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

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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] , perimeters must be considered at a distance of less than 2 d if the concentrated load is counteracted by a high back pressure (for example, soil pressure on the foundation). The position of the critical perimeter must usually be determined iteratively.

The German National Annex [2] allows for a simplified calculation in the NCI to 6.4.4 (2) for floor slabs and slender foundations with λ = a λ/d> 2 (a λ = shortest distance between load application surface and foundation edge). In this case, the critical perimeter can be applied at a distance of 1 d.

RF-PUNCH Pro generally determines the position of the critical perimeter for foundations/floor slabs iteratively. To perform the punching shear design on a foundation or a floor slab, make sure in RF-PUNCH Pro that the "Foundation" is selected as "Component" in the 1.5 Punching Nodes window.

Figure 01 - 1 - Window 1.5 with Definition of Structure Elements for Punching Shear Design

The resulting acting force is calculated according to Equation (6.48) in [1] V Ed, red = V Ed - ΔV Ed . Where ΔV Ed according to 6.4.4 (2), the resulting upward force (upward soil pressure minus the foundation residual load) is within the considered perimeter.

The input of the sole pressure, which is to be applied as favorable for the punching shear design, is also found in the window "1.5 Punching Nodes" at the end of the table of punching node details. The size of the surface load to be deducted as well as the percentage deductible part of it are to be specified by the user. Furthermore, it is necessary to define for the iterative determination of the critical perimeter that the maximum deductible surface load is within the iteratively determined critical perimeter. For this, select "a_crit".

Figure 02 - 2 - Deductible Surface Load

Example for the iterative determination of the position of the critical perimeter

In the following, the iterative determination of the critical perimeter in RF-PUNCH Pro will be checked with a comparative calculation in which the individual perimeters are specified manually.

First, a small foundation plate (plate thickness d PL = 500 mm, length ∙ width = 2.00 m ∙ 2.00 m) is modeled in RFEM on which a short reinforced concrete column (cross-section: Rectangle 350 mm ∙ 350 mm, length L = 2.00 m). The material used is a concrete of strength class C30/37. The self-weight of the entered structure is also taken into account. The column is acted upon by vertical loads on the column head. In the dead load load case, a vertical load of G k = 800 kN is applied, in the payload load case, a vertical load of Q k = 450 kN. This results in a design value of the action of V Ed = 1763.27 kN for the load combination CO1 = 1.35 ∙ G + 1.50 ∙ Q.

To determine the surface load to be subtracted, the contact stresses σ z for CO1 are evaluated in RFEM. For this example, a contact stress of 458 kN/m² is applied and entered as the size of the surface load to be subtracted according to the previous graphic in window 1.5.

The position of the longitudinal reinforcement in the foundation plate can be defined in Window 1.4. For this example, a concrete cover of d 1 = 5.50 cm and d 2 = 6.50 cm has been specified. This results in a static height d of 44.0 cm. A basic reinforcement for determining the punching resistance of the foundation plate is not specified in this example.

After the calculation has been carried out with the described data, a check criterion of 0.87 can be read in the result window 2.1. In the result details, you can find the intermediate values for determining the resulting applied shear force V Ed, red .

Figure 03 - 3 - Results with Iterative Determination of Basic Control Perimeter Area

RF-PUNCH Pro determines the position of the critical perimeter at a distance l w, it = 0.334 m from the edge of the load application area. This results in an area within the critical perimeter of:
A = 0.334² ∙ π + 4 ∙ 0.334 ∙ 0.35 + 0.35² = 0.94 m²

The resulting counteracting shear force ΔV Ed or the resulting acting shear force V Ed, red results in:
ΔV Ed = 0.94 m² ∙ 458 kN/m² = 430.78 kN
V Ed, red = 1763.27 kN - 430.78 kN = 1332.49 kN

Figure 04 - 4 - Display of Design Criterion VEd / VRd,c in Basic Control Perimeter

Check of the iteratively determined position of the critical perimeter

The result of the first calculation and the position of the critical perimeter determined in RF-PUNCH Pro iteratively will be checked in a second calculation.

For this, the position of the critical perimeter can be specified manually in RF-PUNCH Pro before starting the calculation. In this case, a stepwise increase of the distance to the load application area of ΔL = 0.05 m is applied. In total, punching is analyzed on 15 manually defined perimeters at a distance of l w, def = 0.05 m - 0.75 m.

Figure 05 - 5 - User-Defined Area of Basic Control Perimeter

As shown in the figure above, it is recommended to copy the previously entered foundation (including loading) several times for this calculation. Thus, the 15 different calculation variants can be analyzed in one calculation run. In Window 1.5, you can specify the distance to the load introduction surface individually for each punching point.

Figure 06 - Definition of Distance to Loaded Area

After performing the calculation with user-defined specification of the position of the critical perimeter 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 position of the critical perimeter) can be confirmed. The maximum design criterion is in a range between l w, def = 0.30 - 0.35 m (previously iteratively determined distance l w, it = 0.334 m).

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

Subsequently, the results from the calculation with manual specification of the position of the critical perimeter can also be evaluated graphically in the form of an Excel diagram. In this case, the quotient of the resulting acting shear force and the punching resistance (ν Ed, redRd, c ) is applied to the ordinate axis. The quotient of the distance to the load application area and the static height (a it/d) is plotted on the axis of abscissa.

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 resulting from the first calculation with iterative determination of the critical perimeter can thus be confirmed.

Reference

[1]   Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings; EN 1992-1-1: 2004 + AC: 2010
[2]  National Annex - Nationally determined parameters - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings; DIN EN 1992-1-1/NA: 2013-04

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Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

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Punching shear design of foundations and slabs with nodal and line supports

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