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أخوانى فى الله أحضرت لكم كتاب Engineering Mechanics R.S. KHURMI
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1. Introduction 1–12 1.1. Science 1.2. Applied Science 1.3. Engineering Mehanics 1.4. Beginning and Development of Engineering Mechanics 1.5. Divisions of Engineering Mechanics 1.6. Statics 1.7. Dynamics 1.8. Kinetics 1.9. Kinematics 1.10. Fundamental Units 1.11. Derived Units 1.12. Systems of Units 1.13. S.I. Units (International System of Units.) 1.14. Metre 1.15. Kilogram 1.16. Second 1.17. Presentation of Units and Their Values 1.18. Rules for S.I. Units 1.19. Useful Data 1.20. Algebra 1.21. Trigonometry 1.22. Differential Calculus 1.23. Integral Calculus 1.24. Scalar Quantitie 1.25. Vector Quantities 2. Composition and Resolution of Forces 13–27 2.1. Introduction 2.2. Effects of a Force 2.3. Characteristics of a Force 2.4. Principle of Physical Independence of Forces 2.5. Principle of Transmissibility of Forces 2.6. System of Forces 2.7. Resultant Force 2.8. Composition of Forces 2.9. Methods for the Resultant Force 2.10. Analytical Method for Resultant Force 2.11. Parallelogram Law of Forces 2.12. Resolution of a Force 2.13. Principle of Resolution 2.14. Method of Resolution for the Resultant Force 2.15. Laws for the Resultant Force 2.16. Triangle Law of Forces 2.17. Polygon Law of Forces 2.18. Graphical (vector) Method for the Resultant Force 3. Moments and Their Applications 28–42 3.1. Introduction 3.2. Moment of a Force 3.3. Graphical Representation of Moment 3.4. Units of Moment 3.5. Types of Moments 3.6. Clockwise Moment 3.7. Anticlockwise Moment 3.8. Varignon’s Principle of Moments (or Law of Moments) 3.9. Applications of Moments 3.10. Position of the Resultant Force by Moments 3.11. Levers 3.12. Types of Levers 3.13. Simple Levers 3.14. Compound Levers 4. Parallel Forces and Couples 43–54 4.1. Introduction 4.2. Classification of parallel forces. 4.3. Like parallel forces 4.4. Unlike parallel forces 4.5. Methods for magnitude and position of the resultant of parallel forces 4.6. Analytical method for the resultant of parallel forces. 4.7. Graphical method for the resultant of parallel forces 4.8. Couple 4.9. Arm of a couple 4.10. Moment of a couple 4.11. Classification of couples 4.12. Clockwise couple 4.13. Anticlockwise couple 4.14. Characteristics of a couple 5. Equilibrium of Forces 55–77 5.1. Introduction 5.2. Principles of Equilibrium 5.3. Methods for the Equilibrium of coplanar forces 5.4. Analytical Method for the Equilibrium of Coplanar Forces 5.5. Lami’s Theorem 5.6. Graphical Method for the Equilibrium of Coplanar Forces 5.7. Converse of the Law of Triangle of Forces 5.8. Converse of the Law of Polygon of Forces 5.9. Conditions of Equilibrium 5.10. Types of Equilibrium. 6. Centre of Gravity 78–99 6.1. Introduction 6.2. Centroid 6.3. Methods for Centre of Gravity 6.4. Centre of Gravity by Geometrical Considerations 6.5. Centre of Gravity by Moments 6.6. Axis of Reference 6.7. Centre of Gravity of Plane Figures 6.8. Centre of Gravity of Symmetrical Sections 6.9. Centre of Gravity of Unsymmetrical Sections 6.10. Centre of Gravity of Solid Bodies 6.11. Centre of Gravity of Sections with Cut out Holes CONTENTS (vii)7. Moment of Inertia 100–123 7.1. Introduction 7.2. Moment of Inertia of a Plane Area 7.3. Units of Moment of Inertia 7.4. Methods for Moment of Inertia 7.5. Moment of Inertia by Routh’s Rule 7.6. Moment of Inertia by Integration 7.7. Moment of Inertia of a Rectangular Section 7.8. Moment of Inertia of a Hollow Rectangular Section 7.9. Theorem of Perpendicular Axis 7.10. Moment of Inertia of a Circular Section 7.11. Moment of Inertia of a Hollow Circular Section 7.12. Theorem of Parallel Axis 7.13. Moment of Inertia of a Triangular Section 7.14. Moment of Inertia of a Semicircular Section 7.15. Moment of Inertia of a Composite Section 7.16. Moment of Inertia of a Built-up Section 8. Principles of Friction 124–148 8.1. Introduction 8.2. Static Friction 8.3. Dynamic Friction 8.4. Limiting Friction 8.5. Normal Reaction 8.6. Angle of Friction 8.7. Coefficient of Friction 8.8. Laws of Friction 8.9. Laws of Static Friction 8.10. Laws of Kinetic or Dynamic Friction 8.11. Equilibrium of a Body on a Rough Horizontal Plane 8.12. Equilibrium of a Body on a Rough Inclined Plane 8.13. Equilibrium of a Body on a Rough Inclined Plane Subjected to a Force Acting Along the Inclined Plane 8.14. Equilibrium of a Body on a Rough Inclined Plane Subjected to a Force Acting Horizontally 8.15. Equilibrium of a Body on a Rough Inclined Plane Subjected to a Force Acting at Some Angle with the Inclined Plane 9. Applications of Friction 149–170 9.1. Introduction. 9.2. Ladder Friction. 9.3. Wedge Friction. 9.4. Screw Friction. 9.5. Relation Between Effort and Weight Lifted by a Screw Jack. 9.6. Relation Between Effort and Weight Lowered by a Screw Jack. 9.7. Efficiency of a Screw Jack. 10. Principles of Lifting Machines 171–184 10.1. Introduction 10.2. Simple Machine 10.3. Compound Machine 10.4. Lifting Machine 10.5. Mechanical Advantage. 10.6. Input of a Machine 10.7. Output of a Machine 10.8. Efficiency of a Machine 10.9. Ideal Machine 10.10. Velocity Ratio 10.11. Relation Between Efficiency, Mechanical Advantage and Velocity Ratio of a Lifting Machine 10.12. Reversibility of a Machine 10.13. Condition for the Reversibility of a Machine 10.14. Self-locking Machine. 10.15. Friction in a Machine 10.16. Law of a Machine 10.17. Maximum Mechanical Advantage of a Lifting Machine 10.18. Maximum Efficiency of a Lifting Machine. 11. Simple Lifting Machines 185–216 11.1. Introduction 11.2. Types of Lifting Machines 11.3. Simple Wheel and Axle. 11.4. Differential Wheel and Axle. 11.5. Weston’s Differential Pulley Block. 11.6. Geared Pulley Block. 11.7. Worm and Worm Wheel 11.8. Worm Geared Pulley Block.11.9. Single Purchase Crab Winch. 11.10. Double Purchase Crab Winch. 11.11. Simple Pulley. 11.12. First System of Pulleys.11.13. Second System of Pulleys. 11.14. Third System of Pulleys. 11.15. Simple Screw Jack 11.16. Differential Screw Jack 11.17. Worm Geared Screw Jack. 12. Support Reactions 217–243 12.1. Introduction. 12.2. Types of Loading. 12.3. Concentrated or Point Load 12.4. Uniformly Distributed Load 12.5. Uniformly Varying Load 12.6. Methods for the Reactions of a Beam 12.7. Analytical Method for the Reactions of a Beam 12.8. Graphical Method for the Reactions of a Beam 12.9. Construction of Space Diagram. 12.10. Construction of Vector Diagram 12.11. Types of End Supports of Beams 12.12. Simply Supported Beams 12.13. Overhanging Beams 12.14. Roller Supported Beams 12.15. Hinged Beams 12.16. Beams Subjected to a Moment. 12.17. Reactions of a Frame or a Truss 12.18. Types of End Supports of Frames 12.19. Frames with Simply Supported Ends 12.20. Frames with One End (viii)Hinged (or Pin-jointed) and the Other Supported Freely on Roller 12.21. Frames with One End Hinged (or Pin-jointed) and the Other Supported on Rollers and Carrying Horizontal Loads. 12.22. Frames with One End Hinged (or Pin-jointed) and the Other Supported on Rollers and carrying Inclined Loads. 12.23. Frames with Both Ends Fixed. 13. Analysis of Perfect Frames (Analytical Method) 244–288 13.1. Introduction. 13.2. Types of Frames. 13.3. Perfect Frame. 13.4. Imperfect Frame. 13.5.Deficient Frame. 13.6. Redundant Frame. 13.7. Stress. 13.8. Tensile Stress. 13.9. Compressive Stress. 13.10. Assumptions for Forces in the Members of a Perfect Frame. 13.11. Analytical Methods for the Forces. 13.12. Method of Joints. 13.13. Method of Sections (or Method of Moments). 13.14. Force Table. 13.15. Cantilever Trusses. 13.16. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Horizontal Loads. 13.17. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Inclined Loads. 13.18. Miscellaneous Structures. 14. Analysis of Perfect Frames (Graphical Method) 289–321 14.1. Introduction. 14.2. Construction of Space Diagram. 14.3. Construction of Vector Diagram. 14.4. Force Table. 14.5. Magnitude of Force. 14.6. Nature of Force. 14.7. Cantilever Trusses. 14.8. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Horizontal Loads. 14.9. Structures with One End Hinged (or Pin-jointed) and the Other Freely Supported on Rollers and Carrying Inclined Loads. 14.10. Frames with Both Ends Fixed. 14.11. Method of Substitution. 15. Equilibrium of Strings 322–341 15.1. Introduction. 15.2. Shape of a Loaded String. 15.3. Tension in a String. 15.4. Tension in a String Carrying Point Loads. 15.5. Tension in a String Carrying Uniformly Distributed Load. 15.6. Tension in a String when the Two Supports are at Different Levels. 15.7. Length of a String. 15.8. Length of a String when the Supports are at the Same Level. 15.9. Length of a String when the Supports are at Different Levels. 15.10. The Catenary. 16. Virtual Work 342–360 16.1. Introduction. 16.2. Concept of Virtual Work. 16.3. Principle of Virtual Work. 16.4. Sign Conventions. 16.5. Applications of the Principle of Virtual Work. 16.6. Application of Principle of Virtual Work on Beams Carrying Point Load. 16.7. Application of Principle of Virtual Work on Beams Carrying Uniformly Distributed Load. 16.8. Application of Principle of Virtual Work on Ladders. 16.9. Application of Principle of Virtual Work on Lifting Machines. 16.10. Application of Principle of Virtual Work on Framed Structures. 17. Linear Motion 361–383 17.1. Introduction. 17.2. Important Terms. 17.3. Motion Under Constant Acceleration. 17.4. Motion Under Force of Gravity. 17.5. Distance Travelled in the nth Second. 17.6. Graphical Representation of Velocity, Time and Distance Travelled by a Body. 18. Motion Under Variable Acceleration 384–399 18.1. Introduction. 18.2. Velocity and Acceleration at any Instant. 18.3. Methods for Velocity, Acceleration and Displacement from a Mathematical Equation. 18.4. Velocity and Acceleration by Differentiation. 18.5. Velocity and Displacement by Intergration. 18.6. Velocity, Acceleration and Displacement by Preparing a Table. (ix)19. Relative Velocity 400–416 19.1. Introduction. 19.2. Methods for Relative Velocity. 19.3. Relative velocity of Rain and Man. 19.4. Relative Velocity of Two Bodies Moving Along Inclined Directions. 19.5. Least Distance Between Two Bodies Moving Along Inclined Directions. 19.6. Time for Exchange of Signals of Two Bodies Moving Along Inclined Directions. 20. Projectiles 417–444 20.1. Introduction. 20.2. Important Terms. 20.3. Motion of a Body Thrown Horizontally into the Air. 20.4. Motion of a Projectile. 20.5. Equation of the Path of a Projectile. 20.6. Time of Flight of a Projectile on a Horizontal Plane. 20.7. Horizontal Range of a Projectile. 20.8. Maximum Height of a Projectile on a Horizontal Plane. 20.9. Velocity and Direction of Motion of a Projectile, After a Given Interval of Time from the Instant of Projection. 20.10. Velocity and Direction of Motion of a Projectile, at a Given Height Above the Point of Projection. 20.11. Time of Flight of a Projectile on an Inclined Plane. 20.12. Range of a Projectile on an Inclined Plane. 21. Motion of Rotation 445–456 21.1. Introduction. 21.2. Important Terms. 21.3. Motion of Rotation Under Constant Angular Acceleration. 21.4. Relation Between Linear Motion and Angular Motion. 21.5. Linear (or Tangential) Velocity of a Rotating Body. 21.6. Linear (or Tangential) Acceleration of a Rotating Body. 21.7. Motion of Rotation of a Body under variable Angular Acceleration. 22. Combined Motion of Rotation and Translation 457–469 22.1. Introduction. 22.2. Motion of a Rigid Link. 22.3. Instantaneous centre. 22.4. Motion of a Connecting Rod and Piston of a Reciprocating pump. 22.5. Methods for the Velocity of Piston of a Reciprocating Pump. 22.6. Graphical Method for the Velocity of Piston of a Reciprocating Pump. 22.7. Analytical Method for the Velocity of Piston of a Reciprocating Pump. 22.8. Velocity Diagram Method for the Velocity of Piston of a Reciprocating Pump. 22.9. Motion of a Rolling Wheel Without Slipping. 23. Simple Harmonic Motion 470–480 23.1. Introduction. 23.2. Important Terms. 23.3. General Conditions of Simple Harmonic Motion. 23.4. Velocity and Acceleration of a Particle Moving with Simple Harmonic Motion. 23.5. Maximum Velocity and Acceleration of a Particle Moving with Simple Harmonic Motion. 24. Laws of Motion 481–502 24.1. Introduction. 24.2. Important Terms. 24.3. Rigid Body. 24.4. Newton’s Laws of Motion. 24.5. Newton’s First Law of Motion. 24.6. Newton’s Second Law of Motion. 24.7. Absolute and Gravitational Units of Force. 24.8. Motion of a Lift. 24.9. D’Alembert’s Principle. 24.10. Newton’s Third Law of Motion. 24.11. Recoil of Gun. 24.12. Motion of a Boat. 24.13. Motion on an Inclined Planes. 25. Motion of Connected Bodies 503–527 25.1. Introduction. 25.2. Motion of Two Bodies Connected by a String and Passing over a Smooth Pulley. 25.3. Motion of Two Bodies Connected by a String One of which is Hanging Free and the Other Lying on a Smooth Horizontal Plane. 25.4. Motion of Two Bodies Connected by a String One of which is Hanging Free and the Other Lying on a Rough Horizontal Plane. 25.5. Motion of Two Bodies Connected by a String One of which is Hanging Free and the Other Lying on a Smooth Inclined Plane. 25.6. Motion of Two Bodies connected by a String, One of which is Hanging Free and the Other is Lying on a Rough Inclined Plane. 25.7. Motion of Two Bodies Connected by a String and Lying on Smooth Inclined Planes. 25.8. Motion of Two Bodies Connected by a String Lying on Rough Inclined Planes. (x)26. Helical Springs and Pendulums 528–552 26.1. Introduction. 26.2. Helical Springs. 26.3. Helical Springs in Series and Parallel. 26.4. Simple Pendulum. 26.5. Laws of Simple Pendulum. 26.6. Gain or Loss in the No. of Oscillations due to Change in the Length of String or Acceleration due to Gravity of a Simple Pendulum. 26.7. Gain or Loss in the No. of Oscillations due to Change in the Position of a Simple Pendulum. 26.8. Compound Pendulum. 26.9. Centre of Oscillation (or Centre of Percussion). 26.10. Conical Pendulum. 27. Collision of Elastic Bodies 553–571 27.1. Introduction. 27.2. Phenomenon of Collision. 27.3. Law of Conservation of Momentum. 27.4. Newton’s law of Collision of Elastic Bodies. 27.5. Coefficient of Restitution. 27.6. Types of Collisions. 27.7. Direct Collision of Two Bodies. 27.8. Loss of Kinetic Energy During Collision. 27.9. Indirect Impact of Two Bodies. 27.10. Direct Impact of a Body with a Fixed Plane. 27.11. Indirect Impact of a Body with a Fixed Plane. 28. Motion Along a Circular Path 572–585 28.1. Introduction. 28.2. Centripetal Acceleration. 28.3. Centripetal Force. 28.4. Centrifugal Force. 28.5. Centrifugal Force Acting on a Body Moving Along a Circular Path. 28.6. Superelevation. 28.7. Effect of Superelevation in Roadways. 28.8. Effect of Superelevation in Railways. 28.9. Equilibrium Speed for Superelevation. 28.10. Reactions of a Vehicle Moving along a Level Circular Path. 28.11. Equilibrium of a Vehicle Moving along a Level Circular Path. 28.12. Maximum velocity to Avoid Overturning of a Vehicle Moving along a Level Circular Path. 28.13. Maximum Velocity to Avoid Skidding Away of a Vehicle Moving along a Level Circular Path. 29. Balancing of Rotating Masses 586–598 29.1. Introduction. 29.2. Methods for Balancing of Rotating Masses. 29.3. Types of Balancing of Rotating Masses. 29.4. Balancing of a Single Rotating Mass. 29.5. Balancing of a Single Rotating Mass by Another Mass in the Same Plane. 29.6. Balancing of a Single Rotating Mass by Two Masses in Different Planes. 29.7. Balancing of Several Rotating Masses. 29.8. Analytical Method for the Balancing of Several Rotating Masses in one Plane by Another Mass in the Same Plane. 29.9. Graphical Method for the Balancing of Several Rotating Masses in One Plane by Another Mass in the Same Plane. 29.10. Centrifugal governor. 29.11. Watt Governor. 30. Work, Power and Energy 599–621 30.1. Introduction. 30.2. Units of Work. 30.3. Graphical Representation of Work. 30.4. Power. 30.5. Units of Power. 30.6. Types of Engine Powers. 30.7. Indicated Power. 30.8. Brake Power. 30.9. Efficiency of an Engine. 30.10. Measurement of Brake Power. 30.11. Rope Brake Dynamometer. 30.12. Proney Brake Dynamometer. 30.13. Froude and Thornycraft Transmission Dynamometer. 30.14. Motion on Inclined Plane. 30.15. Energy. 30.16. Units of Energy. 30.17. Mechanical Energy. 30.18. Potential Energy. 30.19. Kinetic Energy. 30.20. Transformation of Energy. 30.21. Law of Conservation of Energy. 30.22. Pile and Pile Hammer. 31. Kinetics of Motion of Rotation 622–650 31.1. Introduction. 31.2. Torque. 31.3. Work done by a Torque. 31.4. Angular Momentum. 31.5. Newton’s Laws of Motion of Rotation. 31.6. Mass Moment of Inertia. 31.7. Mass Moment of Inertia of a Uniform Thin Rod about the Middle Axis Perpendicular to the Length. 31.8. Moment of Inertia of a Uniform Thin Rod about One of the Ends Perpendicular to the Length. 31.9. Moment of Inertia of a Thin Circular Ring. 31.10. Moment of Inertia of a Circular Lamina. 31.11. Mass Moment of Inertia of a Solid Sphere. 31.12. Units of Mass Moment of Inertia. 