Punching shear

Punching shear arises when a concentrated load is applied to a small area of a slab or, most commonly, the reaction of a column against a slab. The resulting stresses are verified along defined control perimeters around the loaded area.

The shear force, V_Ed acts over an area ud_eff, where

u    = the length of the perimeter. The basic perimeter, u₁ is at 2d_eff from the column.

d_eff  = the effective depth of the slab taken as the average of the effective depths in two orthogonal directions.

Design for punching shear should allow for the effects of moment transfer at the column/slab junction. For structures, the lateral stability of which do not rely on the frame action between the slab and columns and in which adjacent spans do not differ in length by more than 25%, the design punching shear may be obtained by enhancing V_Ed by  1.15 for internal columns, 1.4 for edge columns and 1.5 for corner columns.

The following checks should be carried out: 

• Ensure that maximum punching shear stress is not exceeded, i.e. v_Ed < v_Rd,max at the column perimeter
• Determine whether punching shear reinforcement is required, i.e. whether v_Ed > v_Rd,c at the basic perimeter, u₁
• Determine whether punching shear reinforcement is required, i.e. whether v_Ed > v_Rd,c at at successive perimeters to establish u_out    = the length of the perimeter where v_Ed = v_Rd,c. Perimeters within 1.5 d from u_out need to be reinforced.

Where required provide reinforcement such that v_Ed ≤ v_Rd,cs.

where

v_Ed  =    applied shear stress. The shear force used in the verification should be the effective force taking into account any bending moment transferred into the slab (see above)

v_Rd,max = design value of the maximum punching shear resistance, expressed as a stress (see Shear Table 7)
v_Rd,c    = design value of punching shear resistance of a slab without punching shear reinforcement, expressed as a stress (see Shear Table 7)
v_Rd,cs    = design value of punching shear resistance of a slab with punching shear reinforcement, expressed as a stress.

v_Rd,cs = 0.75 v_Rd,c + 1.5 (d/s_r)A_sw f_ywd,ef (1/u₁d)sin a

where:

A_sw = area of shear reinforcement in one perimeter around the column (subject to A_sw,min)
s_r    = radial spacing of perimeters of shear reinforcement
f_ywd,ef = effective design strength of reinforcement (250 + 0.25d) ≤ f_ywd
d    = mean effective depth in the two orthogonal directions (in mm)
u₁   = basic control perimeter at 2d from the loaded area
sin a = 1.0 for vertical shear reinforcement

Where required each perimeter should have
A_sw = (v_Ed – 0.75 v_Rd,c)s_r u₁/(1.5 f_ywd,ef)

For further details see How to Design Concrete Structures using Eurocode 2: 7 Flat slabs and Concise Eurocode 2 Section 8.