The reference mechanical load is the point load; all the other mechanical load types can be established by integrating the results for a point load over the loaded part of the beam.

The basic approach to calculating the load on the beam for a force at position is to consider the beam split at into two separate beams. Flexibility matrices can be established for axial, torsional and flexural loading

There must be continuity of displacement and rotation between the two beams and the forces and moment must balance the applied load. This allows a set of equations to be set up for the sub-beams and which can be solved for the shear force and bending moment at the loaded point.

Where the vector is respectively for unit force and unit moment

Once the force and moment at the loaded point have been established the end forces and moments (and hence the equivalent nodal forces) result from equilibrium of the two sub-beams.

The general distributed loading in the patch load, varying in linearly in intensity from position to position . The nodal forces and moments are then given by integrating the results for a point load

where is the force due to a point load at and

The tri-linear load option is simply a repeated set of patch loads.