Surfaces

Surfaces describe the geometry of planar or curved components whose surface dimensions are significantly larger than the thicknesses. The stiffness of a surface results from its material and thickness. When generating the FE mesh, 2D elements are created on surfaces. These are applied for the calculation in the surface centroidal axis.

To enter a surface, you can use existing boundary lines. If you describe the surface graphically using the options in the Navigator context menu or the buttons in the toolbar (see image Buttons for planar surfaces), the definition lines are automatically created after setting the surface parameters and clicking OK in the dialog.

The Basic tab manages elementary surface parameters. By checking check boxes, further tabs are added where you can make the specific entries.

Stiffness Type

The stiffness type controls in which way internal forces can be absorbed or which properties are assumed for the surface. Various types are available for selection in the list.

Standard

The surface transfers moments and membrane forces. This approach describes the general behavior of a homogeneous and isotropic surface model. The stiffness properties of the surface are direction-independent.

Without Thickness

The surface has no stiffness. This type is to be used for the boundary surfaces of a solid.

Rigid

With this stiffness type, very stiff surfaces can be modeled in order to represent a rigid connection between objects.

Membrane

The surface has a uniform stiffness in all directions. However, only membrane forces in the tension state (n_x, n_y) as well as membrane shear forces (n_xy) are transferred. Under compressive and shear forces as well as moments, the affected surface elements fail.

Without Membrane Tension

Only moments and membrane forces in the compression state are transferred. For membrane forces causing tension, the affected surface elements fail (example: hole bearing).

Load Transfer

With this type, surface loads can be applied to areas that are not filled with surfaces, such as wind loads on windows or the members of a hall. The load of this surface is distributed to the edges or the integrated objects. If member loads are created, the load is converted to the true member lengths in the global directions (load directions X_L, Y_L, Z_L). The surface itself has no stiffness.

The criteria for the load transfer can be defined in the Load Transfer tab.

The 'Load transfer direction' describes the direction(s) in which the load should be applied to the objects. The list offers options for an isotropic distribution based on an FEM calculation as well as for an orthotropic arrangement on surface strips that are applied to one or both local surface axes for determining the tributary width.

With the option 'Isotropic | FEM', RFEM uses a separate partial model for determining the load distribution, in which the surface is represented by a rigid surface element. All objects integrated into the surface (members, line and nodal supports, lines connected with model entities, couplings or nodes, etc.) are replaced by rigid lines or rigid nodal supports. The reactions of this partial model are then applied as loads for the 3D calculation of RFEM. If certain objects are not to transfer loads, you can specify them in the 'Without effect on' section.

For the load transfer via surface strips, you can specify how RFEM should perform the 'load distribution'. By default, the load is distributed to the adjacent objects with a variable distribution. However, if you want to achieve a constant load distribution, select the corresponding entry in the list. The difference between the two variants is compared in the following image.

The input options for the 'surface strip width', the 'smoothing factor', and the 'minimum number of strips on the surface' are accessible when the Advanced distribution settings check box is activated in the 'Options' section. Adjustments are only required for problematic load distributions. The effect of these parameters is explained in the technical article Advanced Distribution Settings for Load Transfer Areas using an example.

For the load transfer area, you can also define a 'basis weight' in order to take into account, for example, the self-weight of a glazing.

In the 'Without effect on' section, you can exclude members, lines, and nodes from the load transfer (for example, bracings). Define the objects individually or select a pattern object that lies parallel to the load-free members or lines.

When the boundary lines of the surface are defined, the loaded members, lines, and nodes are specified in the 'Loaded objects' section. If you want a specific load distribution, check the Load distribution factor check box in the 'Basic' tab. You can then individually define the factors for the load-bearing objects in the Load Distribution Factors tab.

For the load transfer via surface strips, you can take into account the 'member eccentricity' or the 'section distribution' in order to correctly capture the geometric position of a member or its course (see chapter Cross-section). The 'Neglect rotational equilibrium' check box is not activated by default. This means that the moment from the surface loads is formed about the center of gravity and compared with the moment from the member loads about the center of gravity. For nodal loads, however, this option is irrelevant. The following image shows how a free line load is distributed to the opposite members with and without taking the rotational equilibrium into account.

