Static Analysis of Beams, Frames, and Arches

This work presents a direct approach to determine the response of beam structures to static loads when the beams can be modeled by the Euler-Bernoulli theory.  It starts by obtaining analytical expressions for the displacement, rotation, moment, and shear force responses of constant cross section beams that rest on an elastic foundation and on in-span rigid supports and are simultaneously subjected to a compressive axial force, concentrated forces, distributed forces, and applied moments.  These expressions are obtained for four sets of boundary conditions: clamped-clamped, clamped-free, clamped-hinged, and hinged-hinged.  Then, the constant cross section beam solutions are used to obtain analytical solutions for beams with a step change in flexural rigidity, rectangular frames with clamped and hinged boundary conditions, and rectangular plates hinged on two opposite edges.  Several of these solutions provide new analytical results for uniform and stepped beams with rigid in-span supports and for the displacement of rectangular frames.  The method is extended to obtain the response of uniform circular arches for various boundary conditions and the simultaneously application of different types of loads.  A set of five interactive graphics programs, one for each system, can be downloaded to explore system configurations that are unavailable elsewhere, verify solutions to exercises and examples found in engineering texts, and to explore more complex models and loading combinations.