Some consistent finite element formulation of 1-D beam models: A comparative study

A consistent Finite Element formulation has been developed for four classical l-D beam models. This formulation is based upon the solution of the homogeneous differential equation (or equations) associated with each model. Results such as the shape functions, stiffness matrices and consistent force vectors for the constant section beam have been found. Some of these results have been compared with the corresponding ones obtained by the standard Finite Element Method (i.e. using polynomial expansions for the field variables). Some of the difficulties reported in the literature concerning some of these models may be avoided by this technique. This one has also been applied here in order to obtain an alternative consistent formulation to the one presented in the Eurocode 3 for the amplification factor of the deflections for built-up compression members