Deformable Structures: Statically Determinate and Indeterminate Systems

This lecture covers the analysis of statically determinate and indeterminate systems, focusing on deformable structures. It begins with a review of basic concepts such as axial loading and stiffness, introducing Young's modulus and its historical context. The instructor presents a simple truss example to illustrate statically determinate systems, explaining how to determine internal forces and displacements using equilibrium equations. The lecture then transitions to statically indeterminate systems, emphasizing the importance of kinematic compatibility and the use of Hooke's law to relate stress and strain. The instructor discusses the method of linear superposition for analyzing hyperstatic systems, demonstrating how to decompose complex structures into simpler isostatic subsystems. Throughout the lecture, practical examples and mathematical derivations are provided to reinforce the concepts, culminating in a discussion on the design of structures to ensure safety and functionality under load. The session concludes with a preview of upcoming topics related to beam bending and finite element analysis.