# 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 purpose, a foundation plate in RF-FOUNDATION Pro is designed on which a jaw support has been applied. The analysis of foundation rotation (design in serviceability limit state) is performed for the 1st and 2nd core width. Subsequently, the results from RF-FOUNDATION Pro will be compared with a surface model in RFEM.

Additional geotechnical designs as well as designs of the steel inner column support are not part of this article.

#### System, loading, and support forces

For this example, a steel pillar collar (cross-section: HEA 160, steel S235) with a length of 2.50 m and rigidly connected to a foundation plate.

Figure 01 - Structural System with Loads

In RFEM, a beam with a length of 2.50 is modeled for this purpose. At its base, a rigid nodal support is arranged. The crutch column is subjected to vertical and horizontal forces at 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. Considering the independent weight of the column, load cell 1 results in a support force of P _{z} = 35.76 kN.

In load case 2, a horizontal force of H _{k} = 10 kN is applied to the column head. Thus, the support force P _{x} = 10.0 kN is obtained.

The following dimensions are provided for the foundation plate:

Length L = 1.80 m

Width B = 1.00 m

Thickness t = 0.25 m

#### Combinatoria for the design of the ultimate limit state and the serviceability

In RFEM, the following combinations are created for the design in the ultimate limit state as well as in the serviceability limit state:

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

#### Foundation check in the ULS and SLS

RF-FOUNDATION Pro creates a new case for the design of the foundation plate. In the design details, all geotechnical designs are deactivated, with the exception of the analysis of the foundation rotation.

Figure 03 - Settings in Design Details

These detailed settings (see Figure 03) provide two tabs for the load input in the "1.4 Loading" window in RF-FOUNDATION Pro. In the "Structural Design (STR) and Soil (GEO)" tab, the COs 1 and 2 are selected for the design. COs 3 and 4 are selected for design in the "Characteristic Values" tab. Selecting the loading in the "Characteristic Values" tab defines the loads for the analysis of the foundation rotation. Attention must be paid to the classification in "Permanent Action G" or "Permanent and Variable Action G + Q".

According to [2] , no gaping joint may arise due to the characteristic loading from permanent actions. This means The resultant pressure has to lie in the 1st core range. Due to the characteristic loading due to permanent and variable actions, a gaping joint may only be created up to the middle of the foundation or at least half of the floor area must be subjected to compression. This means The resultant pressure has to lie in the 2nd core width.

We will not go into the following regarding the bending design of the foundation plate, which can not be deactivated in RF-FOUNDATION Pro and must always be carried out. Only the results from the analysis of the foundation rotation should be evaluated.

For this example, the criterion criterion for the 1st core width is zero because only one vertical load was entered in LC1 (permanent load).

For the design of the 2nd core width, a design criterion of 0.989 is obtained.

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

M _{Res, x} = 25.55 kNm + 0.25 m · 10 kN = 28.05 kNm

The characteristic value of the vertical force in the soil joint results from the governing ultimate axial force and the self-weight of the foundation plate:

V _{Res} = 35.76 kN + 1.80 m · 1.00 m · 0.25 m · 25.0 kN / m³ = 47.01 kN

Thus, the resulting eccentricity ex in x-direction is calculated as follows:

${\mathrm e}_\mathrm x\;=\;\frac{28,05\;\mathrm{kN}/\mathrm m}{47,01\;\mathrm{kN}}\;=\;0,597\;\mathrm m$

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

The design of the 2nd core width results in:

$\begin{array}{l}\left(\frac{{\mathrm e}_\mathrm x}{{\mathrm b}_\mathrm x}\right)^2\;+\;\left(\frac{{\mathrm e}_\mathrm y}{{\mathrm b}_\mathrm y}\right)^2\;\leq\;\frac19\;=\;0,111\\\left(\frac{0,597\;\mathrm m}{1,80\;\mathrm m}\right)^2\;+\;\left(\frac{0\;\mathrm m}{1,00\;\mathrm m}\right)^2\;=\;0,110\;\leq\;\frac19\;=\;0,111\end{array}$

The check criterion results in $ \ frac {0,110} {0,111} \; = \; 0.989 $.

The calculated result values are documented summarized in RF-FOUNDATION Pro in the result window "2.2 Governing Design Titles." See also the following graphic.

Figure 05 - Results of Highly Eccentric Loading in Core

#### Checking the contact stresses in RFEM

The Foundation Plate Dimensions verified in RF-FOUNDATION Pro can now optionally be checked in RFEM. For this, it is possible to check, as described in [2] under "Geotechnical Engineering" in clause 3.4, whether the gaping joint is formed at the maximum up to the center of the foundation plate.

First, an RFEM model is created for which the rigid nodal support is replaced by a foundation plate. The foundation plate is given exactly the same dimensions as the single foundation with a design criterion of 0.989 that has been verified in RF-FOUNDATION Pro with regard to the foundation rotation.

Figure 06 - Dimensions of Foundation Plate in RFEM

The input foundation plate must be provided with a surface support in RFEM. It should be noted that this surface support should be defined with realistic values for the spring in z-direction. The setting as "rigid" in z-direction is not expedient.

In RF-FOUNDATION Pro, you can optionally determine the spring stiffness of the nodal support by specifying a soil profile. This spring stiffness for the single foundation can then be converted and applied by the user into a spring stiffness for a surface support.

After the calculation, RFEM shows the "Contact stresses σ _{Z} " for the COV relevant for the determination of the foundation rotation in the results. Furthermore, you can adjust the value range for the display of results in the result panel so that only contact stresses> 0 kN / m² are displayed. With this setting, you can then graphically check up to which point of the foundation a gaping joint is formed. The following graphic shows the contact stresses σ _{Z} for CO4.

Figure 07 - Display of Contact Stresses Under Foundation Plate

It can be seen here that the gaping joint projects almost to the center of the foundation. This is also confirmed by the result from RF-FOUNDATION Pro and the design criterion given there for the determination of the foundation rotation.

The model created for this article was edited in RFEM 5 with RF-FOUNDATION Pro. The design of foundation rotation according to DIN EN 1997-1 is, of course, also included in FOUNDATION Pro for RSTAB 8 in the same form. In RSTAB, only the surface model of the foundation plate can not be represented in this way.

In RSTAB 8, this situation could also be represented for a uniaxial loading (as shown in this example). For this, the foundation could be modeled by a foundation beam (beam member). The member can be provided with a "Restraint if Contact Voltages Negative" with a member foundation.

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