Mechanics of Composite Beams

Abstract

A structural element having one dimension many times greater than its other dimensions can be a rod, a bar, a column, or a beam. The definition actually depends on the loading conditions. A beam is a member mainly subjected to bending. The terms rod (or bar) and column are for those members that are mainly subjected to axial tension and compression, respectively. Beams are one of the fundamental structural or machine components. Composite beams are lightweight structures that can be found in many diverse applications including aerospace, submarine, medical equipment, automotive and construction industries. Buildings, steel framed structures and bridges are examples of beam applications in civil engineering. In these applications, beams exist as structural elements or components supporting the whole structure. In addition, the whole structure can be modeled at a preliminary level as a beam. For example, a high rise building can be modeled as a cantilever beam, or a bridge modeled as a simply supported beam. In mechanical engineering, rotating shafts carrying pulleys and gears are examples of beams. In addition, frames in machines (e.g. a truck) are beams. Robotic arms in manufacturing are modeled as beams as well. In aerospace engineering, beams (curved and straight) are found in many areas of the plane or space vehicle. In addition, the whole wing of a plane is often modeled as a beam for some preliminary analysis. Innumerable other examples in these and other industries of beams exist. This chapter is concerned with the development of the fundamental equations for the mechanics of laminated composite beams. Two classes of theories are developed for laminated beams. In the first class of theories, effects of shear deformation and rotary inertia are neglected. This class of theories will be referred to as thin beam theories or classical beam theories (CBT). This is typically accurate for thin beams and is less accurate for thicker beams. In the second class of theories, shear deformation and rotary inertia effects are considered. This class of theories will be referred to as thick beam theory or shear deformation beam theory (SDBT). This chapter can be mainly divided into two sections. First, static analysis where deflection and stress analysis for composite beams are performed and second dynamic analysis where natural frequencies of them are assessed. In many applications deflection of the beam plays a key role in the structure. For example, if an aircraft wig tip deflection becomes high, in addition to potential structural failure, it may deteriorate the wing aerodynamic performance. In this and other applications, beams can be subjected to dynamic loads. Imbalance in driveline shafts, combustion in crank shaft applications, wind on a bridge or a