# Design of Foundation Rotation

### Technical Article

Using RF-/FOUNDATION Pro, it is possible to perform geotechnical design according to EN 1997‑1 [1] for single foundations. The following article explains the design of highly eccentric loading in the foundation core according to DIN EN 1997‑1, A 6.6.5 (see [3]).

For this, a foundation plate with a cantilever beam is designed in RF‑FOUNDATION Pro. The design of the rotational displacement of the foundation (serviceability limit state design) is carried out for the first and the second core width. Subsequently, the results from RF‑FOUNDATION Pro will be compared with a surface model in RFEM.

Further geotechnical designs and the designs of the steel cantilever beam are not explained in this article.

#### System, Loads, and Support Forces

In this example, a steel cantilever beam (cross‑section: HEA 160, structural steel S235) with a length of 2.50 m is rigidly connected to a foundation plate.

Figure 01 - Structural System with Loads

For this, a beam with a length of 2.50 m is modelled in RFEM. A rigid nodal support is arranged on this base point. The cantilever beam is subjected to vertical and horizontal forces on the column head. The load is entered in two load cases:

- Load Case 1 = Self‑weight
- Load Case 2 = Wind in + X

In Load Case 1, a vertical load of G_{k} = 35 kN is applied to the column head. Taking into account the self‑weight of the column, the support force of P_{z} = 35.76 kN results in Load Case 1.

In Load Case 2, a horizontal force of H_{k} = 10 kN is applied to the column head. Thus, the resulting support force P_{x} = 10.0 kN.

The foundation plate has the following dimensions:

#### Combinatorics for Ultimate and Serviceability Limit State Design

In RFEM, the following combinations are created for the ultimate and the serviceability limit state designs:

- Combination 1 (ULS) = 1.35 ⋅ G
- Combination 2 (ULS) = 1.35 ⋅ G + 1.50 ⋅ Q
- Combination 3 (SLS) = 1.00 ⋅ G
- Combination 4 (SLS) = 1.00 ⋅ G + 1.00 ⋅ Q

Figure 02 - Load Cases and Combinations

#### ULS and SLS Design of Foundation

To design the foundation plate, a new case is created in RF‑FOUNDATION Pro. In the design details, all geotechnical designs are deactivated except for the highly eccentric loading in the core.

Figure 03 - Settings in Design Details

Due to these detailed settings (see Figure 03), there are two tabs available for entering loads in Window ‘1.4 Loading’ of RF‑FOUNDATION Pro. In the ‘Structural (STR) and Geotechnical (GEO)’ tab, LC 1 and LC 2 are selected for the design. LC 3 and LC 4 are selected for the design in the ‘Characteristic Values’ tab. By selecting loading in the ‘Characteristic Values’ tab, the loads for the foundation rotation design are defined. In this case, the classification in ‘Permanent Action G’ or ‘Permanent and Variable Action G + Q’ must be respected.

According to [2], no gaping joint may arise due to the characteristic loading of the permanent actions. In other words, the ground pressure resultant must lie in the first core width. Due to the characteristic loading of the permanent and variable actions, the maximum of one gaping joint may arise up to the foundation centre, or at least half the foundation base must be subjected to compression. In other words, the ground pressure resultant must lie in the second core width.

The bending design of the foundation plate, which cannot be deactivated in RF‑FOUNDATION Pro and must always be performed, will not be discussed in the following. Only the results of the highly eccentric loading in the core should be evaluated.

In this example, the design criterion of zero results for the first core width as the vertical load was only entered in LC 1 (permanent load).

For the design of the second core width, the design criterion of 0.989 results.

First, the resulting design moment is determined in the x‑direction. For this, the moment in the soil joint from the foundation height and the amount of the support force P_{x} is added to the support moment about the y‑axis from RFEM:

The characteristic value of the vertical force in the soil joint results from the governing column normal force and the self‑weight of the foundation plate:

$${\mathrm V}_\mathrm{Res}\;=\;35.76\;\mathrm{kN}\;+\;1.80\;\mathrm m\;\cdot\;1.00\;\mathrm m\;\cdot\;0.25\;\mathrm m\;\cdot\;25.0\;\mathrm{kN}/\mathrm m^3=\;47.01\;\mathrm{kN}$$Accordingly, the resulting eccentricity e_{x} in the x‑direction is calculated as follows:

Since the load in the y‑direction is zero in this example, the eccentricity in the y‑direction is also zero.

The design of the second core width gives the result:

$$\begin{array}{l}\left(\frac{{\mathrm e}_\mathrm x}{{\mathrm b}_\mathrm x}\right)^2\;+\;\left(\frac{{\mathrm e}_\mathrm y}{{\mathrm b}_\mathrm y}\right)^2\;\leq\;\frac19\;=\;0.111\\\left(\frac{0.597\;\mathrm m}{1.80\;\mathrm m}\right)^2\;+\;\left(\frac{0\;\mathrm m}{1.00\;\mathrm m}\right)^2\;=\;0.110\;\leq\;\frac19\;=\;0.111\end{array}$$The design criterion is:

$$\frac{0.110}{0.111}\;=\;0.989$$The calculated result values are summarized in the ‘2.2 Governing Design Criteria’ result window of RF‑FOUNDATION Pro. For this, see the following figure.

Figure 05 - Results of Highly Eccentric Loading in Core

#### Checking Soil Contact Stresses in RFEM

The foundation plate dimensions designed in RF‑FOUNDATION Pro can optionally be checked in RFEM now. For this, it can be checked whether the gaping joint forms maximally up to the foundation plate centre, as described in [2], paragraph 3.4 under ‘Geotechnik’.

First, an RFEM model is created where the rigid nodal support is replaced by a foundation plate. The foundation plate has exactly the same dimensions as the single foundation with a design criterion of 0.989 designed in RF‑FOUNDATION Pro with regard to the foundation rotation.

Figure 06 - Dimensions of Foundation Plate in RFEM

The entered foundation plate must have a surface support in RFEM. In this case, it should be noted that this surface support should be defined with values for the spring in the z‑direction that are close to reality. The setting as ‘rigid’ in the z‑direction is not effective here.

Optionally, it is possible to determine the spring stiffness of the nodal support when specifying the soil profile in RF‑FOUNDATION Pro. Then, you can convert and set this spring stiffness for the single foundation in the spring stiffness for a surface support.

After the calculation, the ‘Contact Stresses σ_{Z}’ can be displayed for the LC that is governing for the foundation rotation design in RFEM under the results. Furthermore, it is possible to adjust the range of values for displaying results in the result panel in such a way that the contact stresses > 0 kN/m² are only displayed. This setting allows you to check graphically up to which location of the foundation the gaping joint arises. The following graphic shows the contact stresses σ_{Z} for LC4.

Figure 07 - Display of Contact Stresses Under Foundation Plate

It is obvious here that the gaping joint goes almost to the centre of the foundation. This is also confirmed by the result from RF‑FOUNDATION Pro and the resulting design criterion for the foundation rotation design.

The model for this article was created in RFEM 5 using RF‑FOUNDATION Pro. The design of highly eccentric loading in the core according to DIN EN 1997‑1 is also included in FOUNDATION Pro for RSTAB 8 in the same form, of course. The only difference is that the surface model of the foundation plate cannot be created in RSTAB in this form.

In RSTAB 8, this situation can be simulated by uniaxial loading (as shown in this example). For this, the foundation can be modelled using a beam with an elastic foundation (beam member). The beam can be provided with a member elastic foundation ‘Failure if negative contact stresses’.

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