Statical Determinacy and Equilibrium in Structural Mechanics

This lecture covers the concepts of statical and kinematical determinacy, focusing on equilibrium in structural mechanics. The instructor begins with a reminder about the types of joints, such as roller and pin joints, and their constraints on motion. The discussion includes the identification of instantaneous centers of rotation and how they relate to the statical and kinematical states of structures. Various configurations of plates in 2D are analyzed to determine their degrees of freedom and constraints, categorizing them as isostatic, hypostatic, or unstable. The instructor provides examples and exercises to illustrate these concepts, emphasizing the importance of understanding the relationships between forces and constraints. The lecture also addresses specific exercises involving equilibrium equations and free body diagrams, guiding students through the calculations necessary to solve for unknown forces in different structural scenarios. Overall, the lecture aims to deepen the understanding of how to assess and analyze the stability and movement of structures in engineering.