Stiffness and Transfer Matrix Analysis in Global Coordinates of a 3D Curved Beam

This article presents the differential equation in the global coordinates governing the structural behavior of 3D curved beams existing in building structures and civil works. This differential equation presented is of the lower-triangular form, which allows us to obtain the transfer matrix, also of lower-triangular form and with unit diagonal, through simple integrals. The stiffness matrix is determined from the transfer matrix expression, only by reordering operations, without employing additional structural methods, energy theorems or other. This rearrangement can be more easily done under the global system, compared with the natural reference system, since the order of the matrices involved has been reduced. The examples presented show the process to apply this general procedure to derivation of the stiffness matrix of a member from its transfer expression, through reordering operations.