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# Punching shear resistance of a lightweight concrete slab without shear reinforcement, vlRd,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"); } }; });  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:

 vlRd,c = ClRd,c k η1(100 ρl flck)1/3 + k2 σcp  ≥ (η1 vl,min + k2 σcp) (11.6.47)

where:

η1
is a coefficient for determining tensile strength of lightweight concrete
flck
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]
ρl
is the reinforcement ratio for longitudinal reinforcement
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
ClRd,c
is a Nationally Determined Parameter, see § 11.6.1 (1)
vl,min
is a Nationally Determined Parameter, see § 11.6.1 (1), or the application for the calculation of vl,min following the Eurocode recommendation
k2
is a Nationally Determined Parameter, see § 11.6.4.1 (1).

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

Input
MPa
mm
MPa
%
kN
kN
mm2
mm2

Output
the punching shear resistance of a slab k
σcy
MPa
σcz
MPa
σcp
MPa
vlRd,c
MPa (11.6.47)