Bending in Beams

This chapter studies flexible beam elements subject to transverse loading. Issues of mechanics of materials will be considered, which mainly deal with stresses (strength) and strains (deflection and stiffness). The main focus of the present chapter will be the analysis of straight beams with symmetric cross-sections. The topic of bending in beams is important in view of the wide applicability of bending members in engineering applications. Building structures, bridges, overhead vehicle guideways, robots, airplanes, ships, ground vehicles, and construction machinery, such as cranes, are examples. Even when beam elements are subjected to other types of loads (e.g., axial forces, torques), in the linear case, one can analyze the bending loading and deflections separately and then add to the effects of other types of loading, by using the principle of superposition. The main contents of the chapter are the following: Importance of flexible beam elements in engineering applications, Sign convention in the analysis, Shear diagram and moment diagram, Graphical method for shear and moment diagrams, Flexure formula (for bending stress), Composite beams and equivalent sections, Transverse shear and shear flow at joints, Deflection in beams, and Statically indeterminate beams.