TABLE OF CONTENTS In this chapter various advanced topics from simple beam theory are discussed. We begin with several methods of solution for bending of continuous beams. Next, unsymmetric bending is analyzed, followed by the analysis of curved beams (including rings and arches). The section on beams on elastic foundations constitutes a large portion of the chapter and also includes, because of mathematical analogy, storage tanks. The emphasis throughout the chapter is on the derivation and usage of influence functions (Green's functions). Symbolic manipulation packages are often used, and some outputs of sessions are provided. Deflections are calculated using mainly Castigliano's theorem. Limit analysis is treated very briefly, as are thermal stresses. This is followed by the application of approximate methods, which are illustrated by examples. Several Fortran programs are included on the disk. The chapter ends with an extensive discussion of piezoelectric and also composite beams. Several examples are solved.
In this section we consider the bending of thin elastic beams with an arbitrary number of spans. Each span may have a different but constant stiffness and may carry arbitrarily distributed or concentrated loads. The equation for bending of an elastic beam is known to the reader from an introductory course of mechanics of materials (see [1], [21, p. 273]). It has the form
where E is Young's modulus, I the moment of inertia of the beam cross section, w( x) the deflection, and q( x) the applied load.
