Concrete punching shear verification formulas for slabs are similar to those used for the concrete shear verification in beams. In this case, instead of using the width of the member as it is done for beams, It is used a perimeter (critical perimeter). This is a concentric perimeter of the loaded area placed at a distance 2d from it, where d is the mean effective depth of the slab. This mean effective depth is calculated as the half of the sum of the effective depths of each orthogonal reinforcement direction.

No punching reinforcement will be necessary if the shear efforts in the critical perimeter is less than the concrete resisting one. This resistance is calculates as follows:

β is a coefficient to be applied when the support reaction is eccentric with regard to the control perimeter. For structures where the lateral stability does not depend on frame action between the slabs and the columns, and where the adjacent spans do not differ in length by more than 25%, the EC-2 provided approximate values for β (see calculation section below).

The punching shear force VEd in a foundation slab may be reduced due to the favourable action of the soil pressure.

In any case the maximum shear force has to comply with the following limitation:

Where the maximum shear force is defined as follows:

This limitation corresponds to the maximum shear effort in the perimeter of the loaded area u0 (perimeter of the column/support) which is different to the critial perimeter explained before, placed at a distance of 2d from the column/support.

When the condition provided above is not fulfilled, the geometry of the support/column has to be changed (increasing the loaded area to increase de Uo perimeter) or resistance of the concrete needs to be increased. In the case of failure in the critial perimeter U1, additional punching shear reinforcement has to be added.

Punching shear reinforcement

The concrete punching shear resistance with punching reinforcement is given by:

Lets break down this formula:

The first term, 0.75*VRdc, stands for the 75% of the concrete punching shear resistance without punching reinforcement.

The second term corresponds to the shear reinforcement resistance. The first part (1.5*d*Asw/Sr) stand for the quantity of reinforcement available the 1.5d length from our column/support. This is similar to the quantity of vertical shear reinforcement placed inside the compressed strut is a beam (to find an analogy with the strut and tie model).

This term is multiplied by the effective steel shear reinforcement resistance (Fywd,ef=250+0.25d in MPa) to obtain units of force, and it is divided by the perimeter*d to get stresses (same units as VRd,c).

It is also defined the perimeter Uout, which is the perimeter at which shear reinforcement is no longer required. The reinforcement has to be place, at least, until a distance k.d (k=1.5) before that perimeter. The first reinforcement perimeter has to be placed at a distance less than 0.5d from the loaded area and the distance between reinforcement perimeters has to be less than 0.75d as it is shown in the following picture:

The punching reinforcement could be closed stirrups, ties or bent bars. There are other prefabricated solutions in the market adas. En mercado el hay otras soluciones prefabricadas específicas para este tipo de refuerzos como los que se muestra a continuación: