ENGINEERING MECHANICS TEXTBOOK
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CONTENTS
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
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
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.
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.
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
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 Cross-
Belt 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 759–765
