Punching Shear Design According to Eurocode 2 in RFEM 6

Structural Modeling

In RFEM 6, the punching shear verification can be performed on both a 2D plate and a 3D structure. In the Concrete Design add-on, it is possible to select the relevant nodes for the punching shear verification. Thus, a structuring of the verifications, for example by levels, is very easily possible.

RFEM 6 automatically recognizes from the structural input the type of punching node (single column, wall corner, or wall end) as well as the position of the punching point (interior, edge, or corner column).

Critical Perimeter

The punching shear verification is to be performed on the so-called critical perimeter. According to 6.4.2, EC 2 [1] the critical perimeter for slabs is located at a distance of 2 d (d = effective depth of the slab) from the load introduction area. To determine the geometry of the critical perimeter, the column dimensions as well as slab openings up to a distance of 6 d from the load introduction area are to be considered. RFEM 6 automatically recognizes the modeled openings.

Critical Perimeter Around Column Considering Two Openings

In the case of floor slabs or foundations, the critical perimeter is usually located within 2 d from the column face. According to 6.4.4 (2) [1] an iterative calculation is required to determine the critical perimeter. The German National Annex [2] permits in the NCI to 6.4.4 (2) for floor slabs and slender foundations with λ = a_λ / d > 2 a simplified calculation (with a_λ = foundation projection). In this case, the critical perimeter may be assumed at a distance of 1 d. In RFEM 6, the iterative solution for determining the critical perimeter is generally performed for foundations/floor slabs.

Referenced Shear Force v_Ed

The design shear force referenced to the critical perimeter is calculated from Eq. 6.38, EC 2 [1]:

To account for the non-rotationally symmetric loading, the punching load V_Ed is increased by the load magnification factor β. For non-sway systems with span differences in the adjacent spans of less than 25%, the following β values may be used according to EN 1992-1-1, Figure 6.21N [1]:
β = 1.15 for interior columns
β = 1.4 for edge columns
β = 1.5 for corner columns
The German National Annex [2] supplements Figure 6.21N with the β factors for wall corners with β = 1.20 and for wall ends with β = 1.35, and adjusts the recommended value for the interior column to β = 1.10.

A generally valid method for determining the load increase factor β is described in Eurocode 2 [1] in Clause 6.4.3 (3). In this case, the factor β is determined assuming a fully plastic shear stress distribution on the critical perimeter. According to EN 1992-1-1 [1] Equation (6.39), the following is obtained:

Fully Plastic Shear Stress Distribution

While Equation (6.39), EN 1992-1-1 [1] only specifies the calculation of β for a uniaxial load eccentricity, the German National Annex [2] includes the extended Equation (NA.6.39.1) below for considering biaxial load eccentricity:

In RFEM 6, both of the above-mentioned options for calculating β are available. The default method selected is the model considering the fully plastic shear stress distribution.

RFEM 6 uses the design value of the shear force V_Ed for the punching shear verification. For the punching shear verification of columns, node supports, and single loads, the design value of the shear force can be determined from the column normal force, support reaction, or load value of the acting concentrated force.

In addition, RFEM 6 offers the possibility to define the critical perimeter and determine the shear force V_Ed acting there. The following two options are available:

• The shear forces present in the critical perimeter are integrated or smoothed over the entire critical perimeter. The resulting design shear force V_Ed must then be multiplied by the load magnification factor β (cf. Eq. 6.38 [1]). If the factor β is determined using the fully plastic shear stress distribution model, then the two bending moments M_Ed,x and M_Ed,y are also determined from the integration of the plate internal forces in the defined perimeter in the slab.

• The maximum value of the shear forces present in the perimeter is used for the punching design. With this method, the influence of the non-rotationally symmetric loading is taken into account by using the maximum value. A further increase of the shear force by the factor β is therefore omitted.

Although the use of the maximum value of the shear force in the perimeter is the most accurate method for determining the design value of the punching load, it is also the method most susceptible to singularity effects or, respectively, most endangered by them. It should be noted in particular that when shear forces are directly taken from the perimeter, sufficient refinement of the FE mesh in the punching area must be ensured. It is recommended to arrange at least two to three elements between the punching node and the critical perimeter by means of FE mesh densification.

Shear Stress Distribution in Section

For foundations and floor slabs, V_Ed may be reduced by the soil pressure within the iteratively determined critical perimeter, cf. 6.4.2 (2) [1]. If, according to the German National Annex [2], the critical perimeter is simplified and defined at 1 d for slender foundations, only 50% of the soil pressure may be taken into account. Both verification forms can be selected in RFEM 6.

Verification Method

When performing the punching shear verification, it is first checked whether the verification can be carried out without punching reinforcement.

