Variational derivation of governing differential equations for truncated version of Bresse-Timoshenko beams

In this paper, we provide a variational derivation of modified Bresse-Timoshenko equations. This process leads to the additional term to so called truncated set of Bresse-Timoshenko equations; this new term is associated with the modified slope inertia. The two sets of truncated versions of the Bresse-Timoshenko equations are contrasted with each other, as well as with the original Bresse-Timoshenko equations on the example of the (a) beam that is simply supported at its both ends, and (b) the cantilever beam with end mass. It is concluded that application of either truncated sets of equations is advantageous over the original Bresse-Timoshenko equations. As far as two truncated sets of equations are concerned, the variationally derived set appears to be preferable.