ENGINEERING MECHANICS

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1 ENGINEERING MECHANICS BASUDEB BHATTACHARYYA Assistant Professor Department of Applied Mechanics Bengal Engineering and Science University Shibpur, Howrah OXJFORD UNIVERSITY PRESS

2 Contents Foreword Preface Parti STATICS 1. Introduction to Statics 1.1 Introduction Body Space Vectors and Scalars Free Vector, Fixed Vector, and Null vector Sliding Vectors and Principle of Transmissibility Unit Vector and Vector Triad Scalar Product or Dot Product Vector Product or Cross Product Scalar Triple Product Vector Triple Product S 1.12 Force Force System Resultant of Force System and Equilibrium Equilibrium of Coplanar, Concurrent Force System 1.16 Moment of a Force about a Point Moment of a Force about a Line Moment of Couple Dimensions and Units Equilibrium of Forces 2.1 Lami's Theorem Theorem of Varignon Equivalence of Force and Force-couple System Equations of Equilibrium Free-body Diagram 58

3 XÜ Contents 3. Truss, Frames, and Cables Introduction Truss Elements of a Truss Assumptions for Truss Analysis Determinacy and Stability Methods of Analysis of a Truss Frame Method of Analysis of a Frame Suspension Cables Elements of Suspension Cables Method of Analysis of Suspension Cables Friction Introduction Classification Probable Mechanism Laws of Friction Coefficient of Friction Angle of Friction Angle of Repose Wedge Friction Screw Jack Differential Screw Jack Rolling Friction Energy of Friction Belt Drives Types of Flat Belt Drives Length of Belt Drive Friction in Belt Drive Centrifugal Tension in Belt Drive Initial Tension in Belt Drive Transmission of Power in Belt Drive Condition of Transmission of Maximum Power Properties of Lines, Surfaces, and Physical Bodies Introduction Centroid and Centre of Gravity Analytical Expression of Centroid Analytical Expression of Centre of Mass and Centre of Gravity Pappus-Guldinus Theorem Second Moment of Area Radius of Gyration Perpendicular Axis Theorem 307

4 Contents Xiii 5.9 Parallel Axis Theorem Mass Moment of Inertia Parallel Axis Theorem for Mass Moment of Inertia Mass Moment of Inertia of Thin Plate Principle of Virtual Work Introduction Work and Virtual Work Principle of Virtual Work 387 Part II DYNAMICS 7. Kinematics of Particle Introduction Kinematics and Kinetics Patterns of Motion Displacement, Velocity, and Acceleration in Linear Motion Kinematic Equations of Motion with Constant Acceleration Relative Linear Motion Displacement, Velocity, and Acceleration in Curvilinear Motion Velocity and Acceleration in Polar Reference System Velocity and Acceleration in n-t Reference System Analysis of Projectile Motion Kinematics of Rigid Bodies Introduction Properties of Rigid Body Motion Governing Kinematic Equations of Rigid Body Motion Fixed Axis Rotation of Rigid Body Contact of Two Rotating Rigid Bodies Contact of Rotating Rigid Body with Translating Rigid Body Instantaneous Centre of Rotation Kinetics of Particle and Rigid Bodies Introduction Newton's Laws of Motion Forcing Functions and Kinematic Parameters D'Alembert's Principle Pure Translation of a Rigid Body Fixed Axis Rotation of a Rigid Body Plane Motion of a Rigid Body 569

5 Xiv Contents 10. Principle of Work, Power, and Energy Introduction Work Done and its Variety Potential Energy Conservative Force and Potential Energy Work-energy Principle for Particle Work Done for Rigid Body Kinetic Energy of Rigid Body Work-energy Principle for Rigid Body Principle of Conservation of Energy Power Principle of Linear Impulse and Momentum 11.1 Introduction Principle of Conservation of Linear Momentum Impact and its Variety Mechanism of Impact Coefficient of Restitution Oblique Central Impact Mechanical Vibration 12.1 Vibration Classification of Vibration Damping and Vibration Features of Vibrating System Free Vibration without Damping Free Vibration with Damping Forced Vibration without Damping Forced Vibration with Damping Pendulum Motion 768 Appendix A Trigonometric and Hyperbolic Relations 814 Appendix В Differentiation Formulae 816 Appendix С Integration Formulae 818 Appendix D Properties of Geometrical Figures 820 Appendix E Properties of Homogeneous Solids 824 Bibliography 828 Index

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