Punching Shear Check Example 2

In the example calculation, a punching calculation will be made for a column whose dimensions are 100x50. Other parameters are listed as follows.

• Slab thickness : 27 cm

• Slab cover: 3 cm

• Material : C35/S420

• f_ctd = 1380.42 kN/m² (Concrete design tensile strength)

The slab useful height, d , is calculated;

d = ( Slab thickness - Slab cover ) = 27 - 3 = 24 cm

Column dimensions

c₁ = 100 cm c₂ = 50 cm

The punching circumference (u_p) is calculated at a distance d/2 from the column surface and is shown in the picture below. In this case, the following operations are performed to find the edges (b₁, b₂) of the punching.

In this case, the punching circumference, (u_p )_, and the punching area (A_z) obtained by multiplying the punching perimeter by the flooring useful height, d , is calculated as shown below.

The shear stresses plotted below are the punching stresses perpendicular to the slab plane.

The J values ​​are the sum of the polar inertia and second moments of inertia of the surfaces forming the punching area (A_z). According to TBDY Equation 7.28, this value is calculated according to the loading direction considering the γ_f coefficient .

Calculation of J and γ_f Coefficients for Strong Axis (Major Direction)

The coefficients γ_f(maj) and γ_v(maj) are calculated as follows.

To find the J _(maj) value, the following operations are performed.

c _(maj) is the center of gravity distance perpendicular to the moment vector, which is considered when finding the J value ( J _(maj) ) on the strong axis of the section. Since the punching circumference is rectangular, the c _(maj) value is calculated as follows.

The polar inertia and second moments of inertia are calculated as follows, respectively.

In this case, the sum of the polar inertia and second moments of inertia about the strong (major) axis of the section, J _(maj) , is found as follows.

Calculation of J and γ_f Coefficients for Weak Axis (Minor Direction)

The following steps are followed for the calculation of the γ _f(min) and γ _v(min) coefficients.

The J_(min) value is found as follows.

The c_(min) value is the center of gravity distance perpendicular to the moment vector, which is considered when finding the J value (J _(min)) on the weak axis of the section. Since the punching circumference is rectangular;

In this case, the polar moments of inertia and the second moments of inertia are found as follows, respectively.

In this case, the sum of the polar inertia and second moments of inertia about the weak (minor) axis of the section, J _(min) , is found as follows.

Finding Punching Stresses

The forces to be considered for punching stresses and the values obtained from the geometry are given below.

• V_d = 679.31 kN

• DM_d(maj) = 394.624 kNm

• DM_d(min) = 65.3914 kNm

• A_z = 0.9504 m²

• γ_f(maj) = 0.537

• γ_v(maj) = 0.463

• γ_f(min) = 0.660

• γ_v(min) = 0.340

• J_(maj) =0.2156608 m⁴

• J_(min) = = 0.0993968 m⁴ ,

• c_(maj) = 0.62 m

• c_(min) = 0.37 m

• c'_(maj) = 0.62 m

• c'_(min) = 0.37 m

The punching stresses are found by substituting all the above values in the stress formulas together with the internal forces essential to the punching design.

The absolute value of τ _pd,1 , τ _pd,2 is τ _pd,1 = 1322.795 kN/m ² . This obtained value is compared with the f_ctd value, which is the concrete design tensile strength.

τ_pd,1 = 1322.795 kN/m² < f_ctd = 1380.42 kN/m²

Upholstery punching strength is sufficient. These values ​​can also be compared with the report results.