Software version: ConSteel 17 Build 3303

Keywords: Modeling; Analysis; Design; Lattice girder; Getting started;

Model examples

**Design objective, choice of design standard**

This design guide is intended for novice ConSteel 17 users and provides a step-by-step guide for designing a simply supported lattice girder. The geometry of the lattice girder to be designed is known from the architectural conceptual design, (**Figure 1**). According to the concept, the lattice girder chords are made of hot-rolled sections of HEA120, while the lattice bars are made of cold-formed SHS80x4 sections. The design of the connections is not included in this guide.

It is well known that structural design is always carried out according to a certain standard or its version. The selection of the standard can be made from the Design Standard menu when creating a new model in the Project Center, or it can be modified later in the Standards tab [S1] selection panel (Figure 2).

The desired design standard can be selected from the list on the left of the panel. In this case, we select the EN Recommended option [**S2**]. The parameters applied by the selected standard can be accessed by selecting the corresponding row of the middle table [**S3**] of contents in the right-hand table [**S4**]. In Figure 2, the combination factors corresponding to Table 1.1 of the EC0 standard have been selected, whose parameters are shown in the right-hand table.

**Setting the grid raster editor**

First, let’s set the size of the raster according to the span of the structure by using the corresponding button [**1**] of the tool group on the left, which will bring up the **Grid and Coordinate System** adjustment panel (**Figure 3**).

For example, for the 19.6m long support, the **Size** window can be set to 20000 millimeters [**2**]. To update the setting, press **Enter**. With the above setting, the raster will be 20m wide in X and Y directions, the raster line density will be 1000mm, and the step spacing will be 250mm. It is convenient to add the grid support model in the X-Z global coordinate plane, so the raster editor will be rotated to the X-Z plane. To do this, select the **XZ** plane option [**3**].

**Loading**** initial cross-sections**

One fundamental characteristic of general structural analysis programs is that they can only work with specifically defined cross-sections. Therefore, the first step is to choose the initial cross-sections for the task, according to the conceptual design. This may seem contradictory to the simple manual methods taught in basic statics courses, where the specific dimensions of the cross-section were often irrelevant information (e.g. calculation of internal forces). When using computer programs, however, we need to provide specific cross-sections even if their dimensions do not affect the static quantities to be calculated (e.g. in the present case, the normal forces of a truss beam). Nevertheless, we should aim to select cross-sections that match the geometrical size of the structure. In this case, the preliminary design served this purpose.

Initially, the section library for the current model is empty, so we first need to select the appropriate cross-sections. To do this, go to the **Structure Members** tab [**4**] and select the **Section Administration** option [**5**] on the left side of the horizontally positioned tool group, then select the “**From Library**…” button [**6**] in the panel that appears (**Figure 4**).

**Figure 5** shows the loading of the HEA120 section, compliant with the European standard, which will be assigned to the chords. We select the region of the cross-section standard (**European**) and then its type (**H profiles**). From the list that appears, we can select the type of section (**HEA**) [**7**] and then the height of the section (**120**) [**8**]. By pressing the **Load** button [**9**], the program learns the cross-section, and from then on it knows everything about the cross-section and can work with it. Repeat the procedure as many times as you need different sections. Finally, the window is closed by pressing the **Close** button [**10**].

In our case, also a **CF-SHS 80×4** closed section (from **Library/Hollow sections – cold formed/CF-SHS/CF-SHS 80×4**) was loaded for the bracing members (**Figure 6**).

Later on, you can obtain all the information about the cross-section using the **Section** **module**. To do this, select the cross-section in the table by clicking on the corresponding row and then click on **Properties…** to display all the properties of the cross-section, such as type data; cross-section characteristics, etc. The program works with two cross-section mechanical models in a dual manner. The **GSS** (General Solid Section) model [**11**] is used for static calculations and the **EPS** (Elastic Plate Segment) model [**12**] for standard design operations (**Figure 7**). The cross-sectional properties (surface area, moments of inertia, etc.) can be displayed by pressing the button [**13**].

