(Solved): Consider a three-dimensional horizontal beam with a rectangular section, elastic, incompressible and ...

Consider a three-dimensional horizontal beam with a rectangular section, elastic, incompressible and isotropic, which is supported at its ends. It is subject to the action of gravity and to a couple M applied at the ends (these torques are due to the reactions of the supports), as shown in figure 4. Obtain the displacement field. The beam constants are E, ?, ?, and its dimensions are L, h, and a.