## Introduction

1 In the preceding chapters we have focused on the behavior of a continuum, and the 15 equations and 15 variables we introduced, were all derived for an infinitesimal element.

2 In practice, few problems can be solved analytically, and even with computer it is quite difficult to view every object as a three dimensional one. That is why we introduced the 2D simplification (plane stress/strain), or 1D for axially symmetric problems. In the preceding chapter we saw a few of those solutions.

3 Hence, to widen the scope of application of the fundamental theory developed previously, we could either resort to numerical methods (such as the finite difference, finite element, or boundary elements), or we could further simplify the problem.

4 Solid bodies, in general, have certain peculiar geometric features amenable to a reduction from three to fewer dimensions. If one dimension of the structural element1 under consideration is much greater or smaller than the other three, than we have a beam, or a plate respectively. If the plate is curved, then we have a shell.

5 For those structural elements, it is customary to consider as internal variables the resultant of the stresses as was shown in Sect. ??.

6 Hence, this chapter will focus on a brief introduction to beam theory. This will however be preceded by an introduction to Statics as the internal forces would also have to be in equilibrium with the external ones.

7 Beam theory is perhaps the most successful theory in all of structural mechanics, and it forms the basis of structural analysis which is so dear to Civil and Mechanical engineers.

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