**Building the structural model**

Building of a structural (geometric) model consists of two main steps:

– creating the member geometry

– determining of supports.

**Creating the member geometry**

First, switch the coordinate input/display type to *Absolute* value setting. This is done using the switch [**14**] located in the bottom row of the editor window (if the Δ sign is yellow, the switch is set to *Relative*) (**Figure 8**).

To begin creating the geometry, start by establishing the editing lines that define the structural shape. To do this, select the **Draw Line** function [**15**] under the **Geometry** tab (**Figure 9**).

It’s a good practice to establish the center of the lower chord of the truss at the origin of the global coordinate system, and from there, initiate the line segments using the drawing option [**16**]. The endpoints of these segments can be defined by specifying their X coordinate. The X (or any other) coordinate can be entered by typing the appropriate letter, entering the coordinate value in the corresponding coordinate window, and pressing **ENTER**. The result is shown in **Figure 10**. Of course, the network can be added in a different, possibly more practical order.

After creating the frame for the geometry, we proceed to add the bars that form the lattice girder. The frame serves as a good starting point for adding the bars, although it should be noted that one can also pick up the bars directly without the frame. The division of the chords into bars can be done in various ways: (i) each straight chord section consists of a single bar member, or (ii) both the upper and lower chords consist of two or more symmetrical bar members, or (iii) each section between nodes is a separate bar member. The choice will be determined by the design principle to be applied later: will the chord sections always consist of a single cross-section, or will the possibility of changing cross-sections within sections be retained? In the present case, we assume that we do not wish to change the cross-section along the chords, and therefore we prefer to choose solution (ii).

To add the members, we need to establish snapping points on the created reference lines. You can set the intercepts in the bottom right of the editor window. Since the bars are divided into eights along the lattice girder chords, we set n=8 [**17**] (**Figure 11**) and press **Enter**.

After the above adjustment, the red snapping points appear close to the reference line. You can create the bars by selecting two-two (start and end) snapping points (red dots) as follows. To add a bar, select the Edit Bar function [18] under the Structural Members tab. This will bring up the Member Editor dialog, where in this case it is sufficient to select the appropriate cross-section [19] (**Figure 12**).

The given bar can then be positioned using the snapping points. The operation is repeated until all the bars have been placed.

Based on the above steps, we create the structural model of the lattice girder: the lower and upper chords are modeled with two members (**Figure 13**), and the lattice members with a series of bar elements (**Figure 14**).

The style of the model display can be selected using the style buttons in the left-hand column of the editor window (**Figure 15**).

**Adding supports**

For general details about adding supports, see chapter **5.9 Supports in the Online Manual**. Here, only the support of the actual lattice girder is shown.

The grid of bars created in the previous section must be made structurally stable in 3D, i.e. properly supported. In the present case, we will add the following supports:

– XYZ fixed-pinned support at the top point on the left end of the truss;

– YZ-directional rolling-pinned support at the top point on the right-hand end of the truss;

– YZ-directional rolling-pinned supports at the end of the truss, in the nodes of the bottom chord.

– Y-directional pinned supports at the inner nodes of the upper chord.

As an example, place XYZ (spatial hinge) support at the top left end node of the truss. Select the **Point Support** function [**20**] under the **Structural Members** tab, which will display the adjustment dialog (**Figure 16**). The support type can be selected in the upper window of the dialog [**21**].

For the graphical display of the point supports, we recommend the hidden line or solid view (**Figure 16. c** or **16.d**). It is possible that the graphical symbol of the placed support may not be visible due to its relatively small size and/or being obscured. It is a common mistake that the user does not see the placed support and places it multiple times on the same node: this will result in a model error later! The size of the graphic symbol can be increased by using the adjustment slider at the bottom right of the editor window [**22**] (**Figure 17**). Use the slider or, if necessary, the arrow to increase the size of the graphic symbol of the support object until it is sufficiently visible. If the support is obscured, it becomes visible by rotating the model.