31.13. Radius of Gyration. 31.14. Kinetic Energy of Rotation. (xi)31.15. Torque and Angular Acceleration. 31.16. Relation Between Kinetics of Linear Motion and Kinetics of Motion of Rotation. 31.17. Flywheel. 31.18. Motion of a Body Tied to a String and Passing Over a Pulley. 31.19. Motion of Two Bodies Connected by a String and Passing Over a Pulley. 31.20. Motion of a Body Rolling on a Rough Horizontal Plane without Slipping. 31.21. Motion of a Body Rolling Down a Rough Inclined Plane without Slipping. 32. Motion of Vehicles 651–669 32.1. Introduction. 32.2. Types of Motions of Vehicles. 32.3. Motion of a Vehicle Along a Level Track when the Tractive Force Passes Through its Centre of Gravity. 32.4. Motion of a Vehicle Along a Level Track when the Tractive Force Passes Through a Point Other than its Centre of Gravity. 32.5. Driving of a Vehicle. 32.6. Braking of a Vehicle. 32.7. Motion of Vehicles on an Inclined Plane. 33. Transmission of Power by Belts and Ropes 670–695 33.1. Introduction. 33.2. Types of Belts. 33.3. Velocity Ratio of a Belt Drive. 33.4. Velocity Ratio of a Simple Belt Drive. 33.5. Velocity Ratio of a Compound Belt Drive. 33.6. Slip of the Belt. 33.7. Types of Belt Drives. 33.8. Open Belt Drive. 33.9. Cross Belt Drive. 33.10. Length of the Belt. 33.11. Length of an Open Belt Drive. 33.12. Length of a CrossBelt Drive. 33.13. Power Transmitted by a Belt. 33.14. Ratio of Tensions. 33.15. Centrifugal Tension. 33.16. Maximum Tension in the Belt. 33.17. Condition for Transmission of Maximum Power. 33.18. Belt Speed for Maximum Power. 33.19. Initial Tension in the Belt. 33.20. Rope Drive. 33.21. Advantages of Rope Drive. 33.22. Ratio of Tensions in Rope Drive. 34. Transmission of Power by Gear Trains 696–717 34.1. Introduction. 34.2. Friction Wheels. 34.3. Advantages and Disadvantages of a Gear Drive. 34.4. Important Terms. 34.5. Types of Gears. 34.6. Simple Gear Drive. 34.7. Velocity Ratio of a Simple Gear Drive. 34.8. Power Transmitted by a Simple Gear. 34.9. Train of Wheels. 34.10. Simple Trains of Wheels. 34.11. Compound Train of Wheels. 34.12. Design of Spur Wheels. 34.13. Train of Wheels for the Hour and Minute Hands of a 12-Hour clock. 34.14. Epicyclic Gear Train. 34.15. Velocity Ratio of an Epicyclic Gear Train. 34.16. Compound Epicyclic Gear Train (Sun and Planet Wheel). 34.17. Epicyclic Gear Train with Bevel Wheels. 35. Hydrostatics 718–741 35.1. Introduction. 35.2. Intensity of Pressure. 35.3. Pascal’s Law. 35.4. Pressure Head. 35.5. Total Pressure. 35.6. Total Pressure on an Immersed Surface. 35.7. Total Pressure on a Horizontally Immersed Surface. 35.8. Total Pressure on a Vertically Immersed Surface. 35.9. Total Pressure on an Inclined Immersed Surface. 35.10. Centre of Pressure. 35.11. Centre of Pressure of a Vertically lmmersed Surface. 35.12. Centre of Pressure of an Inclined Immersed Surface. 35.13. Pressure Diagrams. 35.14. Pressure Diagram Due to One Kind of Liquid on One Side. 35.15. Pressure Diagram Due to One Kind of Liquid Over Another on One Side. 35.16. Pressure Diagram Due to Liquids on Both Sides. 35.17. Centre of Pressure of a Composite Section. 36. Equilibrium of Floating Bodies 742–758 36.1. Introduction. 36.2. Archimedes’ Principle. 36.3. Buoyancy. 36.4. Centre of Buoyancy. 36.5. Metacentre. 36.6. Metacentric Height. 36.7. Analytical Method for Metacentric Height. 36.8. Types of Equilibrium of a Floating Body. 36.9. Stable Equilibrium. 36.10. Unstable Equilibrium. 36.11. Neutral Equilibrium. 36.12. Maximum Length of a Body Floating Vertically in Water. 36.13. Conical Buoys Floating in a Liquid. Index A Absolute units of force, 535 Acceleration, 407, 427, 428, 431, 436 – Angular, 493, 688 – by differentiation, 428 – by integration, 431 – by preparing a table, 436 – of a particle (S.H.M.), 522 – Uniform, 408 – Variable, 408 Addendum circle, 764 Advantages of gear drive, 763 – rope drive, 756 Amplitude, 522, 526 Analytical method for balancing, 647 – forces in perfect frames, 270 – metacentric height, 820 – reactions of a beam, 240 – resultant force 15, 43 – equilibrium of coplanar forces, 56 – velocity of a piston of a reciprocating pump, 501 Angle of friction, 141 – projection, 464 Angular acceleration, 493, 501, 688 – displacement, 493 – momentum, 680 – velocity, 492 Anticlockwise