ABSTRACT
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.
