Abstract
This chapter presents the analysis of two-dimensional (2D) and three-dimensional (3D) frames. The theoretical background from Chapter 6 is used to develop the stiffness matrix of inclined beams subjected to combinations of nodal and varying loads that are arbitrarily oriented in space. Emphasis is given to the transformation of the loads and displacements from the local to the rotated coordinate system, and to the correlation of the stiffness matrix to the orientation angle of the beam. The procedure showing how to compose the special structural matrix equation incorporating both the global stiffness matrix and the boundary conditions submatrix is presented for frames. Analytical solutions of 2D and 3D frames as well as detailed development of CALFEM/MATLAB algorithm and step-by-step ANSYS implementation on framed structures are also presented. Finally, a computational methodology for solving hybrid structures, that is, structures composed of beams and bars, is described as an example of a cable bridge.
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