A direct procedure for the determination of the axis of twist and correlation with shear centers

A very simple numerical procedure is described for the determination of the axis of twist for beam-like structures subjected to torsional loading. The procedure utilizes the displacements obtained from an independent torsion calculation, e.g., a finite element simulation, to determine the coordinates of a space curve about which all points rotate along the axial length of the structure. Using a least squares algorithm, the axis of twist is determined as a finite element post-processing step for cutting planes defined along the axial length of the structure. The equivalence of a beam’s center of twist and its shear center is reviewed and demonstrated using specific 3-D numerical examples. • A straightforward and direct method for the determination of the axis of twist. • Least squares calculation based on finite element displacement data files. • Correlation with shear centers (center of flexure) for cantilever structures. • Resolution of controversies in theory of elasticity associated with definition of shear center. • Numerical examples that demonstrate accuracy of shear center computations. • Clarification of classical strength of materials vs elasticity controversies concerning the centers of twist and shear centers. • Graphical visualization of axis of twist for nonsymmetric elastic structures. • Examination of boundary condition effects on shear center deviation.