You can place the supports one after the other, using the left mouse button, at the corresponding nodes of the model. The complete support system, and thus the complete structural model, is shown in **Figure 18**.

**Load model creation**

**Load model structure**

First, let’s determine the structure of the load model. Select the **Load Cases and Load Groups** function [**23**] under the **Load** tab, which will bring up a panel defining load groups and load cases (*load case* = a group of loads that are inseparable in time and space; *load group* = a group of load cases where the loads can be mutually exclusive in load combinations) (**Figure 19**). When a new model is created, the load structure on the left side of the dialog box contains by default one load group with one load case. Start by selecting the appropriate load group or load case name on the left, then rename it on the right to a name that suits your needs.

For example, change the initial name of the load group to *‘Dead load’* [**24**] and the name of the load set to *‘Self-weight’* [**25**]. Confirm the action with the **Apply** button.

If you have more than one load case in the ’Dead Load’ load group, you can add them [**27**] by using the **New load case** button [**26**] in the bottom table of the dialog (**Figure 20**).

You can add a new load group by clicking on the **New load group** button [**28**] at the top of the dialog, but first select the appropriate category in the window [**29**] next to it. In this case, the new load group contains snow, so select the ’*Snow*’ option (**Figure 21**).

Based on the well-thought-out load model, all load groups and load cases are added by repeating the above operations (**Figure 22**).

As a final step, assign the automatically generated structural self-weight to a selected load case. To do this, open the drop-down list **Load case including self-weight** [**30**] at the bottom of the table and select the appropriate load case, in this case the load *‘Self-weight’* (**Figure 23**). Finally, close the window by clicking on **OK**. This defines the structure of the load model. In the next step, we will apply loads to the appropriate load cases.

**Loading load cases**

We start to add actual loads to the load cases recorded in the load model structure. This can be a lengthy process, so we will first summarise the most important technical elements of applying loads and then present the actual loads.

*Technical elements*

Let us open the window under the **Loads** tab [**31**], where we select the load case to which we will assign specific load components (**Figure 24**).

The loads added next are added to this load case until the selection above is overwritten by another selection. We will now describe the elements and technical aspects of load application. In the case of lattice girders, the loads are usually concentrated forces (the bars of a lattice girder are usually not directly loaded). Therefore, only the definition of the concentrated force is discussed below.

**Concentrated load in the global system**

Select the **Point Load** function [**32**] under the **Loads** tab, and then enter the components of the concentrated force as interpreted in the global system [**33**] in the corresponding input fields [**34**]. Clicking on the corresponding structural node will place the concentrated force in the structural model as part of the current load case (**Figure 25**).

**Concentrated load in the local system**

In certain types of loads, the direction of the concentrated force may not align with the direction of the global coordinate system. For example, in the case of wind loads, the load may act perpendicular to the roof surface, in our case the upper chord. In such cases, instead of calculating components in the global directions, we switch to the local system. To do this, we select the **Local coordinate system** option [**35**], after which the concentrated load [**36**] can be placed on the structural model in two steps: (1) selecting the appropriate structural node with the mouse, and then (2) selecting the relevant member whose axis forms the **X** coordinate axis of the local system (**Figure 26**).

*Applied load cases*

Using the above technical elements, the following load cases have been applied:

**Load combinations**

The next step is to create load combinations. To do this, select the **Load Combinations** button [**37**] under the **Loads** tab, which will bring up the **Load Combinations** table. Select the option **“ Automatic generation of load combinations“** [

**38**], which will display the symbolic formulas of the load combination types for the design situations (

**Figure 27**).

In our case, we need the options *‘Persistent and transient design situations – Eq. 6.10’* and *‘Accidental design situation – Eq. 6.11.b’*. The setting is confirmed with the **Apply** button, which causes the generated load combinations to appear in the table (**Figure 28**). In the table, if necessary, undesirable combinations can be deleted after selection [**39**], partial factors can be rewritten, and new combinations can be created if necessary [**40**].

