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How do I ensure that my 3D beam elements are oriented correctly?

Unless using completely symmetrical 3D beams in a LUSAS analysis, geometric properties for 3D thin and thick beams require the local axes of the beams to be rotated so that the beam axes lie in a desired orientation.  For example when using 3D thick beams (e.g. element type BMS3) 2nd moment of area properties are required about both the local beam y and z axes.  Therefore the local beam axes must be in the correct orientation before the analysis is carried out.  If the local beam axes are not explicitly defined by the user then LUSAS will assign the axes automatically.  However this method is not recommended as the local beam orientation may not be as required

It is possible to view local element axes from the “Mesh” layer.  Mesh layer properties can be seen by right-clicking on the Mesh layer in the Layers tab of the Tree-view and selecting Properties…  The option to “Show element axes” can then be selected and all local element axes are then displayed if the Apply or OK button is pressed.  The local x direction is represented by an arrow with two heads, the local y direction by an arrow with one head and the local z direction by an arrow without a head.  Local Cartesian coordinate systems follow the same rules as the global Cartesian coordinate system and are always in terms of a right-handed system.  The difference between left and right handed systems is shown in the diagram below.

The local element x axis will always be in the direction of the line representing the beam to which the elements have been assigned and cannot be changed.  The direction of the axis will point in the direction determined by the line direction.  The line direction can be visualised by selecting the option “Line directions” from the Geometry layer Properties window.  Another option is to show the  "Line axes".  An example is shown below, note that default the element axes will follow that of the line (shown by a single pink axes).  In this case the local element axes also correspond with the global axis as shown.

The local element x direction can be reversed by reversing the line direction, however the positive direction of the local x axis has no significance when considering the geometric properties of the beam.  The positive z direction of the local z axis is important when the beam is given an eccentricity value.  Eccentricity is measured from the bending plane to the nodal line.

In the diagram above, the local coordinate system was determined by LUSAS when the mesh was assigned to the line, which simply aligned the local system to be the same as the global system.  This however may not be the correct beam orientation, it may, for example, be required that the local z direction be pointing vertically upwards.  For this system to be used the easiest method would be to define a 90 degree angle between element and line axes, about the x-axis.  Such an angle can be defined on assigning the beam mesh to the line and it is called a Beta angleWhen the beam element attribute is assigned to selected lines the following dialog appears:

The rotation of the element axes (grey) 90 degrees about the x axis from the line axes (pink) is shown below:

Another method that can be used requires first define a local coordinate system in Modeller.  A local coordinate system can be defined using the menu command:

Attributes > Local Coordinate…  

To create the system as described above a rotation angle of –90 degrees should be entered which acts about the global X axis (ie in the global YZ plane).

Once defined, the local Cartesian coordinate system will then appear on the graphics screen at the origin specified in the window.  The coordinate system is coloured magenta to distinguish it from the global coordinate system.

This local coordinate system can then be used when assigning beam elements to the lines of the model.  

The local coordinate system created earlier can then be used in the assignment by selecting “By specified local coordinates” and selecting the system from the drop-down list.  Pressing OK will show that the local coordinate system has been used in the mesh assignment and that the local element axes are in the desired orientation.

Joint elements can be oriented using local coordinate systems in a similar manner.

For more information regarding local coordinate systems please see following reference:

Modeller Reference Manual > Chapter 5 : Model Attributes > Other Attributes > Local Coordinates

There is a further method to orientate the axes.  If a point is created and then selected and put into selection memory (right-click in the graphics window and choose Selection Memory>Set or Add) before assigning the Line Mesh, then the option "By point in selection memory" can be selected.  

The point is used in combination with the line assigned to define the XY-Plane.  For the example above where the line runs along the global X axis (Y=0, Z=0), a point could be created and selected at the coordinate (0, 0, -1) for example as shown below.

For more complex orientation of beam elements there is a script available to download from the scripts downloads page which may be helpful.


  1. There are vector rules that are used to decide the orientation of the line axes, however in general, the line's z axis will tend to match the global z axis if possible, then the global y axis, then the global x. Please see the Element Reference Manual > Appendix C : Local Element Axes > Standard Line Element

  2. Local coordinate attributes should not be assigned directly to a line for the purposes of orientating beam element axes.  This will actually transform nodal freedoms and will affect the direction of global loads and supports.

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