Stiffening

With this stiffness type, the stabilizing effects of trapezoidal sheeting, purlins, and bracings can be easily and realistically taken into account in the modeling.

A stiffening surface is not taken into account as an object with effective stiffness. Rather, it represents the geometric basis for defining the members and objects located in the stiffening surface and for determining their stiffening effect. Therefore, for a stiffening surface, the Deactivate for Calculation check box is automatically checked and cannot be deactivated.

The criteria of the stiffening surface can be defined in the Stiffening, Parameters, and Tolerances tabs.

Stiffening

Two stiffening types are available for selection, which fundamentally differ.

• Surface

The stiffening effect of a trapezoidal sheeting is represented by an orthotropic surface that is connected to the attached members via rigid couplings. The stiffness of the fasteners is taken into account by line hinges in the rigid couplings.

The 'stress direction' defines the orientation of the trapezoidal sheeting. It influences the orientation of the orthotropic surface and is taken into account when defining the orthotropy properties. The axes x and y refer to the local xyz axis system of the surface.

In the 'Members connected to surface' section, the members that are taken into account as secondary beams and longitudinal beams of the trapezoidal sheeting are automatically entered. These are all members within the defined Tolerances in the plane of the stiffening surface and perpendicular or parallel to the stress direction of the trapezoidal sheeting.

The 'Without effect on' section offers the possibility to exclude certain members from the automatic assignment as connected members.

• Member Support

The stiffening effect of trapezoidal sheeting, purlins, or bracings is captured by member supports on the members of the surface: For these connected members, corresponding member shear panels and rotational restraints are created.

The 'Stiffening direction' defines the orientation of the trapezoidal sheeting or the purlins. The axes x and y refer to the local xyz axis system of the surface.

In the 'Supported members' section, the members that bound the end field of the stiffening surface or lie closest to a boundary of the stiffening surface or are located in an interior field of the surface are automatically entered. The Tolerances apply in the plane of the stiffening surface and for the orientation perpendicular to the stiffening direction.

The 'Without effect on' section offers the possibility to exclude certain members from the automatic assignment as connected members.

Parameters

The 'Parameters' tab is adapted to the Stiffening type: For a surface, you define the properties of the trapezoidal sheeting and the fasteners; for a member support, you define the stabilizing components.

• Surface

In the 'Panel' category, define the trapezoidal sheeting. In the list, you can select an already defined cross-section or create a trapezoidal sheeting with the 'New cross-section' option. Use the library, which is accessible via the button. From the cross-section parameters, the properties required for the orthotropic surface are automatically adopted. They are used for a thickness with the thickness type Geometric Orthotropy and the orthotropy type 'Trapezoidal sheeting'.

In the 'Longitudinal joints' category, define whether the trapezoidal sheets are arranged regularly or irregularly. A separate orthotropic surface is created for each area between two adjacent longitudinal joints. These surfaces are coupled at the longitudinal joints via line hinges. The stiffness of the longitudinal joint connection is taken into account by the spring stiffnesses defined in the line hinges, which result from the elasticity of the fasteners selected in the 'Longitudinal joint fastening' category. The positions of the longitudinal joints are automatically derived from the arrangement of the trapezoidal sheets.

The 'Eccentricity' describes the position of the trapezoidal sheeting relative to the connected secondary beams. With the option 'Top', for example, the trapezoidal sheeting is arranged so that its underside lies on the top side of the secondary beams.

In the 'Panel – Secondary beam fastening' category, define the parameters for connecting the orthotropic surface to the secondary beams. It takes place via rigid couplings. The line hinge of the rigid couplings represents the stiffness of the connection, including the influence of the cross-section deformation. Selected fasteners are available for fastening the trapezoidal sheeting to the secondary beams.

For a trapezoidal sheeting in negative position, you can specify whether the sheeting is fastened at the bottom flange or at the top flange. For trapezoidal sheeting in positive position, the fastening is always at the bottom flange.

The connection of the orthotropic surface to the longitudinal beams also takes place via rigid couplings with line hinges, which result from the stiffnesses of the fasteners. In the 'Panel – Longitudinal beam fastening' category, some fasteners are available for selection.

In the 'Longitudinal joint fastening' category, specify the fasteners for the longitudinal joints. Here too, certain types are available in the list.

