ABSTRACT
This chapter considers a more complex structural member, the beam, wherein it first develop approximate equations for determining stress and deformation of the beam via the method of total potential energy. It also considers approximate solutions to the deformation of beams by using the Ritz method and a method stemming from the Reissner principle. The chapter utilizes Castigliano's second theorem to consider statically indeterminate supporting force systems for beams. It presents the full theory of linear elasticity, and then makes simplifying assumptions as to stress distributions (plane stress) by stating that certain stresses were to be taken as zero or constant in the domain of interest. The technical theory of beams presented in the previous section does not include the effects of shear deformation. For short stubby beams this contribution clearly cannot be neglected, and for this reason authors present the Timoshenko theory of beams as a means of accounting for the effects of shear in a simple manner.