**Verifying the structural model**

Before performing a final analysis, it is useful to ensure that the structural model is correct. Select the **Analysis Parameters** button [41] under the **Analysis** tab, which will bring up the analysis setup dialog, where you should first select only the “*First order analysis*” option [42] (Figure** 29).**

Switch to the load combinations table [**43**] and switch off all combinations (select all the checkboxes in the Load combination set field with a left-click, then right-click on any checkbox to clear the checkmarks), except one in which only symmetric loads are present (in our case, this is *load combination 3 (Lc-3)*, in which only the permanent load and the total snow load are present) (**Figure 30**).

After the setup, press the **Apply** and **Calculate **buttons, wait for the analysis to run, and then examine the results. Possible aspects of the analysis are summarised below.

After the analysis is performed, the deformed shape of the structure is displayed. The deformation diagram can be scaled by using the slider next to the adjustments fields [**44**]. The content of the graphical display can be adjusted by using four fields (**Figure 31**). The contents of the windows are as follows:

– selection of analysis types (first-order; second-order; stability; etc.) [**45**];

– selection of load combination or load set [**46**];

– selection of the type of data to be displayed (displacements; stresses; etc.) [**47**];

– select the type of drawing (diagram; color overlay; etc.) [**48**].

Let’s examine the displayed deformed shape. Aspects of the test are usually the following:

- Is the deformed shape symmetric for symmetric loads…?
- Does the deformed shape stay within the plane of the model for loads in the plane…?
- Is the maximum displacement value realistic…?
- Does the deformed shape adhere to engineering judgment…!?

In the next step, let us switch to the internal forces, in our case the “**N**” normal force plot [**49**] (**Figure 32**), and examine the plot from the following points of view:

- Does the axial force decrease in the top chords of the trusses toward the ends of the beams…?;
- Is the value of the maximum normal force in the chords realistic…?;
- Does the axial force decrease in the diagonal bracing towards the center of the beam…?;
- Does the shape of the diagram adhere to engineering judgment (e.g., are there tensioned bars along the top chord of a two-span beam or compressed bars along the bottom chord)…!?

**Analysis **

If the result of the model check in the previous step is successful, we can proceed to the final analysis. To do this, enable all relevant load combinations and then perform the first-order analysis. If the calculation finishes without an error message, the model is ready for design.

The first step is to determine the relevant load combination (perhaps the first two or three) for which you want to save the figures and use them in other documents. This is done by using the automatic cross-section check function of the program (**Figure 33**). Switch to the **Global checks** tab and press the **Design Settings** button [**50**], which will bring up the *Design…* control panel, where only the options *‘Cross section check’* [**51**] and *‘First-order’* analysis [**52**] are activated.

After the setting, the **Calculation** button causes the program to perform a cross-sectional resistance test for every finite element node. The program displays the final results of the check in a color-coded graph and a table (**Figure 34**). The cross-sectional utilization is shown in the last column [**53**] and the corresponding load combination is shown in the fourth column from the left [**54**]. Based on the contents of the last column, the relevant load combination (or at most two or three load combinations) can be selected to determine the design. In the present case, this is the load combination Lc-14.

** **

**Documenting the results**

The ConSteel software has advanced documentation features (*Online Manual, 13. Documentation*), the use of which is beyond the scope of this manual. Therefore, only the saving of the most important graphical diagrams and their use in other (e.g. Word or Mathcad) working documents is presented here.

For the internal forces, it is sufficient to document Figure N for now, as the effect of bending moment and shear force is negligible in the design of light lattice girders. In general, the procedure for documenting a figure is described below.

Select the “N” normal force figure (**Figure 35**) calculated from the first-order analysis for the load combination of interest (in our case Lc-14). Adjust the scale of the diagram’s largest ordinate using the upper slider [**55**]. A value of the figure can be marked by right-clicking on the corresponding point of the model and selecting the ’*Marker*’ option [**56**] in the window that appears. This attaches a label indicating the value of the force. We place as many labels as necessary to make the diagram meaningful from an engineering perspective. In the present case, the maximum compressive and tension forces are specified, to which the other values can be related.

