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RFEM – Online Manual

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4.13 Cross-Sections

General description

Before you can enter a member, you have to define a cross-section. The cross-section properties and assigned material characteristics determine the stiffness of the member.

Each cross-section has its own Color that can be used to represent different profiles in the model. Colors are controlled in the Display navigator with the Colors in Rendering According to option (see Chapter 11.1.9).

You do not have to use each defined cross-section in the model. Thus, when modeling the structure, it is possible to experiment without deleting cross-sections. Please note, however, that the cross-sections cannot be renumbered.

To display a tapered beam, you have to define different start and end cross-sections for the member. RFEM automatically determines the variable stiffnesses along the member.

Figure 4.122 New Cross-Section dialog box, Cross-Section Properties tab
Figure 4.123 Table 1.13 Cross-Sections

You do not need to enter the cross-section properties manually. RFEM provides an extensive and expandable cross-section library, as well as import options.

Cross-Section Description

The cross-section's Description can be freely chosen. When the entered cross-section name corresponds to an entry of the cross-section library, RFEM imports the cross-section parameters. In this case, it is not possible to change the values for the Moments of Inertia and area Axial A. For user-defined cross-section descriptions, you can enter moments of inertia and cross-section areas manually.

The characteristic values of parametrized cross-sections are also imported automatically. For example, when you enter "Rectangle 80/140", the parameters of this cross-section appear. The selection of cross-sections from the library is described below.

It is also possible to use a rigid dummy cross-section to model couplings. For this cross-section type, RFEM applies the stiffnesses as for a coupling member. Enter the name Dummy Rigid as the description for the cross-section without defining the cross-section values in detail. This way, you can use members with a high degree of stiffness, taking releases or other member properties into account. A new variant in RFEM 5 is the member type Rigid Member, so the definition of a Dummy Rigid is no longer necessary.

Material No.

The cross-section's material can be selected from the list of previously defined materials. The assignment is facilitated by material colors that are by default used for the rendered graphical display.

In the New Cross-Section dialog box, there are three buttons below the material list. They allow you to access the material library, create a new material, or edit materials.

For more detailed information on materials, see Chapter 4.3.

The Hybrid option can only be accessed for parametrized timber profiles. Use this option to assign specific material properties to cross-section elements if different material grades are provided (e.g. timber of low class for webs).

Click the [Edit] button to open the Edit Hybrid Material dialog box.

Figure 4.124 Edit Hybrid Material dialog box

Assign materials to the individual cross-section parts according to the graphical scheme. They can be selected from the list. One of these materials must be defined as a Reference Material to determine the ideal cross-section properties.

Moments of Inertia

The moments of inertia are required for the cross-section stiffness: The torsional constant IT describes the stiffness against rotation about the longitudinal axis. The second moments of area Iy and Iz describe the stiffnesses against bending about the local axes y and z. Axis y is considered to be the "strong" axis. The local cross-sectional axes are shown in the graphic of the New Cross-Section dialog box.

For asymmetrical sections, the moments of inertia are displayed around the cross-section's principal axes u and v.

Moments of inertia as well as cross-sectional areas can be adjusted with the help of factors in the Modify dialog tab. In the table, you can access the tab with the button that appears when you click into the table cell. The adaption factor for the cross-sectional area A does not affect the cross-section weight.

Figure 4.125 New Cross-Section dialog box, Modify tab

With the specification set in Figure 4.125, RFEM only considers the torsional moment of inertia with 5 %.

By default, the multiplication factor of the cross-section values is only considered for load combinations (see Figure 7.19). However, for load cases, all stiffness factors are deactivated by default so that the corresponding Options have to be selected if necessary.

Cross-Sectional Areas

The cross-section parameters of the cross-sectional areas are subdivided into the total area Axial A and the shear areas Shear Ay and Shear Az.

Shear area Ay is in relation to the moment of inertia Iz, shear area Az accordingly to Iy. Using a correction factor κ, there is the following correlation between the shear areas Ay and Az, as well as the total area A.

Ay=Aκy ;    Az=Aκz 

κy/z=AIz/y2·ASz/y(x)2t(x)2dA 

where

    • A: Total area of cross-section

    • Iz/y: Moments of inertia of cross-section

    • Sz/y(x): Statical moments of cross-section at location x

    • t(x): Width of cross-section at location x

The shear areas Ay and Az affect the shear deformation, which should especially be taken into account for short, massive members. When the shear areas are set to zero, the influence of shear is not considered. The parameters can also be controlled in the Global Calculation Parameters dialog tab of the Calculation Parameters dialog box (see Figure 7.25). If extremely low values are set for shear areas, numerical problems may occur, because the shear areas are contained in the denominator of equations.

