Virtual Work Principles: Energy and Mechanics

This lecture introduces the concepts of work and potential energy, focusing on the principle of virtual work (PVW) and its applications in structural mechanics. The instructor begins by reviewing previous topics related to internal load analysis in beams and frames, emphasizing the relationships between distributed forces, shear forces, and internal moments. The lecture transitions to the new topic of virtual work, explaining how it can be applied to solve static problems even with zero displacement. The instructor discusses the significance of virtual displacements, which are fictitious and infinitesimally small, and how they relate to the equilibrium of mechanical systems. The principle of virtual work is defined, stating that a mechanical system is in equilibrium if the virtual work of external forces vanishes during arbitrary virtual displacements. The lecture also highlights the historical contributions of Johann Bernoulli to the development of these concepts. Examples are provided to illustrate the application of PVW in analyzing rigid structures, showcasing its advantages over traditional force and moment equilibrium methods.