ABSTRACT
Due to their slenderness, a number of composite elements (mechanical components or structural parts) can be considered as beams. The behavior under loading of these elements becomes a complex problem when the 3D aspect is discussed. We propose in this chapter a monodimensional approach of the phenomenon through an original method based on the definition of resultants for displacements, which will constitute the counterpart of the traditional stress resultants (shear force, normal force, and bending moment). This leads to a homogenized formulation for bending. We obtain equilibrium and behavior relationships formally identical to those of classical homogeneous beams. Then using similar equations to those of classical beams does the application of these relationships to the calculation of stress values and displacements. The study is limited here to composite beams with constant characteristics from one cross section to another (geometry, materials), with any-shaped components or phases, which are assumed to be isotropic and perfectly bonded to each other. Various examples of composite beams are provided in Application Chapters 19 and 21.
