# Skew Frame Properties

Beam type spring elements are best defined using three nodes (Figure 1). Nodes 1 and 2 are the two ends of the element and define the local X axis. Node 3 allows the local Y and Z axes to be defined. However, this node does not need to be supplied.

If all three nodes are defined, the local reference frame is calculated by:(1)
$\stackrel{\to }{x}=\overline{{n}_{1}{n}_{2}}$
(2)
$\stackrel{\to }{z}=\stackrel{\to }{x}×\overline{{n}_{1}{n}_{3}}$
(3)
$\stackrel{\to }{y}=\stackrel{\to }{z}×\stackrel{\to }{x}$
If node 3 is not defined, the local skew frame that can be specified for the element is used to define the Z axis. The X and Y axes are defined in the same manner as before.(4)
$\stackrel{\to }{z}=\stackrel{\to }{x}×{\stackrel{\to }{y}}_{skew}$
If no skew frame and no third node are defined, the global Y axis is used to replace the Y skew axis. If the Y skew axis is collinear with the local X axis, the local Y and Z axes are placed in a totally arbitrary position. The local Y axis is defined at time zero, and is corrected at each cycle, taking into account the mean X axis rotation.