Engineering Mechanics

1. Introduction to Statics
1.1 Introduction
1.2 Idealization of matter
1.2.1 Continuum
1.2.2 Particle
1.2.3 Rigid body
1.2.4 Deformable body
1.3 Space
1.4 Scalars and vectors
1.5 Force
1.5.1 Force field
1.5.2 Classification of force
1.5.3 Force system
1.6 Superposition and transmissibility of force
1.7 Equilibrium
1.8 Resultant of a force system
1.9 Resultant and equilibrium of a coplanar, concurrent force system
1.9.1 Triangular law of forces
1.9.2 Parallelogram law of forces
1.9.3 Polygon law of forces
1.10 Resolution of a force into components
1.11 Moment of a force about a point
1.12 Moment of a force about a line
1.13 Moment of a couple
1.14 Resultant of a coplanar, non-concurrent force system
1.15 Resultant of a non-coplanar, concurrent force system
1.16 Resultant of a non-coplanar, non-concurrent force system
2. Equilibrium of Forces
2.1 Lamiâs theorem
2.2 Theorem of Varignon
2.2.1 Resultant of two like parallel forces
2.2.2 Resultant of two unlike parallel forces
2.3 Parallel shifting of forces
2.4 Equivalence of force and forceâcouple system
2.5 Generalized equations of equilibrium
2.5 Generalized equations of equilibrium
2.6 Active and reactive forces
2.7 Different types of supports
2.8 Free-body diagrams
3. Truss, Frames, and Cables
3.1 Introduction
3.2 Truss
3.3 Elements of a truss
3.4 Types of truss
3.5 Assumptions for truss analysis
3.6 Determinacy, stability, and redundancy
3.7 Methods of analysis of a truss
3.7.1 Method of joints
3.7.2 Method of sections (Ritterâs method)
3.7.3 Hybrid method
3.8 Frames
3.9 Method of analysis of a frame
3.10 Suspension cables
3.11 Elements of suspension cables
3.12 Suspension cables subjected to point loading
3.13 Suspension cables subjected to uniformly distributed loading
3.13.1 Catenary cables
3.13.2 Parabolic cables
4. Friction
4.1 Introduction
4.2 Classification
4.3 Probable mechanism
4.4 Laws of friction
4.5 Coefficient of friction
4.6 Angle of friction
4.7 Angle of repose
4.8 Wedge friction
4.9 Rolling friction
4.10 Energy of friction
4.11 Belt drives
4.12 Types of flat belt drives
4.13 Length of belt drives
4.14 Friction in belt drives
4.15 Centrifugal tension in belt drives
4.16 Initial tension in belt drives
4.17 Transmission of power in belt drives
4.18 Condition of transmission of maximum power
5. Properties of Lines, Surfaces, and Physical Bodies
5.1 Introduction
5.2 Centroid, centre of mass, and centre of gravity
5.3 Analytical expressions of centroid
5.4 Analytical expressions of centre of mass and centre of gravity
5.5 PappusâGuldinus theorems
5.6 Second moment of area
5.7 Radius of gyration
5.8 Perpendicular axis theorem for second moment of area
5.9 Parallel axis theorem for second moment of area
5.10 Product moment of area
5.11 Parallel axis theorem for product moment of area
5.12 Rotation of axes
5.13 Principal axes and principal moments of area
5.14 Mass moment of inertia
5.15 Parallel axis theorem for mass moment of inertia
5.16 Relationship between mass moment of inertia and second moment of area
6. Virtual Work
6.1 Introduction
6.2 Work done by force and moment
6.3 Virtual displacement, virtual rotation, and virtual work
6.4 Principle of virtual work
6.5 Stability of equilibrium
7. Simple Lifting Machines
7.1 Introduction
7.2 Simple and compound machines
7.3 Some basic definitions
7.3.1 Effort and load
7.3.2 Mechanical advantage
7.3.3 Velocity ratio
7.3.4 Efficiency and loss of energy
7.3.5 Ideal machine
7.3.6 Ideal effort, ideal load, and loss
7.3.7 Reversibility and irreversibility
7.3.8 Law of machine
7.4 Inclined plane
7.5 Simple screwjack
7.6 Differential screwjack
7.7 System of pulleys
7.8 Weston differential pulley block
7.9 Gear pulley block
7.10 Simple wheel and axle
7.11 Wheel and differential axle
7.12 Worm and worm wheel
7.13 Crab and winch
7.13.1 Single purchase crab and winch
7.13.2 Double purchase crab and winch
7.14 Worm geared screwjack
7.15 Worm geared pulley block
8. Kinematics of Particles
8.1 Introduction
8.2 Kinematics and kinetics
8.3 Patterns of motion
8.4 Kinematic parameters in linear motion
8.5 Equations of linear motion with constant acceleration
8.6 Kinematic parameters in angular motion
8.7 Equations of angular motion with constant acceleration
8.8 Equations of linear motion with variable acceleration
8.9 Relative motion along linear path
8.10 Relative motion along curvilinear path
8.11 Velocity and acceleration in polar reference system
8.12 Velocity and acceleration in nât reference system
8.13 Analysis of projectile motion
8.13.1 Along horizontal plane
8.13.2 Along inclined plane
9. Kinematics of Rigid Bodies
9.1 Introduction
9.2 Properties of rigid body motion
9.3 Governing kinematic equations of rigid body motion
9.4 Fixed axis rotation of a rigid body
9.5 Contact of two rotating rigid bodies
9.6 Contact of a rotating rigid body with a translating rigid body
9.7 Instantaneous centre of rotation
10. Kinetics of Particles and Rigid Bodies 10.1 Introduction
10.2 Newtonâs laws of motion
10.3 Forcing functions and kinematic parameters
10.4 DâAlembertâs principle
10.5 Pure translation of a rigid body
10.6 Fixed axis rotation of a rigid body
10.7 Planar motion of a rigid body
11. Principle of Work, Power, and Energy 11.1 Introduction
11.2 Work done and its varieties
11.3 Potential energy
11.4 Conservative force and potential energy
11.5 Workâenergy principle for particle
11.6 Work done for rigid body
11.7 Kinetic energy of rigid body
11.8 Workâenergy principle for rigid body
11.9 Principle of conservation of energy
11.10 Power
12. Principle of Impulse and Momentum 12.1 Introduction
12.2 Linear impulse and momentum
12.3 Angular impulse and momentum
12.4 Principle of conservation of momentum
12.5 Impact and its variety
12.6 Mechanism of direct central impact
12.7 Coefficient of restitution
12.8 Perfectly elastic collision
12.9 Inelastic or semi-elastic collision
12.10 Loss of energy in direct central impact
12.11 Mechanism of oblique central impact
13. Mechanical Vibration
13.1 Vibration
13.2 Classification of vibration
13.3 Damping and vibration
13.4 Features of vibrating systems
13.5 Free vibration without damping
13.6 Free vibration with damping
13.7 Forced vibration without damping
13.8 Forced vibration with damping
13.9 Pendulum motion
13.9.1 Simple pendulum
13.9.2 Compound pendulum
13.9.3 Torsional pendulum