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This paper deals with curved beams with polynomial free geometry. The problem is approached analytically and the differential equations that govern the mechanical behavior of curved beams are presented. A system of twelve linear ordinary differential equations is solved using either an analytical or a customized numerical method with boundary conditions. Results of the different components of forces, moments, rotations, and displacements are given and plotted in the examples for different polynomial-shaped beams of the fourth degree. It is concluded from the present analyses that the parabolic shape has better response to distributed loads than the other polynomial-shaped beams considered. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]