# Iterative Determination of Basic Control Perimeter According to EN 1992-1-1 in RF-PUNCH Pro

### Technical Article

The RF‑PUNCH Pro add‑on module allows you to perform the punching shear design of floor slabs and foundation plates according to EN 1992‑1‑1. In the case of a floor slab, the basic control perimeter is applied according to 6.4.2 (1), EN 1992‑1‑1 [1] at a distance of 2d from the loaded area.

According to 6.4.2 (2) [1], control perimeters at a distance less than 2d should be considered where the concentrated force is opposed by a high pressure (for example, soil pressure on a base). The basic control perimeter area is usually determined iteratively.

The German National Annex [2], NCI to 6.4.4 (2), allows for a simplified calculation in the case of floor slabs and slender foundations with

$$\mathrm\lambda\;=\;\frac{{\mathrm a}_\mathrm\lambda}{\mathrm d\;>\;2}$$where a_{λ} is the shortest distance between the loaded area and the foundation edge).

In this case, the basic control perimeter can be applied at a distance of 1d.

Generally, RF‑PUNCH Pro determines the basic control perimeter area in foundations and floor slabs iteratively. In order to perform the punching shear design on a foundation or a floor slab, it is necessary to select ‘Foundation’ as ‘Structure Element’ in Window 1.5 Nodes of Punching Shear in RF‑PUNCH Pro.

Figure 01 - Window 1.5 with Definition of Structure Elements for Punching Shear Design

The resulting effective force is calculated according to Expression (6.48) of [1]:

$${\mathrm V}_{\mathrm{Ed},\mathrm{red}}\;=\;{\mathrm V}_\mathrm{Ed}\;-\;\triangle{\mathrm V}_\mathrm{Ed}$$According to 6.4.4 (2), ΔV_{Ed} is the net upward force within the control perimeter considered (upward pressure from soil minus self‑weight of base).

The ground pressure, which should be set as a favourable action, can also be entered in Window 1.5 Nodes of Punching Shear at the end of the table including details of the individual node of punching shear. The values of the deductible surface load and the percentage deductible portion should be specified here. Furthermore, it is necessary to define the maximum deductible surface load within the iteratively determined basic control perimeter. For this, ‘a_{crit}’ is set.

Figure 02 - Deductible Surface Load

#### Example of Iterative Determination of Basic Control Perimeter Area

The iterative determination of the basic control perimeter will now be checked in RF‑PUNCH Pro by using a comparative calculation, in which the individual control perimeters are set manually.

First, a small foundation plate (plate thickness d_{PL} = 500 mm, length ⋅ width = 2.00 m ⋅ 2.00 m) is modelled in RFEM and a short reinforced concrete column (cross‑section: rectangle 350 ⋅ 350 mm, length L = 2.00 m) is applied on it. As a material, the concrete of strength class C30/37 is set. The self‑weight of the structure will be considered, too. A column is loaded by vertical loads at the column head. The self‑weight load case includes the vertical load of G_{k} = 800 kN, the imposed load case includes the vertical load of Q_{k} = 450 kN. Thus, the load design value of V_{Ed} = 1763.27 kN results for the load combination CO1 = 1.35 ⋅ G + 1.50 ⋅ Q.

In order to determine the deductible surface load, the contact stresses σ_{z} for CO1 are calculated in RFEM. In our example, the contact stress of 458 kN/m² applies and is entered as the deductible surface load value in Window 1.5, as you can see in Figure 02.

The location of longitudinal reinforcement in the foundation plate can be defined in Window 1.4. In this example, the concrete cover of d_{1} = 5.50 cm and d_{2} = 6.50 cm is set. The resulting statical height d is 44.0 cm. Basic reinforcement for determining the punching resistance of the foundation plate is not specified in this example.

After performing the calculation using the data mentioned above, the design criterion of 0.87 can be found in the result window 2.1. Result details show the intermediate values used to determine the resulting applied shear force V_{Ed,red}.

Figure 03 - Results with Iterative Determination of Basic Control Perimeter Area

In this case, RF-PUNCH Pro determines the basic control perimeter area at a distance of l_{w,it} = 0.334 m from the edge of the loaded area. The resulting area within the basic control perimeter is:

Based on this, the resulting reducing shear force ΔV_{Ed} or resulting applied shear force V_{Ed,red} is:

Figure 04 - Display of Design Criterion V_{Ed} / V_{Rd,c} in Basic Control Perimeter

#### Check of Iteratively Determined Basic Control Perimeter Area

The results of the first calculation and the basic control perimeter area iteratively determined in RF‑PUNCH Pro will now be checked in the second calculation.

For this, the basic control perimeter area can be specified manually before starting the calculation in RF‑PUNCH Pro. The distance will be incrementally increased, starting with the basic control perimeter area of ΔL = 0.05 m. Punching on a total of 15 manually defined control perimeters at a distance from l_{w,def} = 0.05 m to 0.75 m will be examined.

Figure 05 - User-Defined Area of Basic Control Perimeter

As you can see in Figure 05, it is reasonable to copy the defined foundation (including loads) several times for this calculation. Thus, it is possible to examine 15 different calculation methods in one calculation process. In Window 1.5, you can set the distance to the loaded area individually for each node of punching shear.

Figure 06 - Definition of Distance to Loaded Area

After calculating all 15 variants with the user-defined area of the basic control perimeter, the results can be evaluated. The following figure shows that the result of the first calculation (with the iterative determination of the basic control perimeter area) can be confirmed. The maximum design criterion is between l_{w,def} = 0.30 and 0.35 m (the previous iteratively determined distance l_{w,it} = 0.334 m).

Figure 07 - Results of Calculation with User-Defined Basic Control Perimeter Area

Subsequently, the results of the calculation with manual definition of the basic control perimeter area can be evaluated graphically in an Excel chart. For this, the quotient of the resulting applied shear force and punching shear resistance (ν_{Ed,red} / ν_{Rd,c}) is applied to the vertical axis. The horizontal axis is used for the quotient of the distance to the loaded area and the static height (a_{it} / d).

Reference values from the first calculation:

$$\begin{array}{l}\frac{{\mathrm\nu}_{\mathrm{Ed},\mathrm{red}}}{{\mathrm\nu}_{\mathrm{Rd},\mathrm c}}\;=\;\frac{952\;\mathrm{kN}/\mathrm m²}{1,094\;\mathrm{kN}/\mathrm m²}\;=\;0.87\\\frac{{\mathrm a}_\mathrm{it}}{\mathrm d}\;=\;\frac{0.334\;\mathrm m}{0.44\;\mathrm m}\;=\;0.75\end{array}$$Figure 08 - Check of Iteratively Determined Basic Control Perimeter Area

The results of the first calculation using iterative determination of the basic control perimeter can thus be confirmed.

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