File Lecture1.pdf - Lecture 11 Outline: -Introduction...

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Lecture 1 1 Lecture 1 1 Outline: -Introduction (Motivation) -Statics (Static Equilibrium, Boundary conditions and Support reactions, Internal forces and types) -Stress (Allowable limit, Normal stress, Shear stress) -Strain (Normal strain, Shear strain) -Mechanical Properties of Materials (Stress-strain relation, Hooke’s law) 1. Introduction to Mechanics of Solids In this course we will be studying the effects of external forces on deformable bodies . Take a look at Figure 1, what is described is that an undeformed solid body changes its shape when you apply some forces on it. Fig.1 Deformation of a solid body under applied load Motivation : Some of the important questions for Engineers are: -Is the body moving or does it stay still under this loads? -Can the body carry the applied loads without breaking? -What shape does the body take under the applied loads, or in other words how much deformation does the body make? In order to be able to answer these questions we will be using the principles of statics, the properties of the material that the body is made of and the kinematic (and support) conditions that the body is in as well as mathematical tools such as integration, differentiation etc. The concepts learnt in this course are necessary in the future for structural analysis, geotechnical analysis, design etc. Statics, Maths, Physics Mechanics of Solids Structural Analysis, Geotechnical Engineering Water Engineering Design of Structures 1 Mechanics of Solids Dr Emre Erkmen
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Lecture 1 2 2. Statics Statics is the study of contrasting forces under which the movement of the body in the space is prevented. For a body to stay still it should be in static equilibrium under the acting forces . Force is a vector which means it has a magnitude and direction. We will be describing forces in a space by using its components adopting a Cartesian coordinate system . Cartesian coordinate system (X,Y,Z) is based on three directions in space that make right angles with each other. The first postulate we adopt in this course is that all the forces and geometric relations are described in a Fixed Cartesian coordinate system. The idea of specification of geometric objects by means of coordinates was first raised by French mathematician and philosopher Descartes. Cartesian coordinates are named in memory of him. 2.1. Static Equilibrium From the definition of force, we can look for the conditions of Static Equilibrium. Fig.2 Static equilibrium of forces coinciding at a point In the X, Y, Z coordinate system Static Equilibrium of forces coinciding at a point requires that the components of the forces in all three directions add up to zero. 0 X F = 0 Y F = 0 Z F = The components of each force in Fig. 2 are shown below. (a) Components of
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File Lecture1.pdf - Lecture 11 Outline: -Introduction...

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