According to 6.4.2 (2) [1], control perimeters at a distance less than 2 d must be considered if the concentrated load is opposed by a high counter pressure (for example, soil pressure on the foundation). The location of the critical control perimeter generally has to be determined iteratively. The German National Annex [2] allows a simplified calculation in the NCI to 6.4.4 (2) for floor slabs and slender foundations with λ = aλ / d > 2 (aλ = shortest distance between the loaded area and the foundation edge). In this case, the critical control perimeter can be set at a distance of 1 d.
In RFEM 6, the location of the critical control perimeter for foundations and floor slabs is generally determined iteratively. A manual definition of the 'Foundation' structural component type is not necessary. The program automatically recognizes the surface as a foundation based on the assigned soil bedding and considers the resulting relieving soil pressure when determining the governing punching load.
The resulting acting force is according to Equation (6.48) in [1] VEd,red = VEd - ΔVEd. Where ΔVEd according to 6.4.4 (2) is the resulting upward force (upward soil pressure minus the self-weight of the foundation) within the considered control perimeter.
The soil pressure that is to be considered as a favorable action in the punching shear design is automatically calculated in RFEM 6 from the existing soil contact stress. The magnitude of the surface load to be deducted, as well as its percentage, can be individually adjusted in the ultimate configurations. For the iterative determination of the critical control perimeter, it can also be specified that the maximum deductible surface load lies within the defined critical control perimeter, for example, at a distance of 1.0·d.
Example for the iterative determination of the critical control perimeter location
Below, the iterative determination of the critical control perimeter in RFEM 6 will be verified with a comparative calculation, in which the individual control perimeters are manually specified.
First, a small foundation slab (plate thickness dPL = 500 mm, length ∙ width = 2.00 m ∙ 2.00 m) is modeled in RFEM 6, on which a short reinforced concrete column (cross-section: rectangle 350 mm ∙ 350 mm, length L = 2.00 m) is placed. A concrete of strength class C30/37 is used. The self-weight of the entered structure is considered here. The column is loaded at the column head by vertical loads. In the self-weight load case, a vertical load of Gk = 800 kN is applied, and in the imposed load case, a vertical load of Qk = 450 kN. This results in a design value of the action of VEd = 1763.27 kN for the load combination LC1 = 1.35 ∙ G + 1.50 ∙ Q.
To determine the surface load to be deducted, the contact stresses σz are evaluated for LC2. For this example, a mean contact stress of σz = 438.12 kN/m² is determined for the governing load combination.
The position of the longitudinal reinforcement in the foundation slab can be defined in the 'Surface Reinforcement' tab. For this example, a concrete cover of d1 = 4.60 cm and d2 = 5.00 cm was specified.
This results in an effective depth d of 44.0 cm. A basic reinforcement for determining the punching shear resistance of the foundation slab was defined as 7.85 cm2/m.
After performing the calculation with the described input, a design criterion of 0.87 can be read. In the result details, the intermediate values for determining the resulting acting shear force VEd,red can be found.
The Concrete Design add-on determines the location of the critical control perimeter here at a distance lw,it = 0.345 m from the edge of the loaded area. This results in an area within the critical control perimeter of:
A = 0.345² ∙ π + 4 ∙ 0.345 ∙ 0.35 + 0.35² = 0.98 m²
The resulting counteracting shear force ΔVEd or resulting acting shear force VEd,red is: ΔVEd = 0.98 m² ∙ 438.12 kN/m² = 429.36 kN VEd,red = 1763.27 kN - 429.36 kN = 1333.91 kN
Verification of the iteratively determined critical control perimeter location
The result from the first calculation and the location of the critical control perimeter determined iteratively in RFEM 6 are to be verified in a second calculation.
For this, the location of the critical control perimeter can be manually specified in RFEM 6 before starting the calculation. A stepwise increase of the distance to the loaded area of ΔL = 0.05 m is applied. In total, punching shear is examined on 15 manually specified control perimeters at a distance of lw,def = 0.05 m - 0.75 m.
As shown in the figure above, it is recommended to copy the previously entered foundation including the loading several times for this calculation. This allows the 15 different calculation variants to be examined in one calculation run. In the ultimate configurations for 'Punching Shear', the distance to the loaded area can be individually specified for each punching point.
After performing the calculation with a user-defined specification of the critical control perimeter location for all 15 variants, the resulting results can be evaluated. A look at the following graphic shows that the result from the first calculation (with iterative determination of the critical control perimeter location) can be confirmed. The maximum design criterion lies in a range between lw,def = 0.30 - 0.35 m (previously iteratively determined distance lw,it = 0.345 m).
Below, the results from the calculation with manual specification of the critical control perimeter location can also be graphically evaluated in the form of an Excel diagram. Here, the quotient of the acting to the resisting shear stress (νEd,red / νRd,c) is plotted on the ordinate axis. On the abscissa axis, the quotient of the distance to the loaded area and the effective depth (ait / d) is plotted.
Reference values from the first calculation:
The results resulting from the first calculation with iterative determination of the critical control perimeter can thus be confirmed.