Introduction

This chapter introduces three topics that expand the usefulness of the Bernoulli–Euler beam bending and extension equations developed in the previous chapter. The first topic is elastic beam end supports. The use of elastic end supports begins the process, developed further in Part V, of modeling beams that are parts (elements) of larger elastic structures. The second topic is partial span distributed loads, and concentrated loads acting at points other than the beam ends. Then, both as another form of loading, and as a prelude to the third topic, combined lateral and axial loading cases are also examined. The third topic is beam buckling. This chapter provides only a brief introduction to beam buckling theory. However, some of the complexities of the topic are mentioned without being explored mathematically. The mathematical differences between the one standard type of buckling analysis introduced here and all the other beam analyses of this chapter and Chapter 10 are underscored. Additional aspects of beam and plate buckling theory are provided in Part VI.

Before proceeding to these three topics, it is worthwhile mentioning again a limitation on the scope of the beam bending theory developed in Chapter 10 which is retained in this chapter. That limitation is that the bending deflections are small. Thus it is possible to confine the axial and bending interactions to the bending equations, and to deal with the bending and twisting deflections separately, without regard for any interaction between them.