ENGINEERING MECHANICS BASUDEB BHATTACHARYYA Assistant Professor Department of Applied Mechanics Bengal Engineering and Science University Shibpur, Howrah OXJFORD UNIVERSITY PRESS
Contents Foreword Preface Parti STATICS 1. Introduction to Statics 1.1 Introduction 3 1.2 Body 4 1.3 Space 5 1.4 Vectors and Scalars 5 1.5 Free Vector, Fixed Vector, and Null vector 5 1.6 Sliding Vectors and Principle of Transmissibility 6 1.7 Unit Vector and Vector Triad 6 1.8 Scalar Product or Dot Product 7 1.9 Vector Product or Cross Product 7 1.10 Scalar Triple Product 8 1.11 Vector Triple Product S 1.12 Force 9 1.13 Force System 10 1.14 Resultant of Force System and Equilibrium 11 1.15 Equilibrium of Coplanar, Concurrent Force System 1.16 Moment of a Force about a Point 13 1.17 Moment of a Force about a Line 75 1.18 Moment of Couple 14 1.19 Dimensions and Units 14 2. Equilibrium of Forces 2.1 Lami's Theorem 53 2.2 Theorem of Varignon 54 2.3 Equivalence of Force and Force-couple System 56 2.4 Equations of Equilibrium 57 2.5 Free-body Diagram 58
XÜ Contents 3. Truss, Frames, and Cables 110 3.1 Introduction 110 3.2 Truss 110 3.3 Elements of a Truss 777 3.4 Assumptions for Truss Analysis 777 3.5 Determinacy and Stability 772 3.6 Methods of Analysis of a Truss 773 3.7 Frame 777 3.8 Method of Analysis of a Frame 777 3.9 Suspension Cables 777 3.10 Elements of Suspension Cables 778 3.11 Method of Analysis of Suspension Cables 77 8 4. Friction 228 4.1 Introduction 228 4.2 Classification 229 4.3 Probable Mechanism 229 4.4 Laws of Friction 230 4.5 Coefficient of Friction 230 4.6 Angle of Friction 232 4.7 Angle of Repose 233 4.8 Wedge Friction 234 4.9 Screw Jack 234 4.10 Differential Screw Jack 235 4.11 Rolling Friction 236 4.12 Energy of Friction 237 4.13 Belt Drives 237 4.14 Types of Flat Belt Drives 239 4.15 Length of Belt Drive 239 4.16 Friction in Belt Drive 241 4.17 Centrifugal Tension in Belt Drive 243 4.18 Initial Tension in Belt Drive 243 4.19 Transmission of Power in Belt Drive 244 4.20 Condition of Transmission of Maximum Power 244 5. Properties of Lines, Surfaces, and Physical Bodies 295 5.1 Introduction 295 5.2 Centroid and Centre of Gravity 295 5.3 Analytical Expression of Centroid 296 5.4 Analytical Expression of Centre of Mass and Centre of Gravity 298 5.5 Pappus-Guldinus Theorem 298 5.6 Second Moment of Area 307 5.7 Radius of Gyration 307 5.8 Perpendicular Axis Theorem 307
Contents Xiii 5.9 Parallel Axis Theorem 302 5.10 Mass Moment of Inertia 303 5.11 Parallel Axis Theorem for Mass Moment of Inertia 304 5.12 Mass Moment of Inertia of Thin Plate 304 6. Principle of Virtual Work 385 6.1 Introduction 385 6.2 Work and Virtual Work 385 6.3 Principle of Virtual Work 387 Part II DYNAMICS 7. Kinematics of Particle 445 7.1 Introduction 445 7.2 Kinematics and Kinetics 446 7.3 Patterns of Motion 446 7.4 Displacement, Velocity, and Acceleration in Linear Motion 447 7.5 Kinematic Equations of Motion with Constant Acceleration 449 7.6 Relative Linear Motion 450 7.7 Displacement, Velocity, and Acceleration in Curvilinear Motion 451 7.8 Velocity and Acceleration in Polar Reference System 452 7.9 Velocity and Acceleration in n-t Reference System 453 7.10 Analysis of Projectile Motion 454 8. Kinematics of Rigid Bodies 505 8.1 Introduction 505 8.2 Properties of Rigid Body Motion 505 8.3 Governing Kinematic Equations of Rigid Body Motion 508 8.4 Fixed Axis Rotation of Rigid Body 509 8.5 Contact of Two Rotating Rigid Bodies 510 8.6 Contact of Rotating Rigid Body with Translating Rigid Body 511 8.7 Instantaneous Centre of Rotation 511 9. Kinetics of Particle and Rigid Bodies 559 9.1 Introduction 559 9.2 Newton's Laws of Motion 559 9.3 Forcing Functions and Kinematic Parameters 562 9.4 D'Alembert's Principle 566 9.5 Pure Translation of a Rigid Body 567 9.6 Fixed Axis Rotation of a Rigid Body 568 9.7 Plane Motion of a Rigid Body 569
Xiv Contents 10. Principle of Work, Power, and Energy 644 10.1 Introduction 644 10.2 Work Done and its Variety 645 10.3 Potential Energy 647 10.4 Conservative Force and Potential Energy 648 10.5 Work-energy Principle for Particle 649 10.6 Work Done for Rigid Body 650 10.7 Kinetic Energy of Rigid Body 657 10.8 Work-energy Principle for Rigid Body 652 10.9 Principle of Conservation of Energy 652 10.10 Power 653 11. Principle of Linear Impulse and Momentum 11.1 Introduction 705 11.2 Principle of Conservation of Linear Momentum 707 11.3 Impact and its Variety 708 11.4 Mechanism of Impact 709 11.5 Coefficient of Restitution 770 11.6 Oblique Central Impact 713 12. Mechanical Vibration 12.1 Vibration 760 12.2 Classification of Vibration 767 12.3 Damping and Vibration 767 12.4 Features of Vibrating System 767 12.5 Free Vibration without Damping 762 12.6 Free Vibration with Damping 763 12.7 Forced Vibration without Damping 766 12.8 Forced Vibration with Damping 767 12.8 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 829 705 760