To save a figure, click on the **Document **tab. When you select the “*Create a snapshot of the current state*” function [**57**], the image setting table appears, where you have to enter the name of the image [**58**] from which the file name is generated (use only the right characters), and then select the appropriate image size [**59**] and font size [**60**] (**Figure 36**).

Once you have set up the image in the image frame indicated by the dashed line using the camera/screen movement, press the **Create** or **Modify** button, which will add the image to the gallery. Then press the **Manage picture** button [**61**], which will display the contents of the gallery, where you can select the current image [**62**], and press the **Save selected picture to file button** [**63**] (**Figure 37**).

These operations will save the image in the selected format and with the specified filename in the selected folder. The resulting image can be inserted into any document (e.g. Word or Mathcad).

**Checking load-bearing capacity**

The program can automatically check the cross-sectional and stability resistance of the structure in a complex way. To do this, switch to the **Global checks** tab and press the **Design settings** button [**64**], which will bring up the **Design…** control panel, where you must select the *’Cross-section check*’ [**65**] and the *’Buckling check’* [**66**] option. According to the standard, the detailed calculation is performed based on the results of the *‘Second order’* elastic [**67**] analysis (**Figure 38**). The calculation of the elastic critical load factor is performed using the *Automatic* option [**68**], where the program determines the value of the critical factor per structural element, which results in a more economical design.

After setting, pressing the **Calculation** button will perform all the necessary load-bearing capacity checks. The program displays the final result in a color-coded graph and table. As already known, any cross-section can be labeled with a label showing the utilization in %. The details of the check can also be viewed by right-clicking on the last data [**69**] in the corresponding row of the table label (**Figure 39**).

At this point, the complete spectrum of checks for the specific cross-section is displayed (Figure 40), where you can find the analysis considered critical by the program [70], as well as its details [71].

**Assessment of results**

If we open the tables of **Compression** and **Bending about the major axis** within the tables of **Pure resistances****, **we can conclude the following (**Figure 41**):

- the dominant cross-section internal force is the normal force
**N**, which results in a utilization of 109.3% [**72**]; - the
**M**bending moment causes only 12.9% utilization of the cross-sectional resistance [_{y}**73**]; - the cross-sectional check by the conservative interaction formula leads to a 122.2% utilization [
**74**]; - however,
**Figure 40**shows that the authoritative check was given by the general global stability check formula according to EN 1993-1-1 6.3.4, which gave a utilization of 162.5% [**70**].

The above dominant utilization is higher than the result of the check assuming pure compression. This is due to the inclusion of the **M _{y}** bending moment. Neglecting the M

_{y}moment for “heavier” lattice girders (e.g. lattice bridge structures) can lead to serious safety issues.

**Design**

After the above quick and automatic check, we can immediately see that our lattice structure does not meet either the strength or the global buckling limit state. The program also allows us to look behind the results and understand the reasons. In the present case, we see that the lattice girder chords and the two-two tensioned lattice bars at the supports are significantly overloaded, with inadequate cross-sectional dimensions. The problem can be eliminated by increasing the indicated cross-sections: with a few minutes of work, we can find the right cross-section types and sizes. A possible solution is to replace the upper chord with an **HEB140** section and the lower flange with an **HEA140 **section**. **Additionally the supports, the last two members are modified to ** SHS100x4 **sections (Figure 37). After checking the new structural configuration, the result is shown in Figure 42. The modification was successful, and the structure now complies (the maximum overshoot of about 3% is still acceptable as it is within the margin of error).

**Consteel recommends to use the General Method from EN 1993-1-1 for the evaluation of out-of-plane strength of members and sturctures. In addition, the scaled imperfection based 2nd order approach is available.**

Did you know, that when linear buckling eigenform affine imperfections are used, Consteel can scale automatically the selected eigenmodes to perform a Eurocode compatible design? And you can even combine several imperfections?

