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 |  موضوع: كتاب Engineering Mechanics الإثنين 18 مارس 2019, 9:52 am | |
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Engineering Mechanics
R.S. KHURMI
ويتناول الموضوعات الأتية :
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
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