Efficient generation of standard and non-standard influence functions using Generalized Beam Theory

In structural analysis and design, influence functions (lines and surfaces) are extremely valuable for identifying the most unfavorable positions of live loads. This paper introduces a computationally efficient method for calculating non-standard influence functions using Generalized Beam Theory (GBT), a thin-walled beam theory that allows cross-section deformation by means of hierarchical and structurally meaningful “cross-section deformation modes”. Consequently, the proposed method enables not only the calculation standard influence functions (for displacements, support reactions and stress resultants), but also those pertaining to higher-order cross-section deformation (torsion, distortion, plate bending, etc.), their strains, stress resultants and mode amplitudes. The computational cost of the procedure is equivalent to that of a single linear analysis of the structure and its implementation is straightforward. Several illustrative examples are presented to show the capabilities of the proposed method.