ABSTRACT
In this chapter, the authors examines a more complex structural member, the beam, wherein they develop approximate equations for determining stress and deformation of the beam via the method of total potential energy. The theory that they shall propose is called the technical or engineering theory of beams. The authors consider approximate solutions to the deformation of beams by using the Ritz method and a method stemming from the Reissner principle. They present Castigliano's second theorem to consider statically indeterminate supporting force systems for beams. The authors also examine the case of a beam simply supported at the ends and having a uniform elastic foundation between the ends. The elastic foundation is indicated graphically as a series of springs. They utilize certain of the results from the technical theory of beams to illustrate the determination of deflections of loading points on beams via the second Castigliano theorem.
