# Rigid Columns in RF-/JOINTS Steel - Column Base

### Technical Article

A structural analysis does not only determine and design internal forces and deformations. It also ensures that the forces and moments in a structure are generated in a reliable way and applied to the foundation. Dlubal Software provides a wide range of products for structural analysis and design of steel and timber connections. The RF-/JOINTS Steel - Column Base add-on module allows you to design footings of hinged and restrained column bases. The design can be performed for both column base plates with or without stiffeners.

This article describes the cross-section designs of a column cast in a bucket foundation. This example is also described in the literature [1] .

#### System

The column is designed as a HEB 280 section. It is made of steel S 235 JR.

Figure 01 - System and Loading According to [1]

In the RF-/JOINTS Window 1.4, the geometry parameters of the column base are defined according to [1]. The selected clamping depth is 65 cm.

Figure 02 - Window 1.4 Footing in RF-/JOINTS

The parameters of the base plate are defined in Window 1.5.

Figure 03 - Window 1.5 Column in RF-/JOINTS

#### Internal forces

The following design internal forces are available.

N _{Ed} = 396.0 kN

V _{Ed} = 21.5 kN

M _{Ed} = -118.0 kN

#### Design of the required bucket depth

The minimum restraint depth due to the concrete strength proves to be governing.

Figure 04 - Window 3.1 Design - Summary Including Details of Required Bucket Depth

A minimum clamping depth of 54.86 cm is required, which is guaranteed with the selected depth of 65 cm.

#### Design of the ultimate limit state of the column cross-section

The distribution of forces and moments within the column base corresponds to the following distribution according to [1].

Figure 05 - Distribution of Forces and Moments in Column Base According to [1]

The normal stress from the maximum moment is determined as follows:

$${\mathrm\sigma}_\mathrm{Ed}\;=\;\frac{\mathrm N}{\mathrm A}\;+\;\frac{\max\;{\mathrm
M}_{\mathrm e,\mathrm d}}{{\mathrm W}_\mathrm y}\;=\;\frac{396,0}{131,0}\;+\;\frac{11.818,7}{1.380,0}\;=\;11,6\;\mathrm{kN}/\mathrm{cm}²$$

The following applies for the maximum shear stress:

$${\mathrm\tau}_\mathrm{Ed}\;=\frac{\max\;{\mathrm V}_{\mathrm e,\mathrm d}\;\cdot\;{\mathrm
S}_\mathrm y}{{\mathrm I}_\mathrm y\;\cdot\;\mathrm t}\;=\;\frac{310,18\;\cdot\;767,00}{19.270,00\;\cdot\;1,05}\;=\;11,76\;\mathrm{kN}/\mathrm{cm}²$$

The corresponding stresses and designs can also be found for the cross-section resistances.

Figure 06 - Window 3.1 Design - Summary Including Details of Column Section Resistance

#### Design of the column within the bucket

Figure 5 shows the locations relevant for the design. Section BB on the flexural compression side proves to be governing (location b in Figure 5):

The normal stress in direction X is determined as follows:

$${\mathrm\sigma}_{\mathrm X,\mathrm d}\;=\;\frac{-\mathrm N}{\mathrm A}\;-\;\frac{{\mathrm
M}_{\mathrm e,\mathrm b,\mathrm d}}{{\mathrm l}_\mathrm y}\;\cdot\;{\mathrm z}_1\;=\;\frac{-396,0}{131,0}\;-\;\frac{3.897,3}{19.720,0}\;\cdot\;9,8\;=\;-5,0\;\mathrm{kN}/\mathrm{cm}²$$

The following normal stress acts in direction Z:

$${\mathrm\sigma}_{\mathrm Z,\mathrm d}\;=\;0,45\;\cdot\;\frac{{\mathrm p}_\mathrm{Rd}}{\mathrm
t}\;\cdot\;{\mathrm\alpha}_\mathrm b\;=\;0,45\;\cdot\;\frac{12,34}{1,05}\;\cdot\;0,55\;=\;2,90\;\mathrm{kN}/\mathrm{cm}²$$

The following applies for the maximum shear stress:

$${\mathrm\tau}_\mathrm{Ed}\;=\;\frac{\max\;{\mathrm V}_{\mathrm e,\mathrm d}\;\cdot\;{\mathrm
S}_{\mathrm y,1}}{{\mathrm I}_\mathrm y\;\cdot\;\mathrm t}\;=\;\frac{310,18\;\cdot\;716,58}{19.270,00\;\cdot\;1,05}\;=\;10,99\;\mathrm{kN}/\mathrm{cm}²$$

In the design details of Window 3.1, you can find the corresponding stresses and ratios:

Figure 07 - Window 3.1 Design - Summary Including Details of Design of Column in Bucket

The analyzes are completed in the program by the design of the connection in the compression area and the welds, but not further elaborated here.

#### Summary

RF-/JOINTS Steel - Column Base can be used to design the base points of hinged and restrained columns. For a column cast in a bucket, the module analyzes the required bucket depth, the bearing capacity of the column cross-section, and the column's resistance within the column base with regard to the occurring tensile and compressive stresses. The analysis is completed by the design of the concrete compression resistance under the base plate as well as the design of the welds between the base plate and the column.

#### Reference

#### Keywords

Shaft foundation Quivers Depth of well Restrained column Column foundation Base plate Weld Depth of Span

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