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Eurocode 2 Punching shear design for internal column with rectangular cross-section (slab support or foundation base)

Description:
Calculation of punching shear reinforcement and verification of concrete strength for slab support or foundation base of rectangular internal column
According to:
EN 1992-1-1:2004+AC2:2010 Section 6.4
Applicable for:
Slab support or foundation base of interior column with rectangular cross-section. Adequate distance of column support from free edges (i.e. for edge columns clear distance greater than c + πd, where d is the static depth and c is the column dimension parallel to the edge).
Supported National Annexes:
Nationally Defined Parameters (NDPs) automatically filled for supported countries with the following exceptions: a) The parameter kmax was newly added in the Amendment A1 (2014) of EN1992-1-1 §6.4.5(1). Some National Annexes have not been altered after this change. This parameter is not updated automatically. Please specify according to the National Annex if different than the recommended value of 1.5. b) The recommended value of the parameter vRd,max in EN1992-1-1 §6.4.5(3) has changed from 0.5νfcd to 0.4νfcd in corrigendum EN 1992-1-1:2004+AC2:2010. Some National Annexes have not been altered after this change. Please specify according to the National Annex if the older less conservative value is desired. c) The National Annex of Finland is NOT supported.
All Calculations
Input
MPa
e.g. 30 MPa for concrete class C30/37. For a list of concrete classes see Table of Concrete Design Properties
MPa
For foundation bases of columns the favorable effect of soil upward pressure within the control perimeter is considered
m
m
For internal circular column the refined method corresponds to EN 1992-1-1 eq. (6.42). The approximate value corresponds to β = 1.15 according to EN 1992-1-1 Fig. 6.21N.
kN
It corresponds to the difference of the corresponding axial forces of the column above and below the slab. For the cases of footings, the upwards soil pressure minus self-weight within the control perimeter increases the resistance and may be subtracted from VEd.
Different expessions are applied for the calculation of coefficient β for the cases of uniaxial eccentrity and biaxial eccentricity, where the latter method is more approximate.
kNm
It corresponds to the difference of the corresponding bending moments of the column above and below the slab.
kNm
It corresponds to the difference of the corresponding bending moments of the column above and below the slab.
kN/m2
Applicable for foundations. Favorable upwards pressure from soil (excluding the unfavorable downwards self-weight of slab) to be subtracted from the punching shear load

For internal circular column the refined method corresponds to EN 1992-1-1 eq. (6.42). The approximate value corresponds to β = 1.15 according to EN 1992-1-1 Fig. 6.21N.
m
°
An angle of 90° corresponds to the bars being perpendicular to the plane of the interface. Values less than 90° mean that the bars are in tension due to the shearing action on the interface.

cm2/m
Mean values taking into account a slab width equal to the column width plus 3d on each side. When in doubt a value of 0 yields conservative results.
m
The effective depth of the cross-section is measured from the centroid of the tensile reinforcement to the opposite concrete edge in compression along the plane of bending
MPa
Mean axial stress due to loading or prestressing along y direction σc,y=NEd,y/Acy corresponding to the longitudinal force across the full bay for internal columns or the longitudinal force across the control section for edge columns (positive when compressive).

cm2/m
Mean values taking into account a slab width equal to the column width plus 3d on each side. When in doubt a value of 0 yields conservative results.
m
The effective depth of the cross-section is measured from the centroid of the tensile reinforcement to the opposite concrete edge in compression along the plane of bending
MPa
Mean axial stress due to loading or prestressing along z direction σc,z=NEd,z/Acz corresponding to the longitudinal force across the full bay for internal columns or the longitudinal force across the control section for edge columns (positive when compressive).
Nationally Defined Parameters
According to EN1992-1-1 §3.1.6(1)P and the National Annex.
According to EN1992-1-1 §2.4.2.4 and the National Annex.
According to EN1992-1-1 §2.4.2.4 and the National Annex.
According to EN1992-1-1 §6.4.4(1) and the National Annex.
This parameter was newly added in the Amendment A1 (2014) of EN1992-1-1 §6.4.5(1). Some National Annexes have not been altered after this change. Please specify according to the National Annex if different than the recommended value of 1.5.
According to EN1992-1-1 §6.4.5(3) and the National Annex. Note that in corrigendum EN 1992-1-1:2004+AC2:2010 the recommended value for this parameter was changed from 0.5νfcd to 0.4νfcd. Some National Annexes have not been altered after this change. Please specify according to the National Annex if the older less conservative value is desired.
According to the National Annex of Switzerland to EN1992-1-1 §6.4.5(3). Recommended values: 1.4 for stirrups with hooks in the tension side, 1.5 for stirrups without anchorage or in tension side, 1.6 for smooth studs with anchorage plate larger than 3 times the stud diameter, 1.7 for corrugated studs with anchorage plate larger than 3 times the stud diameter.
m
According to the National Annex of Switzerland to EN1992-1-1 §6.4.5(3).
Note: Always verify the validity of the Nationally Defined Parameters (NDPs). Please inform us of any discrepancy using our Contact Form. The NDP value is left blank for all NDPs that we do not have this information available. Interested users who have access to the corresponding NDPs can notify us using our Contact Form to fill-in the missing information.