Punching shear design - Internal circular column support

Eurocode 2 Punching shear design for internal column with circular 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 circular 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 circular cross-section. Adequate distance of column support from free edges (i.e. for edge columns clear distance greater than 0.285D + πd, where d is the static depth and D is the column diameter).

Supported National Annexes:

Nationally Defined Parameters (NDPs) automatically filled for supported countries with the following exceptions: a) The parameter k_max 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 v_Rd,max in EN1992-1-1 §6.4.5(3) has changed from 0.5νf_cd to 0.4νf_cd 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.

Characteristic strength of slab concrete

f_ck

MPa

e.g. 30 MPa for concrete class C30/37. For a list of concrete classes see Table of Concrete Design Properties

Characteristic yield strength of steel of punching shear reinforcement

f_ywk

MPa

Type of punching region

For foundation bases of columns the favorable effect of soil upward pressure within the control perimeter is considered

Diameter of circular column

Calculation method for the coefficient β accounting for increased shear forces due to eccentric loading

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.

Custom value of the coefficient β accounting for increased shear forces due to eccentric loading

Design value of the vertical shear force transmitted from slab to column

V_Ed

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 V_Ed.

Design value of the bending moment transmitted from slab to the column (resultant vector)

M_Ed

kNm

It corresponds to the difference of the corresponding bending moments of the column above and below the slab.

For foundations: Upward pressure from soil excluding self-weight of slab

p_Ed

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

Type of punching shear reinforcement

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.

Radial spacing between perimeter of punching shear reinforcement

s_r

Angle between shear reinforcement and the beam axis perpendicular to the shear force (α=90° for typical perpendicular shear reinforcement)

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.

Area of tensile reinforcement per meter along y direction

(A_sl/s)_y

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.

Effective depth (static depth) of the cross-section along y direction

d_y

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

Mean axial stress along y direction due to loading or prestressing (compression positive)

σ_cy

MPa

Mean axial stress due to loading or prestressing along y direction σ_c,y=N_Ed,y/A_cy 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).

Area of tensile reinforcement per meter along z direction

(A_sl/s)_z

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.

Effective depth (static depth) of the cross-section along z direction

d_z

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

Mean axial stress along z direction due to loading or prestressing (compression positive)

σ_cz

MPa

Mean axial stress due to loading or prestressing along z direction σ_c,z=N_Ed,z/A_cz 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).