Constraints in Structural Mechanics: Determinacy and Indeterminacy

This lecture covers the concepts of hyperstatic, hypostatic, and hyperstatic-hypostatic systems in structural mechanics. The instructor begins by discussing statical determinacy and the adequacy of constraints necessary for equilibrium in two-dimensional systems. Examples of isostatic and non-isostatic systems are presented, illustrating how certain structures can move despite having multiple reaction forces. The lecture emphasizes the importance of understanding redundancy in constraints, defining it as the presence of supports that do not introduce new degrees of freedom. The instructor explains that the number of redundant supports corresponds to the degree of statical indeterminacy. The discussion then shifts to hypostatic systems, which have more constraints than necessary for equilibrium, leading to kinematic indeterminacy. The lecture concludes with examples demonstrating how to analyze these systems, including the use of instantaneous centers of rotation to identify degrees of freedom. Overall, the lecture provides a comprehensive overview of how constraints affect the behavior of structures in mechanical systems.