RDM 1 S3 / S4
École Supérieure Agronomie L2 · DEUXIEME ANNÉE L2
7 chapitres · 0 séance
Bloqué sur le calcul des moments d'inertie ou le tracé des efforts intérieurs? Bienvenue dans votre module de renforcement en ligne ! Ce cours est spécialement conçu pour vous aider à maîtriser la RDM 1 étape par étape, avec méthode et sans stress. 💡 Au programme : 1:Principes fondamentaux & calcul des réactions d'appuis 2: Torseur des efforts intérieurs (N, T, M) & méthodes simples pour les diagrammes 3 : Caractéristiques géométriques des sections (centres de gravité G, moments d'inertie Iz). 4 : Sollicitations simples : Traction, Compression, Cisaillement, Torsion & Flexion plane. 🎯 Ce que vous trouverez ici :Explications claires, fiches synthétiques, démarches étape par étape et exercices types d'examens entièrement corrigés pour réussir vos contrôles. 🎓 Adapté aux étudiants en Génie Civil, Génie Mécanique, ST , classes préparatoires ST , école supèrieure d'enseignement et filières techniques.
Au programme
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Chapter 1: Fundamental Concepts and Assumptions of Strength of Materials " Notions Fondamentales et Hypothèses de la RDM
Par Mme asma
This introductory chapter lays the essential theoretical and conceptual foundation for the entire study of Strength of Materials (Mechanics of Deformable Bodies). It bridges the gap between rigid-body mechanics and deformable body analysis. Students will learn how to model a real-world structure into an idealized beam model, identify boundary conditions and support types, and master key simplifying assumptions (Navier-Bernoulli, Saint-Venant, linear elasticity) that make structural analysis both practical and rigorous. Ce premier chapitre pose les bases théoriques et conceptuelles indispensables à toute l'étude de la Résistance des Matériaux. Il permet d'effectuer le passage de la mécanique des solides rigides à la mécanique des corps déformables. L'étudiant y apprend à modéliser une structure réelle sous forme de poutre, à identifier les types de liaisons et d'appuis, et à maîtriser les hypothèses simplificatrices qui rendent le calcul des structures accessible et rigoureux.
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chapter 2: Internal Forces & Diagrams (N, V, M) "Torseur des Efforts Intérieurs & Diagrammes (N, T, M)"
Par Mme asma
This second chapter is the core of Strength of Materials 1. It bridges the gap between the overall external analysis of a structure and the internal stress behavior within the material itself.Using the method of sections (fictitious cut method), students will learn how to isolate a beam segment to determine the internal cohesion forces: Axial Force (N), Shear Force (V), and Bending Moment (M). The main objective is to establish the analytical equations for these internal forces along the beam length and to plot their corresponding diagrams, which are essential for identifying critical stress zones and safely sizing structural elements.
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Chapter 3: Geometric Properties of Cross-Sections "Caractéristiques Géométriques des Sections Droites"
Par Mme asma
Before analyzing stress distributions in beams under bending or torsion, it is essential to determine the geometric features of their cross-sections. This chapter covers the mathematical and graphical methods used to calculate key geometric parameters—such as the centroid, first moment of area, and second moment of area (moment of inertia)—for both simple and composite cross-sections.
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Chapter 4: Simple Tension and Compression " traction et compression"
Par Mme asma
This chapter introduces the first elementary load case in Strength of Materials. It covers structural members subjected to axial forces that act to either stretch (tension) or shorten (compression) the element along its centroidal axis.Students will explore the fundamental relationships between applied force, internal normal stress ($\sigma$), and the resulting strain ($\epsilon$). The chapter emphasizes analyzing tensile test curves to determine key material properties (Young's modulus, yield strength, ultimate strength) and applying safety criteria for proper component sizing.
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Direct Shear (Simple Shear) "Cisaillement simple"
Par Mme asma
This chapter is dedicated to direct shear (simple shear), a loading condition where external forces act tangentially to the cross-sectional plane, causing adjacent parallel sections to slide past one another.This concept is essential for analyzing and designing fasteners and mechanical joints in structural engineering (bolts, rivets, pins, keys, welded joints). Students will learn how to compute the average shear stress , apply Hooke’s law for shear deformation, and design secure mechanical connections.
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Simple Torsion (ou Pure Torsion)
Par Mme asma
This chapter is dedicated to the analysis of structural and mechanical components (primarily circular shafts and drive axles) subjected to equal and opposite torque couples applied about their longitudinal axis, causing them to twist.Students will learn how an applied torque ($M_t$) generates a shear stress distribution ($\tau$) that varies linearly from zero at the center to a maximum at the outer surface. The chapter also covers the calculation of the angle of twist ($\theta$) and the structural design of solid vs. hollow shafts
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Simple Bending (Pure Bending) " flexion simple"
Par Mme asma
This chapter is a core pillar of Strength of Materials. It is dedicated to the study of slender structural elements (beams, joists, shafts) subjected to pure bending moments, where external loads cause the member to curve without applying axial or shear forces.Students will learn how a bending moment (Mfor M) generates a linear normal stress distribution across the cross-section, creating tension and compression zones separated by a stress-free neutral axis. The chapter also covers calculating the radius of curvature ($\rho$) and sizing cross-sections based on their area moment of inertia (I)