# Background

The EU steel column calculator can be used to calculate both the demands as well as the resistance of a straight column.
The analysis capabilities include:

• Point Axial and lateral forces
• Point moments in the major and minor axis (excluding torsion)
• Line Loads (including linearly varying)
• Distributed Loads (including varying tributary width). For details on tributary widths, refer to article, What is tributary width?

The design capabilities include:

• Cross-section classification (Class 4 section design not available)
• ULS: Axial compression and tension resistance (EN 1993-1-1:2005 Cl 6.2.3 & 4)
• ULS: Reduced bi-axial moment resistance taking into account axial and shear forces (EN 1993-1-1:2005 Cl 6.2.5)
• ULS: Shear resistance (EN 1993-1-1:2005 Cl 6.2.6)
• ULS: Lateral torsional buckling resistance of uniform member in bending (EN 1993-1-1:2005 Cl 6.3.2)
• ULS: Buckling resistance in combined bending and axial compression (EN 1993-1-1:2005 Cl 6.3.3)
• ULS: Flexural buckling resistance in axial compression (EN 1993-1-1:2005 Cl 6.3.1)
• ULS: Shear web buckling resistance of uniform member (EN 1993-1-5:2006 Cl 5.1-5.5) including transverse stiffeners.
• SLS: Deflection analysis
• Penetrations or fastener holes (checks if they may be ignored)

Coordinate System:

Within ClearCalcs, the z-z axis is taken axis as the longitudinal axis of a member and the x–x and y–y axes to denote the respective major and minor axes. In the Eurocode suite the longitudinal axis, in contrast, is the x–x axis and the y–y and z–z axes are the respective major and minor axes. The ClearCalcs terms are used below.

# Tutorial

In this worked design example, we will go through the design process of a single-span simply supported steel column with axial and lateral point loads. The span is 7.2m long and the column is laterally restrained at the location of concentrated loads.

The calculation (including for biaxial moment) may be accomplished in any Steel Column Calculator shown below. When choosing concentric-loading only, options for bending moment/shear checks will only be shown once lateral forces/eccentricities are applied. We will choose an "Interior Single Story Column" as the most similar to our final column arrangement.

## 1. Entering our key properties

First, we enter the key properties of our column:

• Total Column Length - The length between the start and end of the column, irrespective of the support conditions.
• Length between lateral restraints - Let’s assume that the column is braced at concentrated load locations, so the length between lateral restraints is equal to a third of the total column span of 7.2m. Note that effective length is defined about both axes, as well as separately for lateral torsional buckling. Where effective lengths are the same in both axes for flexural buckling, the section will always buckle in the minor axis.

• Position of Supports from Left - The support conditions may be at any position along the column. A cantilever can be created on either end by moving the support condition away from "0" or the "Total Column Length"

## 2. Informational and National Annexes

Eurocode allows location-specific factors and/or calculation methods to be utilised. These are usually stipulated within National Annexes to EN1993-1-1:2005. The following customisations are provided within ClearCalcs:

• Partial Factors for cross-section resistance - The recommended values within EN1993-1-1:2005 Cl 6.1(1) are provided by default, however, modified values should be used specifically to the relevant National Annex. As we are designing this example in accordance with the UK annex, we will amend the Gamma_M2 value to 1.1 from the default 1.25.

• Interaction Factors for compression and bending buckling resistance - 2 methods are provided within the informational annexes. The engineer should consider both the national annex requirements as well as the validity of each method for the type of sections they are designing. Annex A has been chosen, which is allowed for doubly-symmetric sections in NA2.21 of NA+A1:2014 to BS EN 1993-1-1:2005.

• Deflection Limits - These vary based on the type of the structure, whether it is a column or beam, as well as national annex preferences. Extension limits are not provided, however where differential deflections of multiple columns may induce secondary impacts, a separate check should be conducted. In this example, we may use NA+A1:2014 to BS EN1993-1-1:2005 Table NA.3 (In each storey of a building with more than one storey -> L/300). These may be adjusted within Project Defaults which apply to all designs within the project, however in this case we will amend them specifically for this column.

NOTE: The column calculator can accommodate any combination of axial and bending moment about either or both axes. E.g. Calculations for bending moment/shear will only be available where lateral loads/eccentricities are applied. Any calculator template

• Axial force - This may be applied as a point load at any location along the column. The self-weight of the member may additionally be added via the toggle. Axial Loads applied in either axes are combined together. This enables linking vertical loads from beams coming in from both axes.
• Axial Eccentricity - Axial Eccentricity may be applied in either x- or y- directions. This can be set as a custom option or one of the default eccentricities may be set as listed below. It is important to familiarise yourself with the logic used for each option, which may be obtained by expanding the explanatory notes for the "Default Eccentricity for Bending about ..." as shown in the figure below.