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**Bending:**

**Copmression:**

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**Have you ever heard about the ‘General Method’? This is an alternative design method to consider the interaction of axial compression with major-axis bending for general buckling situations, where the main interaction formulas are not applicable. **

This basically includes every member with monosymmetric or asymmetric cross-sections or with cross-sections not uniform along the length (welded tapered sections) or laterally stabilized by sheeting or anything else without providing full fork supports.

Did you know, that the General Method is fully supported by Consteel and provides an automated buckling verification possibility? Of course, for the use of the General Method in a general case the traditional 12DOF beam finite elements are not applicable. But the special 14DOF beam elements used by Consteel are perfectly compatible?

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## Introduction

When a beam, bent in a plane, is allowed to move and twist freely between its two support points, in addition to bending, sudden perpendicular displacement and twisting may occur: causing the beam to deviate out of its original plane. This phenomenon is illustrated in Figure 1, showing a single supported beam with I-section bent around the strong axis. As the bending moment in the vertical plane increases, reaching a critical value, the beam undergoes abrupt lateral movement and twisting between the supports. This phenomenon is called **lateral torsional buckling (LTB)**, which is a loss of stability mode that can apply to both perfect beams and real beams.

The design of the beam against LTB is fully analogous to the design of a compressed column against flexural buckling. The analogy is illustrated in Table 1, where the corresponding parameters are shown that affect the two buckling resistances:

Flexural (column) buckling | Lateral torsional buckling |
---|---|

design force ($N_{Ed}$) | design moment ($M_{Ed}$) |

critical force ($N_{cr}$) | critical moment ($M_{cr}$) |

column slenderness ($\frac{}{\lambda}$) | beam slenderness ($\frac{}{\lambda}_{LT}$) |

buckling reduction factor ($\chi$) | buckling reduction factor ($\chi_{LT}$) |

buckling resistance ($N_{b,Rd}$) | buckling resistance ($M_{b,Rd}$) |

The critical moment of the perfect beam is determined at the location of the maximum value of the *M _{y,Ed }*design bending moment diagram. For a doubly symmetrical I cross-section:

$$M_{cr}=C_1\frac{\pi^2EI_z}{(k_z⋅L)^2}\left[\frac{I_\omega }{I_z}+ \frac{(k_zL)^2GI_t}{\pi^2EI_z}\right] ^{0.5} $$

where *k _{z}* is the coefficient of restraint about the weak axis of the cross-section,

*G*is the shear modulus, and

*I*and

_{t}*I*are the pure (St. Venant) and warping torsional moments of inertia of the cross-section. The value of the factor

_{ω}*C*depends on the shape of the bending moment diagram and its value can be found in appropriate tables and manuals. For a constant moment diagram,

_{1}*C*=1.0. The formula for the other design parameters, in particular the buckling reduction factor $\chi_{LT}$, depends on the design standard considered.

_{1}## Lateral torsional buckling resistance by EN1993-1-1

The design of the beam against LTB (load capacity check) according to EC3-1-1 shall be carried out in the following steps:

gate## Designing a lattice girder

The design of the bars of a truss (lattice girder) structure does not require any special theoretical knowledge: normally, the truss bars are designed as **compressed** and/or **tensioned** bars, neglecting bending moments and shear forces. The dimensioning of compression bars is nowadays carried out using a model-based computer procedure. For details, see the knowledge base material **Design of columns against buckling**. Here, only the determination of the deflection length of the compressed bars is presented.

The most important parameter for the dimensioning of a compressed bar is the slenderness:

$$\overline{\lambda}=\sqrt\frac{Af_y}{N_{cr}}$$

where

$$N_{cr}=\frac{\pi^2El}{(kL)^2}$$

where the buckling length factor *k* is recommended by EN1993-1-1 to facilitate manual calculations:

Type of the bar | Direction of buckling | k |
---|---|---|

chord | – in-plane – out-of-plane | 0.9 0.9 |

bracing | – in-plane – out-of-plane | 0.9 1.0 |

Software using model-based computational methods (e.g. Consteel software) determines the elastic critical force *N _{cr} *directly by

**finite element numerical methods,**taking into account the behaviour of the entire lattice girder, instead of the above conservative formula. The following example is intended to illustrate the relationship between the manual design procedure proposed by the standard and the results of the modern model-based numerical procedure.