Punching Shear Resistance without Punching Reinforcement

The punching shear resistance without shear reinforcement v_Rd,c is to be determined according to 6.4.4 (1), EN 1992-1-1 [1] as follows:
v_RD,c = C_RD,c ∙ k ∙ (100 ∙ ρ_l ∙ f_ck)1/3 + k₁ ∙ σ_cp ≥ (v_min + k₁ ∙ σ_cp)
with
C_Rd,c = 0.18 / γ_c for flat slabs
C_Rd,c = 0.15 / γ_c for floor slabs/foundations
k = 1 + √(200 / d)
ρ_l,x/y = A_sl,x/y / (b_w · d_x/y)
ρ_l = √( ρ_l,x ∙ ρ_l,y ) ≤ 0.02
A_sl = area of tensile reinforcement
k₁ = 0.1
σ_cp = normal stress on the critical perimeter
v_min = 0.035 · k^3/2 · f_ck^1/2

In the German National Annex [2], the above parameters are modified as follows:
C_Rd,c = 0.18 / γ_c for flat slabs
C_Rd,c = 0.18 / γ_c ∙ (0.1 ∙ u₀ / d + 0.6) for interior columns of flat slabs with u₀ / d < 4
C_Rd,c = 0.15 / γ_c for floor slabs/foundations
ρ_l = √( ρ_l,x ∙ ρ_l,y ) ≤ min [0.02 ; 0.5f_cd/f_yd]
vmin = (0.00525 / γ_c) ∙ k^3/2 ∙ f_ck^1/2 for d ≤ 600 mm
vmin = (0.00375 / γ_c) · k^3/2 · f_ck^1/2 for d > 800 mm

The punching shear verification without additional punching reinforcement is satisfied if v_Ed ≤ v_Rd,c. Due to the structurally difficult execution of shear reinforcement, the aim is usually to dispense with punching reinforcement and instead use the maximum applicable longitudinal reinforcement ratio ρ_l. In RFEM 6, the required longitudinal reinforcement ratio for avoiding punching reinforcement is determined. However, it is also possible to define the existing longitudinal reinforcement manually for the calculation of v_Rd,c.

Maximum Punching Shear Resistance v_Rd,max

If the verification without punching reinforcement cannot be fulfilled, the maximum punching shear resistance must be verified in the next step.

According to 6.4.5 (3) EN 1992-1-1 [1], the maximum punching shear resistance is to be verified at the column face. The length u₀ of the face to be considered is to be determined parallel to the critical perimeter and directly at the load introduction area. The maximum punching shear resistance v_Rd,max at the column face is to be determined according to 6.4.5 (3), EN 1992-1-1 [1] as follows:
v_Rd,max = 0.4 · ν ·f_cd
with ν = 0.6 · (1 - f_ck / 250) (f_ck in [N/mm²])

The acting design shear force at the column face is given by:
v_Ed,u0 = β · V_Ed / (u₀ · d)

The verification is satisfied if v_Ed,u0 ≤ v_Rd,max.

The German National Annex [2] does not perform the verification of the maximum punching shear resistance at the column face, but rather in the critical perimeter u₁ using Equation NA6.53.1 as follows:
v_Ed,u1 ≤ v_Rd,max = 1.4 · v_Rd,c,u1

Punching Shear Resistance with Punching Reinforcement

If the verification of v_Rd,max could be successfully performed, the required punching reinforcement is determined in the next step. The required punching reinforcement is to be determined by rearranging Equation 6.52 from EN 1992-1-1 [1]. The required reinforcement A_sw in one row is thus obtained as follows:

Arrangement of Punching Reinforcement in Control Perimeter

It should be noted that v_Rd,cs cannot be greater than k_max · v_Rd,c:

According to DIN EN 1992-1-1/NA [2], the amount of reinforcement in the first reinforcement row is to be increased by the factor κ_sw,1 = 2.5 and in the second reinforcement row by κ_sw,2 = 1.4.

The punching reinforcement is to be arranged up to a distance of 1.5 d from the outer perimeter. The required length u_out,ef of the outer perimeter, for which no punching reinforcement is required any longer, is to be determined according to Eq. 6.54, EC 2 [1] as follows:

Summary

The regulations for punching shear verification according to Eurocode 2 cannot be implemented effectively without a software solution. Examples include the calculation of the load magnification factor β according to the model with fully plastic shear force distribution on the perimeter or the iterative determination of the location of the critical perimeter for foundations. Furthermore, building layouts are becoming increasingly free-form and complex, so that regulations for applying any simplifications are not complied with and therefore cannot be applied. With the Concrete Design add-on and the verification of punching shear in selected nodes, all required data for the geometric determination of the critical perimeter as well as the design loads for the punching shear verification can be taken directly from the FEM input or FEM calculation. Thus, punching shear verification for columns, wall corners, and wall ends can be carried out very efficiently and conveniently. For columns, it is also possible to consider a column head reinforcement. The results of the performed punching shear verifications are displayed in clear tables with all intermediate results required for the respective verifications. A graphical display of the results, such as required punching reinforcement, shear force distribution, and punching shear resistances, is possible in the RFEM graphic window.