4.13 Cross-Sections

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.

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.

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.

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.

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.

The moments of inertia are required for the cross-section stiffness: The torsional constant I_T describes the stiffness against rotation about the longitudinal axis. The second moments of area I_y and I_z 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.

With the specification set in Figure 4.126, RFEM only considers the torsional moment of inertia with 5 %.

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

Shear area A_y is in relation to the moment of inertia I_z, shear area A_z accordingly to I_y. Using a correction factor κ, there is the following correlation between the shear areas A_y and A_z, as well as the total area A.

$A_y=\frac{A}{{\kappa }_y} ; A_z=\frac{A}{{\kappa }_z}$

${\kappa }_{y/z}=\frac{A}{I_{z/y}^2}·{\iint }_A\frac{S_{z/y\left(x\right)}^2}{t_{\left(x\right)}^2} dA$

where

• A : Total area of cross-section
• I_z/y : Moments of inertia of cross-section
• S_z/y(x) : Static moments of cross-section at location x
• t_(x) : Width of cross-section at location x

The shear areas A_y and A_z 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 7.27). If extremely low values are set for shear areas, numerical problems may arise, 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

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:

$\tan 2\alpha =\frac{2 I_{yz}}{I_z-I_y}$

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 (see Figure 4.127) provides the option to Mirror asymmetrical cross-sections. You can use this option to put an L-section into the correct position, for example.

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.

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

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

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

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, just like the function key [F7], opens the cross-section library.

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

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.

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.

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.

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.

Rolled cross-sections can be combined by specifying parameters.

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.

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 4.134), if possible.

Parameter a represents the weld root, not the fillet radius (see Figure 4.133). The weld thicknesses only have an influence on the lengths of the c/t parts. They are not included in the cross-section properties.

Use the button shown on the left to import the parameters of a rolled cross-section. The selection function allows you to preset certain geometry data.

Use the [Save] button to save a parametric cross-section with its exact name, for example IS 330/160/8/12/0 in the figure above. Click the [Load] button to import it again.

In the text boxes, you can freely define parameters for solid cross-sections (e.g. reinforced concrete sections). The cross-section values are calculated according to the theory for massive cross-sections, which presupposes elements with distinct wall thicknesses.

In the text boxes, you can freely define parameters for timber cross-sections. The cross-section values of both solid and combined cross-sections are calculated according to the theory for massive cross-sections.

If the cross-section is combined by a Coefficient of compliance, you can use the effective stiffnesses of flexural members according to EN 1995-1-1, Annex B.2. For this, you need to specify the reduction factors γ. For the modeling, the restrictions according to Annex B.1.2 apply. Composed compression members according to Annex C are not considered with this option!

When you work with a material of the type Hybrid, use the [Edit] button to assign the properties of the cross-section parts (see Figure 4.125).

In the Standardized Timber Cross-Sections dialog box, you can select standardized rectangle cross-sections for boards, battens, as well as sawn and solid timber. Standardized American timber cross-sections are also available for designs according to AWC and CSA.

• Importing saved cross-sections

Click the [Load] button shown on the left to open a dialog box where all cross-sections created with the Save function are displayed.

• Creating user-defined cross-sections

You can freely enter user-defined cross-section properties in a dialog box.

Enter the Table to define the place where the cross-section is managed, and the Name to describe the new cross-section. Then, enter the cross-section parameters and define the buckling curves.

It is also possible to import cross-sections from the Dlubal cross-section programs SHAPE-THIN and SHAPE-MASSIVE.

Use the button in the bottom left corner of the library to import an entire cross-section table from a file. The file must be a CSV file, i.e. a text file where the table columns are separated by a semicolon (;). Any Excel file can be saved in this format. Make sure that the syntax of the ASCII table corresponds to the definition parameters of the corresponding RFEM cross-section table.

Example: Import of double symmetrical I-sections.

The cross-sections are managed in the IS table (see Figure 4.133). For IS cross-sections, the following parameters are required: h, b, s, t, a. The table in Excel is structured as shown below:

In the import dialog box, specify the directory of the CSV file and use the list to select the cross-section table where you want to manage the imported cross-sections.

The imported cross-sections are subsequently available in the User-Defined Cross-Sections category (see Figure 4.137).

When importing cross-sections, RFEM calculates the cross-section values and stress points in such a way that stress designs can be performed as well.