- Let the structural model of the lattice girder under consideration be the Consteel model shown in Figure 1.
- Let the load shown correspond to the design load combination of the girder.
- Determine the deflection length of the most stressed compressed chord member using finite element numerical stability analysis.

## Relationship between procedures

The steps of the calculation are:

### Buckling stability analysis

The stability analysis of the elastic model shows the governing buckling mode of the lattice structure and the corresponding **elastic critical load factor α_{cr}** (Figure 2).

We can see that the upper chord of the perfectly elastic model is deflected laterally under load. The load that causes this elastic buckling is the **critical load**, whose value is given by the product of the design load and the critical load factor *α _{cr}*=5.99.

## The evolution of compressed bar (column) design

One of the characteristic features of steel structures made of bars (e.g. lattice girders) is the compressed bar. We speak of a compressed bar when the structural element, which usually has a straight axis, is loaded by a compressive force * P* applied centrally (Figure 1).

Figure 2 illustrates the evolution of compressed bar (column) design. In the beginning (in the old days), master builders determined the load-bearing capacity of compressed columns of different materials and sizes on the basis of the **experience accumulated over the centuries**, passed down from master to apprentice. A significant change was brought about by the application of classical mathematical differential analysis to engineering. The Swiss mathematician and physicist Euler (1707-1783) solved the problem of the deflection of a compressed elastic line, which could be applied to the solution of the elastic compressed bar (**Euler’s force**). In the following centuries, engineers recognised that Euler’s force only gave an acceptable approximation to the real load capacity of a compressed bar in certain cases (mainly for large slender bars). Many solutions for the bearing capacity of a compressed bar were developed that were more advanced than the Euler formula, but it was not until the huge structural engineering boom following World War II that significant changes were made. **Compression bar experiments** were carried out in every major structural laboratory in the world, and a database of over two thousand experiments was compiled from the results. The load capacity of the pressure bar was given by a formula based on the database, using the method of mathematical statistics.

This methodology is still dominant today:

‘the dimensioning of the compressed bar has become a political issue for the steel construction profession…’. Understanding the principle of compressed bar design is therefore essential for the structural engineer.

The right side of the Figure 2 also contains a hint for the future. At the level of scientific research, it is already present that the load capacity of a real compressed column can be determined by mathematical-mechanical simulation. Indeed, in the near future, databases that go beyond anything we know today can be created using supercomputers. On the basis of such a gigantic database, **artificial intelligence** could, at least in principle, supersede existing engineering knowledge and methodology. But the reality is that structural engineering is not one of the pull sectors (such as the defense or automotive industries), so this new shift in design theory is certainly a long way off.

In the following, the **Euler force** and the **experimentally based** standard design formula, which are of major importance to structural steel engineering today, are discussed in detail.

## Buckling strength of the ideal columns: the Euler force

Assume that the hinged compressed column shown in the Figure 3 has the following properties:

- perfectly
**straight**, - its material is perfectly linearly
**elastic**, **centrally**compressed.

Under the above conditions, perform the compressed column experiment using Consteel software: run the Linear Buckling Analysis (LBA) calculation. The result is illustrated in Figure 3.

gate**Did you know that you could use Consteel to perform dual analysis with 7DOF beam and/or shell elements?**

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**Did you know that you could use Consteel to consider connection stiffness for global analysis?**

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Assumed rigid connection without considering connection’s actual rigidity

Considering connection’s actual rigidity **52% increase of deflection!**

Considering connection’s actual rigidity **33% increase of deflection!**

**Did you know that you could use Consteel to** **determine automatically the second order moment effects for slender reinforced concrete columns?**

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**Did you know that you could use Consteel to** **calculate effective cross-section properties for Class 4 sections?**

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