• Member Support

Select which components contribute to the stabilization in the calculation. In addition to the components 'sheeting', 'purlins', and 'bracings', the 'Manual stiffness' option is also available. Sheeting and purlins are mutually exclusive. Bracings, however, can be combined with both sheeting and purlins.

Tolerances

In the 'Tolerances' tab, define the permissible deviations according to which members are automatically assigned to the longitudinal and secondary beams (stiffening type Surface) or to the end field and interior field (stiffening type Member Support).

The 'Tolerances for members in plane' control within which deviation members are considered to lie in the stiffening surface. You can define this value absolutely as a distance or relatively by an angle.

Result Surface

This stiffness type makes it possible to convert stresses and forces of other objects into surface internal forces using an integration method. This allows you, for example, to determine the membrane and bending stresses of a solid that are to be designed with different partial safety factors.

Further criteria for integrating results can be defined in the Result Surface tab.

In the 'Integrate stresses and forces' section, select whether the results should be captured purely object-related or also geometrically within an area. In the 'Include objects' section, define the relevant surfaces and solids. Alternatively, select 'All' objects and then exclude certain elements in the 'Excluded from inclusive objects' section.

If the results of a certain area 'below' and 'above' the surface are to be integrated, you can define the relevant distances in the 'Parameters' section. They refer to the local z-axis perpendicular to the surface plane.

Geometry Type

The geometry type describes the formal concept of a surface. Various types are available for selection in the list.

Plane

In a planar surface, all boundary lines lie in one plane. Various shapes of planar surfaces are accessible via the list button.

You can define the surface (after clicking OK in the dialog) graphically by dragging a rectangle, circle, etc. If you 'select the boundary', RFEM automatically recognizes the surface as soon as a sufficient number of boundary lines is fixed.

Quadrangle

In its basic form, this surface type describes a general four-sided surface. Straight lines, arcs, polylines, and splines are possible as boundary lines. This allows curved surfaces to be modeled.

Define the boundary lines of the quadrangle surface in the 'New Surface' dialog. If the closed surface cannot be formed by four lines, more than four lines are also permitted. In the 'Quadrangle' tab, the four corner nodes are then specified. They control how the curved surface is spanned.

NURBS

NURBS surfaces are formed from four closed NURBS lines (see chapter Lines). This allows almost any free-form surfaces to be modeled.

Define the boundary lines of the NURBS surface in the 'New Surface' dialog. The respective opposite pairs of NURBS lines must have the same number of control points so that the order of these NURBS lines is 'compatible'. In the 'NURBS' tab, you can then influence the shape of the surface via the 'control point weights'. The coordinates of the selected control point are specified in the 'Coordinates – Control point' section.

Trimmed

When surfaces intersect, you can quickly create the intersection: Select the surfaces and then call up the context menu. Various options are available for selection.

With the 'Create intersection' option, only the intersection line is generated. If you select one of the 'Split by intersection' options, RFEM creates partial surfaces and assigns them the type 'Trimmed'. You can then delete components, for example, if you want to remove protruding surfaces.

Rotation

A rotated surface is created when an existing line is rotated about an axis. RFEM creates the surface from the start and end nodes as well as the rotated definition points of the line. New lines are generated in the process.

In the 'Rotation' tab, define the boundary line of the surface to be rotated. Specify the rotation angle α. You can determine the points of the rotation axis via the coordinates or graphically with the button.

Pipe

A pipe surface is created when the center line of the pipe is rotated about this axis with a radius. New lines are generated in the process: two circles and a polyline parallel to the pipe axis.

In the 'Pipe' tab, define the radius of the pipe. This value describes the distance from the pipe axis to the center of the surface. Specify the number of the center line or select the pipe axis graphically with the button.

If the pipe cross-section is conical, activate the 'Different radius at end' check box and enter the corresponding value.

Spline with Minimum Curvature

With this geometry type, you can create a curved surface using control nodes that lie on or outside the surface. This allows, for example, terrain surfaces to be modeled.

Define the 'coordinate system' of the reference plane and enter the 'sample coordinates in the coordinate system'. These points represent the control nodes of the spline surface. Then define the 'boundary lines of the reference plane' or select the lines graphically via the button.

Thickness with Material

In the list of existing thicknesses, select the appropriate type or define a new thickness (see chapter Thicknesses).

