Equilibrium in 3D: Statical and Kinematical Analysis

This lecture covers the principles of equilibrium in three-dimensional systems, focusing on system isolation and free-body diagrams. It discusses the categories of equilibrium in 3D, emphasizing constraints and statical determinacy. The instructor presents an example problem involving the opening of a box, illustrating how to analyze kinematic indeterminacy and the adequacy of constraints. The lecture highlights the importance of identifying degrees of freedom and visualizing systems of concurrent forces. It also explains how to confirm results using linear algebra, providing a comprehensive understanding of the conditions necessary for static and kinematic determinacy in three-dimensional structures. The concepts are reinforced through practical examples, ensuring that students grasp the critical aspects of structural mechanics in 3D environments.