Punching Shear Verification

Punching shear phenomenon

The risk of punching shear exists in slabs subjected to bearing or point loads. This occurs when a concentrated load or a reaction acts on a relatively small area of a slab or foundation, generally referred to as the loaded area.

For low load magnitudes, tangential strains exceed radial strains. Consequently, radial cracks form first, and only at higher load levels do circular cracks develop. Punching shear failure is a brittle collapse mechanism that occurs without warning.

In this regard, the standards provide for the verification of shear resistance along certain perimeters, defined as “effective perimeters“.

Effective perimeters

In this context, design standards require the verification of shear resistance along specific perimeters, known as effective perimeters.

In the Italian NTC 2008, the calculation procedure for punching shear verification of concrete slabs was not explicitly defined. Only guidance on the effective perimeter was provided, leaving the designer free to adopt a suitable failure criterion.

NTC 2008 states:
“Punching shear resistance must be evaluated, using formulas of proven reliability, based on the tensile strength of the concrete, considering the stress distributed over an effective perimeter located at a distance of 2d from the loaded area.”

NTC 2018 and Eurocode 2

The new Italian NTC 2018, in addition to specifying the effective perimeter for punching shear design, requires reference to the relevant provisions of Eurocode 2 for:

• elements without shear reinforcement (§6.4.4);
• elements with shear reinforcement (§6.4.5).

According to EC2, punching shear verification must be performed along an effective perimeter located at a distance of 2d from the column perimeter, where d is the effective depth of the slab.

The effective depth d is calculated as the average of the effective depths in the X and Y directions.

Verification perimeters

Punching shear verification must be carried out on two effective perimeters:

• a critical perimeter, located at 2d from the column face;
• an external perimeter, used to verify that shear stresses decrease below the allowable limit.

If the verification on the critical perimeter is not satisfied, punching shear reinforcement must be provided.

AUDIT PERIMETERS

The punching check must be carried out on two effective perimeters:

6.53) Perimeter flush with pillar U₀                             v_and < v_Rd,max

6.47) Effective perimeter U₁                                         v_and < v_Rd,c

If this verification is not satisfied, it is necessary to insert special punching shear-punching reinforcements as proposed in paragraph 6.4.5 of EC2 (see_and < v_Rd,cs). It is also advisable to calculate the perimeter U_out beyond which the presence of shear reinforcement is not required (6.54).

The calculation stress shear stress, as proposed by the Eurocode, is calculated by the ratio of the punching stress V_and of the column and the lateral surface, of the solid inscribed in the verification perimeter, amplified by a coefficient β.

Verification 6.53) In the case of flush with the column design, the side surface area is calculated as the product U₀*d, with U₀ the perimeter of the column considered and the useful height of the section described above.

Verification 6.47) In the case of the test along the effective perimeter, the lateral surface area shall be calculated as the product U₁*d, with U₁ the effective perimeter considered is of the useful height of the section described above. Below is an image with the example of calculation of the perimeters described above for a rectangular column with sides C₁ and C_2.

The amplification β coefficient is dependent on the eccentricity (and_x and it is_y), calculated as the distance of the infinitesimal stretch of the perimeter from the axis around which the moment M acts_edX and M_edy, and the geometry of the column.

However, given the burden of calculation for the amplification coefficients, the Eurocode recommends adopting a series of approximate values to be used based on the arrangement of the column in the plan of the concrete slab, distinguishing internal, edge and corner columns.

In addition, the punching stress stress can be reduced in the case of a foundation slab, due to the favorable effect of soil pressure.

Plates without shear reinforcement

The punching resistance in the case of plates without shear reinforcement is entrusted to the resistant mechanisms of a comb model (meshing of the aggregates, pin effect, comb effect), as recommended in paragraph 6.4.4 of the Eurocode.

This resistance will be a function of the useful height d within the coefficient k (contribution of inert meshes), of the geometric percentage of reinforcement ρ (contribution of the pin effect), calculated as an average between the percentages in the x and y directions, by the characteristic cylindrical strength f_ck (resistente alla sezione d’incastro) e dallo sforzo di compressione della piastra. Tale resistenza dovrà essere superiore alla minima v_min del solo calcestruzzo.

