Structural Mechanics: Isostatic and Hyperstatic Systems

This lecture discusses the concepts of isostatic and hyperstatic systems in structural mechanics. It begins with definitions, explaining that an isostatic system has an equal number of unknowns and equilibrium equations, while a hyperstatic system has more unknowns than equations. The instructor highlights the advantages of hyperstatic systems, such as increased rigidity and resistance, but notes the complexity in calculations. The differences between the two types of structures are elaborated, emphasizing that isostatic structures are flexible and their internal forces are independent of rigidity, whereas hyperstatic structures are sensitive to support settlements and temperature variations. The lecture includes examples of beams under different support conditions, illustrating how the number of unknowns affects the calculations of internal forces and moments. The instructor also explains the significance of rigidity in hyperstatic systems and how it influences the behavior of structures under various loads. The lecture concludes with a discussion on the implications of these concepts for structural design and analysis.