couple, 49 – moment, 27 Application of the principle of virtual work, 389 – for beams, 389, 394 – for framed structures, 402 – for ladders, 397 – for lifting machines, 399 – of moments, 31 Applied science, 2 Archimede's principle, 817 Arm of couple, 49 Assumptions for forces in members of a perfect frame, 270 Axis of reference, 81 B Balancing of rotating masses, 643, 644, 645, 646 Beat, 522 Beginning and development of Engineering Mechanics, 2 Belt, Length of, 738, 740 – Power transmitted by, 742 – Skip of, 736 – Speed for maximum power, 752 – Types of, 735 Brake power, 658 Braking of a vehicle, 723 Buoyancy, 818 C Cantilever trusses, 325 Catenary, 380 Centre of buoyancy, 818 Centre of gravity, 91 – by geometrical considerations, 79 – by graphical method, 93 – moments, 94 – of sections with cut out holes, 91 – of plane figures, 81 INDEX Contents760 ? A Textbook of Engineering Mechanics – of solid bodies, 87 – of symmetrical sections, 82 – of unsymmetrical sections, 84 Centre of pressure, 797 – of an inclined surface, 801 – of a composite section, 811 – of a vertical surface, 789 – of oscillation, 600 Centrifugal force, 628, 629 – tension, 748 Centripetal acceleration, 628 – force, 627 – governor, 630 – tension, 748 Centroid, 78 C.G.S. Units, 4 Characteristics of couples, 49 – force, 14 Classification of coupl, 49 – parallel forces, 42 Clearance, 764 Clockwise couple, 49 – moments, 27 Coefficient of friction, 141 – restitution, 610 Collnear forces, 17 Composition of forces, 15 Compound epicyclic gear train, 781 – levers, 39 – machine, 188 – pendulum, 597 – train of wheels, 760 Compressive stress, 270 Concentrated load, 239 Concept of virtual work, 388 Concurrent forces, 17 Conditions of equilibrium, 72 – for transmission of maximum power, 751 – for reversibility of a machine, 190 – for simple harmonic motion, 522 Conical bodies floating in a liquid, 830 – pendulum, 603 Construction of space diagram, 241, 324 – vector diagram, 241, 324 Converse of the law of polygon of forces, 71 – triangle of forces, 71 Coplanar forces, 17 Couple, 48 Cross belt drive, 738 D D' Alembert's principle, 543 Dedendum circle, 764 Deficient frame, 269 Depth of thread, 177 – tooth, 764 Derived units, 4 Design of spur wheels, 772 Differential pulley block, 211 – screw jack, 231 – wheel and axle, 208 Direct impact of two bodies, 609 – of a body on a fixed plan, 620 Disadvantages of gear drive, 763 Distance traversed, 408 – travelled in nth second, 420 Divisions of Engineering Mechanics, 3 Double purchase crab winch, 221 Driving of a vehicle, 720 Dynamics, 3 – friction, 140 E Effect of a force, 14 – superelevation, 631, 632 Efficiency of an engine, 658 – of a machine, 189 – of a screw jack, 181 Energy, 668 – Law of conservation of, 673 – Transformation of, 672 – Units of, 668 ContentsIndex ? 761 Engineering mechanics, 2 Epicyclic gear train, 777 – with bevel wheels, 785 Equation of the path of a projectile, 468 Equilibrium of a body lying over a rough horizontal plane, 142 – inclined plane, 146, 147, 151, 157 – moving on a level circular path, 636 – noncoplanar forces, 81 – speed for superelevation, 633 External gearing, 765 F Face of tooth, 764 – width of tooth, 764 First system of pulleys, 225 Flank of tooth, 764 Flywheel, 686 Force, 15 – Characteristics of, 16 – Composition of, 17 – Effects of, 16 – Moment of, 31 – Resultant, 17 table, 271, 325 Frame with simply supported ends, 254 – with one end hinged and the other supported on rollers, 255, 257, 294, 302, 342, 247 – with both ends fixed, 262, 353 Frequency, 522 Friction, Angle of, 141 – Coefficient of, 141 – Dynamic, 140 – in a machine, 192 – Ladder, 163 – Laws of, 141, 142 – Limiting, 140 – Screw, 176 – Static, 140 – Wedge, 170 – wheels, 762 Froude and Thornycraft transmission dynamometer, 661 Fundamental units, 4 G Grain in no. of oscillation due to change in length of string or acceleration due to gravity, 593 Gain or loss in the no. of oscillations due to change in the position of a simple pendulum, 595 Geared pulley block, 213 General conditions of H.S.M., 522 Graphical method for balancing of several bodies rotating in one plane, 649 – resultant force, 22, 45 – equilibrium force, 70 – reactions of a beam, 241 – velocity or piston of a reciprocating pump, 509 Graphical representation of