Lectures on Solid Mechanics

These Lecture Notes introduce the theoretical basics of solid mechanics to environmental engineering students. Born out of and supported by the European Project DEREC TEMPUS JEP Development of Environmental and Resources Engineering Curriculum, it collects the lectures held by the Authors during the course of Mechanic of Solids at the University of Florence, Degree of Environmental Engineering and Resources. Although the course is extended to basic structural engineering principles, such as mechanics, statics, kinematics and fundamental equations of beam structures, inertia, iso static and hyper static solution methods, these Lecture Notes reect only the content of the lectures of continuum mechanics. Several approaches are possible to the subject depending on the concern, either mathematically or physically oriented. The volume aims to provide a synthesis of both approaches, presenting in an organic whole the classical theory of solid mechanics and a more direct engineering approach. It is the Authors' opinion that a topdown learning process may oer to the engineering students those critical and autonomy tools necessary to gain awareness of that continuous learning process that is required; it characterizes the cultural and technical personality of an engineer. An ongoing learning is all the more necessary today, where the rapid development of powerful computers and computer solving methods (finite element methods, discrete volume methods, boundary methods, etc.) have opened up the way to new horizons that the classical approaches were only able to formulate. This fast and impressive growth of computer methods seems to be replacing the importance of gaining a consolidated knowledge of solid mechanics background. On the contrary, the Authors believe that only a conscious knowledge of theory can be that cultural instrument through which an engineer can really hope to control the use of computer methods. With this aim, the Reader addressed by this volume is mainly the under graduate student in Engineering Schools: it is organized in eight Chapters: Chapter 1 proposes a synthesis of the basic concepts of mathematics and geometry that the readers need in the following chapters. Chapter 2 and Chapter 3 are devoted to the elementary framework of strain and stress in an elastic body. The concept of nite strain and Cauchy stress state is introduced, together with Mohr's representation of a general state of stress. Chapter 4 focuses on the classical law of linear elasticity. Chapter 5 deals with the Principle of Virtual Works. Chapter 6 treats the energy principles and provides a basic introduction to the variational methods. Finally, Part I ends with a chapter introducing the notion of strength of materials. At the end of each chapter of the rst part the basics of the tensorbased shell theory are also presented and then an application to some standard shell geometries is provided in appendix A. The second part, Chapter 8, is dedicated to De SaintVenant's problem where the classical beam theory is presented focusing on the four fundamental cases: beam under axial forces, terminal couples, torsion, bending and shear. The volume, that consolidates the Lecture Notes prepared by the Authors for the secondyear undergraduate students in environmental engineering, proposes a widening of the classical theories approached, giving a list of references used during its preparation as a possible suggestion to the Reader. The Authors wish to express their heartfelt gratitude to professor Marco Modugno for the inspiring discussions and stimulating suggestions. It is also our pleasure to thank Eng. Seymour Milton John Spence for kindly revising the English text. The publication of this book has been possible thanks to the financial support of the European Commission (DEREC Tempus Project) and Ente Cassa di Risparmio di Firenze to whom the Authors are extremely grateful.