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Line Orientation ("Beta angle")

"Beta" angles are used to define the orientation of straight section of beams. In the .tdl file, the beta angle is defined in *NODE. From the interface, for a line based on beam element, if the shape is selected at "straight", a field beta angle appears. If "beta" angle is selected, then the orientation of the line is based on the "beta" angle convention.

The convention originated with ISYMOST and therefore .tdl file generated from an ISYMOST model already have the "beta" angle properly defined. When loading a .tdl file with beta angle defined, the beta angle option is automatically selected in the interface. The main use is to define the orientation of non- circular beams. The following conventions applies:

Coordinate system :

The beam (in blue below) has its axis defined from START to END node (defines the Zl vector) The β angle fixes the local reference system defining the Xl and Yl axis around the Zl axis. Therefore the local frame (Xl,Yl,Zl) is such that

  • Zl is the beam axis
  • Yl is parallel to (Xg, Zg) global frame
  • (Xl,, Yl, Zl) is an orthonormal frame

Then (Xl,Yl) is rotated around Zl by beta degrees

In the case where Zl is aligned with Yg, Yl=Zg

For an inclined beam:

The red plane is defined by Zl (Zl perpendicular to that plane) Yl is the intersection of that plane with the plane (Xg,Yg), with Xl.Yg>0 (two possible directions) (Xl and Yl are vectorsFor an inclined of the red plane) If Zl=Yg, the two planes are equal then Yl=Zg

Note that in order to check that the beam of a model are properly oriented, it is recommended to perform a static equilibrium of the line and to dislplay the equilibrium in the 3D window of the .dss file. Then by clicking on the display button:

It is possible to display the orientation frame of any line in the model.