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The introduction to the Mechanics of Materials is described in the first four chapters. The first chapter has an introductory character and explains fundamental physical notions, such as continuity and rheological behaviour. It also explains why the topics that compose Solid Continuum Mechanics are divided into three chapters: the stress theory, the strain theory and the constitutive law. The second chapter contains the stress theory. This theory is expounded almost exclusively by exploring the balance conditions inside the body, gradually introducing the mathematical notion of tensor.
[...]... Mechanics of Materials I Introduction I.1 General Considerations Materials are of a discrete nature, since they are made of atoms and molecules, in the case of liquids and gases, or, in the case of solid materials, also of fibres, crystals, granules, associations of different materials, etc The physical interactions between these constituent elements determine the behaviour of the materials Of the different... IV.9 XIII Examples and Exercises 106 Part II Strength of Materials V Fundamental Concepts of Strength of Materials 119 V.1 Introduction 119 V.2 Ductile and Brittle Material Behaviour 121 V.3 Stress and Strain 123 V.4 Work of Deformation Resilience and Tenacity ... interior of the material, or on its mass Examples of the first kind are axial and shear forces and bending and torsional moments which act on the crosssections of slender members (bars) Examples of the second kind would be gravitational attraction or electromagnetic forces between two parts of the body However, the second kind does not play a significant role in the current applications of the Mechanics of Materials. .. definition is used throughout this book I.3 Subdivisions of the Mechanics of Materials The Mechanics of Materials aims to find relations between the four main physical entities defined above (external and internal forces, displacements and deformations) Schematically, we may state that, in a solid body which is deformed as a consequence of the action of external forces, or in a flowing liquid under the action... the displacement of the points of the body This set of relations defines the theory of strain It is also independent of the rheological behaviour of material In the form explained in more detail in Chap III, the theory of strain is only valid if the deformations and the rotations are small enough to be treated as infinitesimal quantities I.3 Subdivisions of the Mechanics of Materials 7 3 – Constitutive... mass of a solid body or liquid Examples of external mass forces are: the weight of the material a structure is made of (earth gravity force), the inertial forces caused by an earthquake or by other kinds of accelerations, such as impact, vibrations, traction, braking and curve acceleration in vehicles and planes, and external electromagnetic forces – Rigid body motion – displacement of the points of. .. conditions, some relations may be established in the interior of the body, as well as in its boundary These fundamental relations are deduced in the following two sub-sections II.3.a Equilibrium in the Interior of the Body The static equilibrium of a body, or a part of it, under the action of a system of forces demands that both its resulting force and its resulting moment vanish If the resulting moment... Equilibrium at the Boundary The balance conditions of the forces acting in the infinitesimal neighborhood of a point belonging to the boundary of the body may be established by considering an infinitesimal tetrahedron defined by three facets, whose seminormals are parallel to the coordinate axes and by a facet on the boundary Figure 6 shows this tetrahedron and the stresses and boundary forces per area... hypothesis of continuity may not be acceptable In the theory expounded in the first part of this book the validity of the hypothesis of continuity is always accepted This allows the material behaviour to be defined independently of the geometrical dimensions of the solid body of the liquid mass under consideration For this reason, the matters studied here are integrated into Continuum Mechanics I.2 Fundamental... Variation of the distance between any two points inside the solid body or the liquid mass These definitions are general and valid independently of assuming that the material is continuous or not In the case of continuous materials two other very useful concepts may be defined: – Stress – Physical entity which allows the definition of internal forces in a way that is independent of the dimensions and geometry of . h0" alt="" Mechanics and Strength of Materials Vitor Dias da Silva Mechanics and Strength of Materials ABC Vitor Dias da Silva Department of Civil Engineering Faculty. between 1989-94, for the disciplines of Applied Mechanics II (Introduction to the Mechanics of Materials) and Strength of Materials, taught by the author in