moment, 27 – velocity, time and distance, 421 – work, 656 Gravitational units of forces, 533 H Helical springs, 581, 586 Helix of a screw, 177 Hinged beams, 248 Horizontal range of a projectile, 469 I Ideal machine, 189 Imperfect frame, 269 Indicated power, 658 Indirect impact of two bodies, 617 Contents762 ? A Textbook of Engineering Mechanics – of a body, on a fixed plane, 623 Initial tension of a belt, 754 Input of a machine, 189 Instantaneous centre, 506 Intensity of pressure, 789 Internal gearing, 765 International system of units, 4 K Kilogram, 5 Kinematics, 4 Kinetic energy, 669, 686 Kinetics, 4 L Ladder friction, 163 Lami's theorem, 56 Law of conservation of energy, 673 – collision of elastics bodies, 610 – conservation of momentum, 609 – machine, 195 – moments, 28 – triangle of forces, 24 – parallelogram of forces, 18 – polygon of forces, 25 – simple pendulum, 591 – friction, 141, 142 Laws of motion, 533 – resultant force, 22 Lead of a screw, 177 Least distance between two bodies moving along inclined directions, 455 Length of belt, 738, 740 – of a string, 374, 377 Levers, 36 Lifting machines, 189 Like parallel forces, 43 Limiting friction, 140 Linear acceleration of a rotating body, 500 – velocity of rotating body, 499 Loss of K.E. during impact, 614 M Machine, 188 Magnitude of forces, 325 Mass, 532 – moment of inertia, 681 Maximum acceleration of a body moving with S.H.M., 526 – efficiency of a machine, 198 – efficiency of a screw jack, 182 – height of a projectile, 470 – length of a body floating vertically in water, 826 – mechanical advantage of machine, 198 – tension in the belt, 749 – transmission of power by belt, 752 – velocity of a body moving with S.H.M., 526 – velocity to avoid overturning of a vehicle, 636 – velocity to avoid skidding away of a vehicle, 637 Measurement of brake power, 658 Mechanical advantage, 189 – energy, 668 Metacentre, 819 Metacentric height, 819 – Analytical method, 820 Methods for balancing of rotating bodies, 643 – equilibrium for coplanar forces, 56 – centre of gravity, 79 – forces in frames, 270, 271 – magnitude and position of the resultant force, 43, 45 – moment of inertia, 101 – reactions of a beam, 240, 241 – relative velocity, 444 ContentsIndex ? 763 – resultant forces, 15 – velocity acceleration and displacement from a mathematical equation, 428 – velocity of piston of a reciprocating pum 509 Method of joints for forces in pefrect frames, 270 – of resolution for the resultant force, 18 – sections for forces in perfect frames, 271 – substitution for analysis of frames, 354 Metre, 5 Miscellaneous structures, 308 Moment of a couple, 49 – force, 26 – Law of, 32 – Principle of, 32 Moment of inertia of built-up section, 118 Moment of inertia by integration, 102 – by Routh's rule, 101 – of circular section, 104, 105 – composite section, 110 – plane area, 101 – rectangular section, 102,103 – semicircular section, 108 – triangular section, 107 – Units of, 114 Momentum, 532 – Law of conservation of, 609 Motion of a boat, 546 – of a body rolling down without slipping on rough place, 703, 706 – of a body tied to a string passing over a pulley, 690 – of a body thrown horizontally into the air, 464 – connecting rod and piston of a reciprocating pump, 509 – lift, 540 – projectile, 467 – rigid link, 505 – rolling wheel without slipping, 517, 704, 706 – two bodies connected by string, 555, 560, 563, 565, 571, 574, 694 – vehicle, 713, 716 – on an inclined surface, 548, 663 – under uniform acceleration, 408 – under constant angular accelera tion, 493 – under the force of gravity, 412 Multi-threaded screw, 177 N Nature of force, 325 Neutral equilibrium, 74 Newton's Law of collision of two bodies, 610 – Laws of motion, 533, 534, 545, 680 Non-coplanar concurrent forces, 17 – non-concurrent forces, 17 Normal reaction, 140 Open belt drive, 737 Oscillation, 522 Output of a machine, 189 Overhanging beams, 245 P Parallelogram, law of forces, 15 Pascal's law, 790 Perfect frame, 269 Periodic time, 522 Phenomenon of collision, 608 Pile and Pile Hammer, 674 pitch, 177, 764 – circle, 764 Point load, 239 Polygon law of forces, 25 Position of the resultant forces by moments, 31 Contents764 ? A Textbook of Engineering Mechanics Potential energy, 668 Power, 657 – developed by a torque, 473 – transmitted