Engineering Mechanics: Problems and Solutions

Contents
Preface
1. Introduction
	1.1 Introduction to Engineering Mechanics
	1.2 Basic Idealizations: Particle, Continuum and Rigid Body
	1.3 Units
		1.3.1 Types of units
		1.3.2 Systems of units
	1.4 Scalar and Vector Quantities
	1.5 Force and its Characteristics
	1.6 Force System
		1.6.1 Classification of force system
	1.7 Laws of Mechanics
		1.7.1 Laws of motion
		1.7.2 The gravitational law of attraction
		1.7.3 Laws of forces
	1.8 Vector Algebra
		1.8.1 Vectors’ representation
		1.8.2 Classification of vectors
		1.8.3 Vector operations
		1.8.4 Vectorial representation of component of force
		1.8.5 Vectorial representation of force passing through two points in space
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
2. Two Dimensional Concurrent Force Systems
	2.1 Resolution of Force and Force Systems
	2.2 Resultant of Two Dimensional Concurrent Forces
	2.3 Principle of Transmissibility of Forces
	2.4 Free Body Diagrams
	2.5 Equations of Equilibrium Conditions
	2.6 Lami’s Theorem
	Numerical Problems
	Multiple Choice Questions
3. Two Dimensional Non-concurrent Force Systems
	3.1 Introduction
	3.2 Moment
	3.3 Couple
	3.4 Moment of Couple
	3.5 Transfer of a Force to Parallel Position
	3.6 Graphical Presentation of Moment
	3.7 Varignon’s Theorem
	3.8 Equations of Equilibrium Conditions
	3.9 Types of Supports and their Reactions on Beams
	3.10 Types of Beams
	3.11 Types of Loading on Beams
	Numerical Problems
	Multiple Choice Questions
4. Friction
	4.1 Introduction
	4.2 Coulomb’s Laws of Dry Friction
	4.3 Static Friction, Limiting Friction, Kinetic Friction
	4.4 Angle of Friction
	4.5 Angle of Repose
	4.6 Cone of Friction
	Numerical Problems
	Multiple Choice Questions
5. Application of Friction
	5.1 Ladder Friction
	5.2 Wedge Friction
	5.3 Screw Friction
	5.4 Belt Friction
	5.5 Band Brakes
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
6. Analysis of Trusses
	6.1 Introduction
	6.2 Classification of Trusses
	6.3 Assumptions for the Analysis of Perfect Truss
	6.4 Analysis of Forces in the Members of the Truss
		6.4.1 Method of joint
		6.4.2 Method of section
	Thoretical Problems
	Numerical Problems
	Multiple Choice Questions
7. Centroid and Centre of Gravity
	7.1 Introduction
	7.2 Centre of Gravity, Centroid of Line, Plane Area and Volume
	7.3 Centroid of L, C, T and I-Sections
	7.4 Importance of Axis of Symmetry in Centroid and Centre of Gravity
	7.5 Centroid of a Triangle
	7.6 Centroid of a Quarter Circle and Semicircle
	7.7 Centroid of Composite Sections and Bodies
	7.8 Centre of Gravity of Cone and Hemisphere
	Numerical Problems
	Multiple Choice Questions
8. Moment of Inertia
	8.1 Moment of Inertia of Plane Area and Mass
	8.2 Radius of Gyration
	8.3 Parallel Axis Theorem and its Significance
	8.4 Perpendicular Axis Theorem
	8.5 Moment of Inertia of a Rectangle
	8.6 Moment of Inertia of a Triangle
	8.7 Moment of Inertia of a Circle, a Quarter Circle and a Semicircle
	8.8 Moment of Inertia of Composite Sections and Bodies
	8.9 Mass Moment of Inertia of Prismatic Bar, Rectangular Plate, Circular Disc, Solid Cone and Sphere about Axis of Symmetry
	Numerical Problems
	Multiple Choice Questions
9. Shear Force and Bending Moment Diagrams
	9.1 Beams
	9.2 Types of Beams
	9.3 Types of Loads and Beams
	9.4 Shear Force and Bending Moment
	9.5 Shear Force Diagram (SFD) and Bending Moment Diagram (BMD)
	9.6 Sign Convention of Shear Force and Bending Moment in SFD and BMD
	9.7 Relationship between Load Intensity (w), Shear Force (S) and Bending Moment (M)
	9.8 Point of Contraflexure or Inflexion
	9.9 Characteristics of SFD and BMD
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
10. Kinematics: Rectilinear Motion of Particles
	10.1 Introduction
	10.2 Displacement, Velocity and Acceleration
	10.3 Rectilinear Motion
	10.4 Rectilinear Motion in Horizontal Direction (X-axis)
		10.4.1 Motion with variable acceleration
		10.4.2 Motion with uniform acceleration
	10.5 Graphical Method for Motion Curves
	10.6 Rectilinear Motion in Vertical Direction (Y-axis)
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
11. Kinematics: Curvilinear Motion of Particles
	11.1 Introduction
	11.2 Rectangular Coordinates
	11.3 Tangential and Normal Components of Acceleration
	11.4 Projectile
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
12 Kinetics of Particles
	12.1 Introduction
	12.2 Laws of Motion
	12.3 D’Alembert’s Principle
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
13. Work and Energy
	13.1 Introduction
	13.2 Work Done by a Force
	13.3 Work Done by a Variable Force
	13.4 Energy
	13.5 Work–Energy Principle
	13.6 Power
	13.7 Principle of Conservation of Energy
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
14. Impulse and Momentum
	14.1 Introduction
	14.2 Principle of Impulse and Momentum
	14.3 Principle of Conservation of Momentum
	14.4 Collisions of Elastic Bodies
		14.4.1 Direct central impact
		14.4.2 Oblique/Indirect central impact
		14.4.3 Coefficient of restitution
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
15. Kinematics of Rigid Bodies
	15.1 Introduction
	15.2 Rotational Motion
	15.3 Angular Displacement, Angular Velocity and Angular Acceleration
	15.4 Relationship between Linear and Angular Velocity
	15.5 Relationship between Linear, Normal and Angular Acceleration
	15.6 Equations of Angular Motion
	15.7 General Plane Motion
	15.8 Instantaneous Centre
	15.9 Relative Velocity
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
16. Kinetics of Rigid Bodies
	16.1 Introduction
	16.2 Kinetics of Rotary Motion
		16.2.1 Moment of momentum
		16.2.2 Torque and angular momentum
	16.3 Kinetic Energy of a Body in Translatory and Rotary Motion
	16.4 Principle of Conservation of Energy
	16.5 Principle of Work and Energy
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
17. Virtual Work
	17.1 Introduction
	17.2 Principle of Virtual Work
	17.3 Work Done by Forces
	17.4 Work Done by Moments
	Theoretical Problems
	Numerical Problems
	Multiple Choice Questions
Index