
σcy
MPa
σcz
MPa
σcp
MPa
the punching shear resistance of a slab vRd,c
MPa (6.47)