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**].

**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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