Plates with the presence of shear reinforcement

The punching resistance in the case of plates equipped with shear reinforcement is the sum of two contributions.

1. The first contribution is 75% to the resistance described above
2. the second contribution, on the other hand, comes to be the strength of the inserted shear reinforcements. The latter term is proportional to the reinforcement that is within the perimeter of 1.5d from the section of the column, to the effective strength of the reinforcement that is taken less than or at most equal to the calculation strength of the steel and to the α angle of inclination of the reinforcements (α=90 vertical reinforcements such as Nelson rungs).

The flush punching test is satisfied if the tangential stresses are less than the maximum resisting stresses v_Rd,max  calculated as described in paragraph 6.3N of the Eurocode. This resisting stress is calculated using the calculation strength of the concrete and a coefficient υ that takes into account the cracking effect.

If punching rebar needs to be inserted, EC2 recommends calculating the U-perimeter_out beyond which shear reinforcement is not required. This perimeter is simply obtained from the formula for calculating the acting shear stresses, setting the shear stresses equal to the punching resistance value for the elements without shear reinforcement and obtaining the perimeter in question as an unknown.

In addition, the Eurocode recommends that the most distant reinforcement should not be placed beyond a distance of k times d (useful height) within U_out, with k advisable to take 1.5.

PRACTICAL APPLICATION PRO_SAP

The example proposed with regard to the punching verification according to EC2 was carried out considering a 3-storey building with concrete slab slabs and foundation slab.

The concrete slabs have a thickness of s=20cm, concrete cover c=3cm, a reinforcement mesh of φ10/20cm in the x and y directions. A class c25/30 concrete and B450C steel were used for the bars.

PRO_SAP automates punch checks.

It calculates and graphs the U1 effective perimeter and performs the 6.47 and 6.53 checks mentioned above.

If punching reinforcement is required, PRO_SAP calculates it automatically.

Outside the critical perimeter, however, PRO_SAP check that the tangential stress is less than the limit for non-shear plates

Verification 6.53

From the analyses carried out, the ratio δ = v was obtained_and / v_Rd,max for the 6.53 EC2 verification mentioned above. This ratio is less than unity, so it satisfies the Eurocode with a value of δ = 0.63 .

Verification 6.47

Then we derived the ratio δ = v_and / v_Rd,c for the 6.47 EC2 verification mentioned above. This ratio is greater than unity, in fact it is δ = 2.15, so a special punching shear-punching reinforcement must be inserted in the point under consideration.

The punching shear reinforcement, obtained as required by paragraph 6.4.5 of EC2, has a minimum value of A_SW = 42.45 cm² distributed within the effective perimeter U_out , a perimeter calculated as recommended by Eurocode in EC2 formula 6.54.

PRO_SAP, moreover, returns an amplification coefficient of d associated with the perimeter U_out. This coefficient is equal to K’ = 6.13.

SUMMING UP

1. The 2008 Construction Technical Standards did not specify the calculation procedure for performing the verification of the plates (but only gave indications on the effective perimeter), while the Construction Technical Standards 2018 specify to refer to the EC2 Eurocode;
2. The necessary punching checks are carried out on two effective perimeters:

6.53) Perimeter flush with pillar U₀       v_and < v_Rd,max

6.47) Effective perimeter U₁                  v_and < v_Rd,c

3. If these checks are not satisfied, it is necessary to insert special punching shear-punching reinforcements (e.g. Nelson Type Rungs, Inclined Shaped By An α Angle, Unifer Reinforcement System, Reinforcing Truss);
4. It would be expensive to manually determine the critical perimeters and make the checks, PRO_SAP automates them, plus also check that the tangential stresses outside the effective perimeter comply with the minimum resistant values of the concrete.

PRO_SAP automatically draws the reinforcements necessary for punching checks post and a video course with a practical application.

Eng. Giuseppe Meringolo
Eng. Nicolò Rossetti