• Load Direction - Where all the loads are applied in one direction (as below) the sign of lateral loads is not important as all checks are conducted with the absolute moments for symmetric sections about the major

• Lateral Point Loads - We apply the loads at the 1/3 and 2/3 of the column length (2400mm and 4800mm). Note how the _"Capped" _axial eccentricity value is automatically inserted for every load created. This may be overridden on a load by load basis where required.

We can now verify that our loads are all properly placed:

Note that the loads shown here are, by default, unfactored. For the factored combinations, you can visualise the applied loads on the right summary column, and choose the combination. The load combination can easily be changed with the dropdown above the graphics.

• Imposed Load factors - based on EN 1990:2002, Table A1.1 are chosen based on the category selection shown below. These populate the "Imposed Load Factors" to be used in the remainder of the calculation.

• Snow Location Category - may be accessed in the _"Project Defaults" _tab on the sidebar.
• Custom load factors - these may be amended in "Project Defaults" tab on the sidebar. Note this will affect load factors for all calculations in your current project. Go to "Load Combinations" section and change the "Load Combination Factors" to custom. This opens a range of options for "Imposed" load factors as well as "Environmental" factors:

## 5. Section selection

At this point, we are ready to revise our member size. We go back to our "Member Type" tab and search for a utilisation close to but not exceeding 100%. The currently selected member is governed by the L/300 deflection limit. This limit may be further discussed with the client/authorities if it is applicable for the building structure being designed. However, in this case, we will amend the section size to obtain a compliant deflection, utilising also the handy filter bar.

The four right-most columns indicate the utilization for five different checks – Axial Compression, Moment about major and minor axis, characteristic deflection, and Governing Limit. The governing column considers all checks and validation requirements within the entire calculation. A cross will signify that a particular requirement is not satisfied and no utilisation may be calculated. Ideally, we want the minimal weight section that will satisfy all three modes. It is then a matter of scrolling to find the best cross-section.

Looking through, we find a candidate – 300 x 200 x 8.8 RHS.

That’s it! We’ve now designed our column!

## 6. Summary of results and internal force diagrams

Once we’ve got our column design, we can quickly glance at relevant values to make sure everything corresponds to what we’d expect. On the right panel is the summary section, where we find things such as the critical moment demand and capacity, shear, moment and deflections. Where a calculation for lateral torsional buckling or web shear buckling was required based on Eurocode criteria, totals will also be shown.

We can also look at the shear, bending and deflection diagrams to make sure they correspond to what we anticipate.

For deflections, we need to switch the load case to reflect a serviceability load case – for here, it is simply “Service CHAR: Imposed Leading Variable”. We can scroll down the graph to see exact deflection values at different points. We clearly see that our deflection is limited by the 5mm hard limit we set. We may need to consider whether that hard limit is in fact required for this specific structure.

While the previous steps are all that is required to design our column, it may be desirable to improve the performance of the selected column by considering the following.

• Penetrations or fastener holes - For bending capacity checks, any reduction due to penetrations in a tension flange or tension part of the neutral axis may be ignored subject to certain limits being satisfied. A check is conducted below of a 14mm diameter hole for 12 diameter bolt holes.

• Moment Distribution - Several options are provided to amend the buckling capacity based on "actual" bending moment profiles. ClearCalcs defaults all options to the worst-case bending moment profile (single curvature constant bending moment). C_1 may be amended for lateral torsional buckling checks and the ratio of end moments for bending/axial interaction may be amended using the psi factors.

• Shear Buckling web stiffeners - For large shear loads in thin-webbed sections. Transverse web stiffeners may increase the load at which the web will buckle.

• Buckling Interaction Factors - Annex A and Annex B methods are implemented in ClearCalcs, however higher capacities are usually obtained using Annex A, which may not be allowed for every section (non doubly symmetric

This concludes this tutorial on designing a steel column per EN1993-1-1:2015 with ClearCalcs.

## Assumptions and Limitations

ClearCalcs fully exposes all code calculations to see every step of the process employed to design the column. Therefore, the engineer should have confidence that they can look at every calculation and conditional statement that is used to derive the final result. A summary of assumptions is provided below:

• Columns are computed by a chosen limit state and load combination. It is up to the user to choose limit states to determine the worst loading case combination. These may be viewed and/or modified in Project Defaults.
• Hollow sections are analysed as cold-formed (more conservative than hot-finished) for the purposes of buckling checks)
• Flexural torsional buckling (Cl 6.3.1.4 EN1993.1.1:2005) is not checked as the database hot-rolled sections and hollow sections will always have more critical flexural buckling limits.
• Supports are equally applied about both axes (i.e. fixed in bending about major and minor axes)

## References

The worked example above is based on " Example 6.9, Gardner, Nethercot, 2011, Designers Guide to EN-1993-1-1-Eurocode-3"

## Get in Touch with ClearCalcs

Chat with our Customer Success team and get product or account support directly to your inbox.