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Energy Methods For the Calculation of Displacements and Statically Indeterminate Systems

par: Pr. M Khenfer
Disponible
Pages 162
Dimensions 16*23.5
Publication 2026-05-30
Éditeur —
Papier : 1 100.00 DA Numérique: 550.00 DA

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.

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Foreword 03
Table of Contents 05
Chapter 1: Internal Energy and Internal Potential 07
1. Introduction 08
2. Work of external forces
3. Expression of work W as a function of applied forces and moment
4. Expression of work as a function of internal forces N, T and M 09
5. Application examples 13
6. Conclusions 15
Chapter 2: Use of Energy Methods 17
1. Introduction 18
2. Maxwell-Betti theorem 18
3. Castigliano's theorem 21
4. Castigliano's theorem in its second form
5. Manabréa’s Method 29
6. Bertrand de Font Violent equation 24
7. Mohr's method 35
8. Conclusions 39
Annex 1: Tables of Mohr integral values 40
Chapter 3: Single-span Statically Indeterminate beams 45
1. Introduction 46
2. Resolution methods 46
3. Conclusions 51
Annex 2: Tables for calculating the deflections of simple Statically
determinate beams
Chapter 4: Continuous Beams 53
1. Introduction 54
2. Three-moment theorem 54
3. Method of focal points 62
4. Conclusions 74
Chapter 5: Plane bar systems and statically determinate frame 75
1. Introduction 76
2. Statically determinate and statically indeterminate systems deformable and indeformable bar systems
3. Kinematic study 78
4. Statically determinate frames 81
5. Conclusions 88
Chapter 6: Method of forces 89
1. Introduction and principle 90
2. Different stages of the method of forces
3. Canonical equations of the force method
4. Conclusions 103
Chapter 7: Method of deformations 105
1. Introduction 106
2. Principle of the method
3. Fundamental equations of the method 107
4. Application examples 114
5. Conclusions 136
Chapter 8: Method of displacements 137
1. Introduction 138
2. Principle of the method 138
3. Theoretical bases 138
4. Application examples 145
5. Conclusions 159
References
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