# 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 presents an example of cross-section designs of a column set in a concrete bucket foundation. This example is also described in [1].

#### System

The column is a cross-section HEB 280 made of steel S 235 JR.

Figure 01 - System and Loading
According to [1]

Geometry parameters of the column
base are set in Window 1.4 of RF-/JOINTS in compliance with [1]. The selected restraining
depth is 65 cm.

Figure 02 - Window 1.4 Footing in RF-/JOINTS

Base plate parameters 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 Required Bucket Depth

The governing value is the minimum restraining depth based on the concrete strength.

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

The minimum restraining depth of 54.86 cm is required. This is provided by the selected depth of 65 cm.

#### Design of Column Section Resistance

The force and moment distribution in the column corresponds to the following distribution, according to [1].

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

Normal stress from the maximum moment is calculated as follows:

$${\mathrm\sigma}_\mathrm{Ed}\;=\;\frac{\mathrm N}{\mathrm A}\;+\;\frac{\max\;{\mathrm M}_{\mathrm e,\mathrm d}}{{\mathrm W}_\mathrm y}\;=\;\frac{396.0}{131.0}\;+\;\frac{11,818.7}{1,380.0}\;=\;11.6\;\mathrm{kN}/\mathrm{cm}²$$

For the maximum shear stress, the following applies:

$${\mathrm\tau}_\mathrm{Ed}\;=\frac{\max\;{\mathrm V}_{\mathrm e,\mathrm d}\;\cdot\;{\mathrm S}_\mathrm y}{{\mathrm I}_\mathrm y\;\cdot\;\mathrm t}\;=\;\frac{310.18\;\cdot\;767.00}{19,270.00\;\cdot\;1.05}\;=\;11.76\;\mathrm{kN}/\mathrm{cm}²$$

The corresponding stresses and design details can also be found in the result table under Cross-section resistance.

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

#### Design of Column Inside Bucket

Figure [5] shows the design-relevant locations. The section B-B on the compression side is governing:

The normal stress in the X-direction is calculated 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 the Z-direction:

$${\mathrm\sigma}_{\mathrm Z,\mathrm d}\;=\;0.45\;\cdot\;\frac{{\mathrm p}_\mathrm{Rd}}{\mathrm t}\;\cdot\;{\mathrm\alpha}_\mathrm b\;=\;0.45\;\cdot\;\frac{12.34}{1.05}\;\cdot\;0.55\;=\;2.90\;\mathrm{kN}/\mathrm{cm}²$$

The maximum shear stress is:

$${\mathrm\tau}_\mathrm{Ed}\;=\;\frac{\max\;{\mathrm V}_{\mathrm e,\mathrm d}\;\cdot\;{\mathrm S}_{\mathrm y,1}}{{\mathrm I}_\mathrm y\;\cdot\;\mathrm t}\;=\;\frac{310.18\;\cdot\;716.58}{19,270.00\;\cdot\;1.05}\;=\;10.99\;\mathrm{kN}/\mathrm{cm}²$$

Design Details of Window 3.1 include the corresponding stresses and ratios:

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

The program completes the design by analyzing the joint in compression and the welds. However, these are not explained in this article.

#### Summary

RF-/JOINTS Steel - Column Base allows you to design footings of hinged and restrained column bases. In the case of a column set in a concrete bucket, the add-on module analyzes the required depth of the bucket, the resistance of the column section, and the resistance of the column inside the footing with regard to the arising tension and compression stresses. The analysis is completed by the design of the concrete under the base plate in compression as well as the design of welds between the base plate and the column.

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