The Euler-Bernoulli beam model does not consider the shear effect present in cross-sections and

longitudinal fibers of the beam. For short beams, shear is important and thus the Timoshenko model

is employed. Its formulation will be derived below. The steps of the previous variational formulation

are employed again. Notice that the same geometrical hypotheses for bars, shafts, and beams in

bending only are valid for the Timoshenko beam; that is, we assume the length to be much larger

than the cross-section dimensions. Subsequently, we present the approximationwith the FEM, using

low-and high-order shape functions.