# Beam TYPE13 Spring (/PROP/SPR_BEAM)

Spring TYPE13 functions like a beam element with several independent modes of deformation:
• Traction / Compression
• Torsion
• Bending (2 modes)
• Shear (2 modes)

Contrary to a beam element, relations between displacements (resp. rotations) and forces (resp. moments) are not deducted from the geometry (area, length, and moment of inertia) and the material properties (Young modulus, shear modulus). Instead, they are user-defined through different stiffness formulations (see Stiffness Formulation for more details).

Spring TYPE13 works only if the length is not equal to zero. Nodes 1 and 2 are always used to define the local X-axis. Local Y direction is defined at time t=0 and its position is updated at each cycle, taking into account the mean X rotation. Initially, the Y-axis can be defined in different ways. A third node can be used for beam elements. It is also possible to use the local Y-axis of a skew frame. If a skew frame and third node are not defined, global Y-axis replaces the Y skew axis. If the Y skew axis is co-linear with the local X-axis, the local Y-axis and Z-axis are put in an arbitrary position. The Z-axis is finally computed as the cross product of X-axis and Y-axis.
An illustration of a beam type spring is shown below (Figure 2).
A bending deformation is illustrated in Figure 3. This deformation only takes into account the difference of the two nodes rotations. Beam double bending does generate bending deformation; but shear deformation is shown below.
The beam type spring behaves as a physical beam, in which the variation of bending moment in length generates the increase in shear. The shear force in the spring implies the change of bending moment.
Note: When defining the spring properties, it is strongly recommended to introduce values with physical meanings. A spring with high shear stiffness and a zero bending stiffness is not recommended and may lead to incorrect results.
Contrary to spring TYPE8, rigid body rotation is possible without any artificial force and moment generation for spring TYPE13. Behaviors of spring TYPE8 and TYPE13 under a rigid body rotation are compared in Figure 5.
To compute the critical time step, the same formula as spring TYPE4 is applied; the minimum overall degree of freedom is finally kept. Therefore to take into account the coupling between bending and shear, and the stiffness' in bending are modified:(1)
${K}_{yy}\approx {K}_{yy}+{l}^{2}{K}_{z}$
(2)
${K}_{zz}\approx {K}_{zz}+{l}^{2}{K}_{y}$
Between spring TYPE8 and TYPE13, the sign conventions is not the same, therefore results may be rather confusing when trying to compare both spring. For spring TYPE13, the deformation sign is based on the variation of initial length.

For a spring subjected to axial tension, the deformation will always be positive (Figure 6). This is not true any longer for spring TYPE8, since this spring can have a zero length for one (or all) direction, positive and negative spring deformations cannot be defined with the variation of initial length. The sign convention chosen for all degrees of freedom is that a deformation is positive (resp. negative), if displacement (or rotation) of node 2 minus displacement (or rotation) of node 1 is positive (resp. negative).

Figure 7 illustrates the difference between spring TYPE8 and TYPE13, resulting from the sign conventions in Radioss.

For further information, refer to Beam Type Spring Elements (TYPE13) in the Radioss Theory Manual.