For more detailed information, take a look at this technical article:
https://www.dlubal.com/en/support-and-learning/support/knowledge-base/000966

Select realistic values for the cross-section areas: Extreme differences in the cross-sectional areas of sections involve significant differences in stiffness that may lead to numerical problems when solving the equation system.

Angle of principal axes α

The principal axes are described with y and z for symmetrical sections and with u and v for asymmetrical sections (see above). The rotation angle of principal axes α describes the position of the principal axes in relation to the standard system of coordinates for symmetrical sections. For asymmetrical sections, this is the angle between the y-axis and the u-axis (see graphic on previous page shown in the left margin). This angle is defined clockwise as a positive angle. For symmetrical cross-sections, α = 0°. The inclination of principal axes for sections from the library cannot be edited.

The angle of rotation for the principal axes is determined with the following equation:

tan 2α=2 IyzIz-Iy 

When you work with 2D models, only 0° and 180° are allowed.

Cross-section rotation α'

The angle of rotation α' describes the angle by which the sections of all members that use this cross-section are rotated. Thus, the angle represents a global cross-sectional angle of rotation. In addition, each member can be separately rotated about a member rotation angle β.

Moreover, the Rotation dialog tab provides the option to Mirror asymmetrical cross-sections. You can use this option to put an L-section into the correct position, for example.

Figure 4.126 New Cross-Section dialog box, Rotation tab

When importing a section from the cross-section library or from the SHAPE-THIN add-on module, you do not need to care about the angle α'. RFEM automatically imports this angle in the same way as the other cross-sectional values. For user-defined sections, however, you have to determine the principal axes angle yourself and adjust it manually by means of the cross-section rotation.

Overall dimensions

The cross-section's Width b and Depth h are significant for temperature loads.

Cross-section library

Numerous cross-sections are already available in a data base.

Opening the library

In the New Cross-Section dialog box and in Table 1.13 Cross-Sections, you have direct access to frequently used cross-sections:

Figure 4.127 Buttons of frequently used cross-sections in table (above) and dialog box (below)

Use the [Import Cross-Section from Library] button to access the complete cross-section database. When working in the table, place the cursor into table column A to enable the button, which you can use to open the cross-section library, just like the function key [F7].

Figure 4.128 Cross-section library

The cross-section library is divided into several sections, which are described on the following pages.

Rolled cross-sections

The table values of many rolled cross-sections are stored in a database.

First, click one of the twelve buttons to define the Cross-Section Type. Another dialog box opens where you select the table. Then, select an appropriate Cross-Section.

Filter for Manufacturer/Standard group
Filter for Manufacturer/Standard group
Figure 4.129 Selecting a rolled cross-section

In the Filter dialog section, you can filter the library according to the following criteria: Manufacturer/Standard group, Manufacturer/Standard, Cross-section shape, and Cross-section note. That way, it is easier to overview the offered tables and cross-sections. Displayed data can be sorted by clicking the headings of table columns.

If cross-sections of old standards are needed, select the Include invalid checkbox in the Filter dialog section to display them.

Creating favorites

Preferred cross-sections can be set as favorites. To access the dialog box for creating favorite cross-sections, use the [Create New Favorites Group] button at the bottom of the Filter dialog section. When the name for the new group has been defined, the following dialog box appears.

Figure 4.130 Rolled Cross-Sections - I-Sections - Favorites dialog box, filtered by EN

The dialog box looks like the cross-section library. You can use the filter options described above. In the Select Favorites dialog sections, you can tag preferred tables and cross-sections with a check mark.

After closing the dialog box, the cross-section library presents a clear overview of favorites, once you activate the Favorites group option.

In this way, it is possible to create different groups of favorites available for selection in the list at the bottom of the Filter dialog section.

Built-up cross-sections

Rolled cross-sections can be combined by specifying parameters.

Figure 4.131 Built-up Cross-Sections - I-Sections dialog box

Use the [Save] button to save a built-up cross-section. RFEM stores it with its accurate description (e.g. 2IK HE B 300 + HE A 340 in the figure above) in the User-Defined category, where you can later reimport it from.

Parametric cross-sections - thin-walled

In the text boxes, you can freely define parameters for a cross-section composed of sheets. The cross-section values are calculated according to the theory for thin-walled cross-sections. The theory only applies to cross-sections whose element thickness is clearly smaller than the respective element length. If this condition is not fulfilled, define the cross-section in the Massive category (see Figure 4.133), if possible.

Parameter a represents the weld root, not the fillet radius (see Figure 4.132). The weld thicknesses only have an influence on the lengths of the c/t parts. They are not included in the cross-section properties.