Timoshenko theory

The algorithm is based on the exact Timoshenko’s solution of a 1D member. The axial force is assumed constant during the deformation. Therefore, the method is applicable for structures where the difference of axial force obtained by 1st order and 2nd order calculation is negligible (so called well defined structures). This is true mainly for frames, buildings, etc. for which the method is the most effective option.

The method is applicable for structures where rotation does not exceed 8°.

The method assumes small displacements, small rotations and small strains.

If 1D members of the structure are in no contact with subsoil and simultaneously they do not form ribs of shells, no fine division of 1D members into finite elements is required. If the axial force is lower than the critical force, this solution is robust. The method needs only two steps, which leads to a great efficiency of the method.

The first step serves only for solution of axial force. The second step uses the determined axial forces for Timoshenko´s exact solution. The original Timoshenko´s solution was generalised in SCIA Engineer and the shear deformations can be taken into account.