by belt, 742 – transmitted by gear, 767 – Units of, 657 Preparation of force table, 271, 325 Presentation of units and their values, 5 Pressure, Centre of, 797 – diagrams, 806, 807, 809 – head, 791 Principles of equilibrium, 56 – moments, 28 – physical independence of forces, 14 – resolution, 17 – transmissibility of forces, 14 – virtual work, 388 Proney brake dyncmometer, 660 Proof of Lami's theorem, 67 Parallel axin theorem, 104 – Pascal's law, 790 – Perpendicular axis theorem, 117 – Polygon Law of forces, 22 – Principle of work, 288 Pulley, 224, 225, 226, 228 R Rack and pinion, 765 Radius of gyration, 685 Range of a projectile, 464 – on a horizontal plane, 469 – on an inclined plane, 486 Ratio of tensions 744, 756 Reactions of a frame, 254 – vehicle moving on a level circular path, 634 Recoil of gun, 545 Redundant frame, 269 Relation between efficiency M.A. and V.R. of a machine, 189 – effort and weight, 178, 179 – kinetics of linear motion and kinetics of motion of rotation, 689 – linear motion and angular motion, 494 – mass and weight, 27 – torque and angular acceleration, 688 Relative velocity of rain and man, 444 – of two bodies moving along inclined directions, Resolution of a force, 17 Resultant force, 15 Reversibility of a machine, 190 Roller supported beams, 248 Rolling friction, 140 Rope brake dynamometer, 658 – drive, 756 Rules for S.I. units, 6 S Soalars and vectors, 11 Science, 1 Screw friction, 178 Screw jack, Differential, 231 – Simple, 229 Sceond, 5 – system of pulleys, 226 Self-locking machine, 191 Shape of a loaded string, 36 Sign conventions of virtual work, 389 Simple gear drive, 766 – levers, 37 – machine, 188 – pendulum, 590 – pulley, 224 – train of wheels, 768 – screw jack, 229 – wheel and axle, 206 Simply supported beams, 242 Single purchase crab winch, 218 – threaded screw, 177 S.I. Units, 4 ContentsIndex ? 765 Slidding friction, 140 Slip of belt, 736 Slope of thread, 177 Speed, 407 Stable equilibrium, 74 Statics, 3 – friction, 140 Stress, 269 Sub-divisions of Engineering Mechanics, 3 Sun and planet wheel, 781 Superelevation, 631 System of forces, 14 – pulleys, 171 – units, 4 T Tangential velocity of rotating body, 499 Tensile stress, 270 Tension in a string, 366, 367, 369, 371 Theorem of parallel axis, 106 – perpendicular axis, 104 – Lami's 67 Third system of pulleys, 228 Time for exchange of signals of two bodies moving along inclined directions, 458 Time of flight of a projectile, 464 – on a horizontal plane, 469 – on an inclined plane, 484 Torque, 679, 688 – work done by, 680 Total pressure, 792 – on horizontal immersed surface, 792 – on inclined immersed surface, 796 – on vertical immersed surface, 793 Train of wheels, 768, 774 – Compound, 769 – Simple, 768 Trigonometry, 7 Triangle law of forces, 22 Trajectory, 464 Types of balancing of rotating bodies, 644 – beles, 644 – belt drives, 737 – end supports, 242, 254 – engine powers, 567 – impacts, 609 – equilibrium 73 – Franches, – Friction – geoms – levers, 37 – lifting machines, 205 – loading, 239 – moments, 27 U Uniform acceleration, 408 Uniformly distributed load, 239 – varying load, 239 Units, 4 Units of moment, 27 – moment of inertia, 101 – power, 657 – work, 656 Unlike parallel forces, 43 Unstable equilibrium, 74 Useful data, 7 V Variable acceleration, 408 Varignon's principle of moments, 28 Vector method for the resultant force, 25 Velocity, 407, 427,428, 431, 436 – Angular, 492 Contents766 ? A Textbook of Engineering Mechanics – by differentiation, 428 – by integration, 431 – velocity by preparing a table, 426 – of particle moving with S.H.M., 522, 526 – of projection, 464 – ratio, 189, Velocity and direction of motion of a projectile, after the given interval of time from the instant of projection, 479 – at a given height from the point of projection, 483 – diagram method for velocity of piston of a reciprocating pump, 514 Virtual work, 387 – Principle of, 388 – Proof of, 388 W Watt governor, 639 Wedge friction, 170 Weight, 528 Weston's differential pulley block, 211 Wheel and axle, Differential, 208 – Simple, 206 Work done by a torque, 680 – Graphical representation of, 656 – Units of, 656 Worm and worm wheel, 215 – geared pulley block, 216 – geared screw jack, 232 Contents Top
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