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An example for a 3D Timoshenko beam element (for static linear elastic
calculations and small deformations) according to [109] is
implemented as element “U1” in CalculiX. It is used in example userbeam.inp
in the test suite. The reader is referred to files resultsmech_u1.f,
e_c3d_u1.f and extrapolate_u1.f for details on how a user elements is coded.
It has to be stated here, that the 2nd order moment 
, which is
used in the torsional stiffness, is such that it is assumed to be identical to
the polar 2nd order moment 
. This, however, restricts the application
of this element to beams with circular cross-sections.
In addition to [109] the current implementation also contains a mass matrix for dynamic analyses, which has been derived based on the assumptions, that