Material of Thickness

The material of the thickness defined in the section above is preset. If necessary, you can select a different material in the list of already created materials or define a new one (see chapter Materials). This material is then assigned to the thickness type.

Hinges

With a hinge, the transfer of the internal forces along a line of the surface can be controlled (see chapter Line Hinges. After checking the check box, you can define the hinge type in the 'Hinges' tab.

Supports

If the surface is elastically founded, you can select or redefine the surface support in the 'Supports' tab (see chapter Surface Supports).

Release

To decouple the model at the surface, you can select or redefine a surface release in the 'Release' tab (see chapter Surface Releases).

Eccentricity

With an eccentricity, a height offset of the entire surface can be modeled (see chapter Surface Eccentricities). You can define the offset type in the 'Eccentricity' tab.

Load Distribution Factor

For a surface of the Load Transfer type, it is possible to define distribution factors for the load-bearing objects. If you check the check box, you can assign these factors individually in a new tab.

The loaded objects of the load transfer area are preset in one row. Each object is assigned the factor 1.00, so that all objects contribute equally to the load transfer. If you want a specific distribution, click in the next free row and select the line or member. Then assign the appropriate 'distribution factor'.

Mesh Refinement

The mesh size of the FE mesh can be adapted to the geometry of the surface (see chapter Surface Mesh Refinements). It is thus independent of the general mesh settings. In the 'Mesh Refinement' tab, you can select or redefine the surface mesh refinement.

Specific Axes

Each surface has a local coordinate system. As a rule, it is aligned parallel to the global axes. However, the coordinate system can also be defined by the user – separately for input and output.

Input Axes

The orientation of the input axes is relevant, for example, for orthotropy and foundation properties or the effect of a surface load.

The list in the 'Category' section offers various options for adjusting the axes position:

• Angular rotation: rotation of the xy surface axes about the z-axis by the angle α
• Axis parallel to lines: orientation of the x- or y-axis along a line
• Axis directed to point: orientation of the x- or y-axis to the intersection of a line with the surface
• Axis parallel to coordinate system: orientation of the axes to a user-defined coordinate system

You can determine the reference objects graphically via the button.

The 'Reverse local axis z' check box allows you to orient the axes z and y in the opposite direction.

Result Axes

Currently, the orientation of the result axes is only possible 'Identical to input axes'.

Grid for Results

Each surface is covered with a grid that is used for the result output in the tables. It enables an output independent of the FE mesh in regular, adjustable result points.

By default, a Cartesian surface grid with a uniform grid point spacing of 0.5 m in both directions is preset. If necessary, you can adjust the 'grid spacings' in the x-direction (b) and in the y-direction (h) here, perform a 'grid rotation', or change the 'grid origin'. For circular surfaces, the 'Polar' grid type offers an alternative for the numerical result output.

If the 'Adjust automatically' check box is checked in the 'Options' section, the grid points are adapted to the new geometry when the surface is changed.

In the 'Points' section, you can check the coordinates of the generated grid points. Changes in the table are not possible.

Integrated Objects

RFEM usually automatically recognizes all objects that lie in the surface but were not used for the surface definition.

The numbers of the nodes, lines, and openings assigned to the surface are specified in the 'Integrated objects in surface' section.

If an object is not recognized, you should integrate it manually: Deactivate the Automatic object detection. The input fields in the 'Integrated objects in surface' section are now accessible. Add the missing object number or use the button to determine the object graphically.

Activate Load Transfer

The check box allows the loading of the surface – regardless of its stiffness type – to be distributed by means of a load transfer area. This makes the surface act in the model through its stiffness. The distribution of the load to the adjacent objects, on the other hand, is controlled by the parameters that you can define in the Load Transfer tab. This function is primarily relevant for surfaces of the Beam Panel thickness type.

Deactivate for Calculation

The check box offers the possibility not to take the surface into account in the calculation, for example, to simulate construction stages or to examine a modeling variant. The stiffness, boundary conditions, and loads of the surface are not applied in this case.

Information | Analytical

This section is displayed as soon as you have defined the boundary lines of the surface. It provides an overview of important properties of the surface such as surface area, solid, and mass as well as the position of the surface center of gravity and the orientation of the surface. Openings are taken into account accordingly.