Energy Methods For the Calculation of Displacements and Statically Indeterminate Systems

In the resistance of materials, energy methods are the basis for calculating displacements and statically indeterminate (hyperstatic) systems. The writing of this document represents the fruit of more than thirty years of teaching the Resistance of Materials courses (RDM I, RDM II and RDM III). Firstly, we present generalities on the internal potential applied to elastic systems with its application for the calculation of displacements (CASTIGLIANO methods, BERTRAND DE FONT VIOLENT method) and (MANABRÉA and MAXWELL BETTI methods) for the calculation of Statically Indeterminate (hyperstatic) beams. Next, single-span Statically Indeterminate beams are studied using the integration method and the displacement comparison method. The fourth chapter is devoted to the study of continuous beams using the three- moment method and the focus method. The fifth chapter studies the plane systems of bars and statically determinate frames so that the student can adapt to the calculation of statically indeterminate (hyperstatic) frames in the following chapters. The last three chapters are reserved for the study of Statically Indeterminate systems (frames) using the force method, the rotation method and the displacement matrix method. Finally, it is noted that the application exercises in this manual are taken from the exam subjects and tutorials proposed by the author himself during his years of teaching. This document is intended for undergraduate and master's students in civil engineering and public works and also for engineers both fields.