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ENGINEERING MECHANICS
A TEXTBOOK OF ENGINEERING MECHANICS
A TEXTBOOK OF
ENGINEERING MECHANICS (In SI Units) For
B.E./B.Tech. Ist YEAR Strictly as per the latest syllabus prescribed by Gautam Buddh Technical University, Lucknow
By Dr. R.K. BANSAL
B.Sc. Engg. (Mech.), M. Tech., Hons. (I.I.T., Delhi), Ph.D., M.I.E. (India) Formerly Professor of Mechanical Engineering Department of Mechanical Engineering Delhi College of Engineering Delhi AND
SANJAY BANSAL B.E. (Computer)
LAXMI PUBLICATIONS (P) LTD Έn ISO 9001:2008 Company)
BENGALURU KOCHI
•
•
CHENNAI
KOLKATA
•
•
GUWAHATI
LUCKNOW
BOSTON (USA)
• •
•
HYDERABAD
MUMBAI
•
RANCHI
NAIROBI (KENYA)
• •
JALANDHAR NEW DELHI
A TEXTBOOK OF ENGINEERING MECHANICS Compiled by Smt. Nirmal Bansal ŽƉLJƌŝŐŚƚΞďLJƚŚĞƵƚŚŽƌƐĂŶĚƚŚĞ>ĂdžŵŝWƵďůŝĐĂƟŽŶƐWǀƚ͘>ƚĚ͘ ůů ƌŝŐŚƚƐ ƌĞƐĞƌǀĞĚ ŝŶĐůƵĚŝŶŐ ƚŚŽƐĞ ŽĨ ƚƌĂŶƐůĂƟŽŶ ŝŶƚŽ ŽƚŚĞƌ ůĂŶŐƵĂŐĞƐ͘ /Ŷ ĂĐĐŽƌĚĂŶĐĞ ǁŝƚŚ ƚŚĞ ŽƉLJƌŝŐŚƚ ;ŵĞŶĚŵĞŶƚͿ Đƚ͕ ϮϬϭϮ͕ ŶŽƉĂƌƚŽĨƚŚŝƐƉƵďůŝĐĂƟŽŶŵĂLJďĞƌĞƉƌŽĚƵĐĞĚ͕ƐƚŽƌĞĚŝŶĂƌĞƚƌŝĞǀĂůƐLJƐƚĞŵ͕ŽƌƚƌĂŶƐŵŝƩĞĚŝŶĂŶLJĨŽƌŵŽƌďLJĂŶLJŵĞĂŶƐ͕ĞůĞĐƚƌŽŶŝĐ͕ ŵĞĐŚĂŶŝĐĂů͕ƉŚŽƚŽĐŽƉLJŝŶŐ͕ƌĞĐŽƌĚŝŶŐŽƌŽƚŚĞƌǁŝƐĞ͘ŶLJƐƵĐŚĂĐƚŽƌƐĐĂŶŶŝŶŐ͕ƵƉůŽĂĚŝŶŐ͕ĂŶĚŽƌĞůĞĐƚƌŽŶŝĐƐŚĂƌŝŶŐŽĨĂŶLJƉĂƌƚŽĨƚŚŝƐ ŬǁŝƚŚŽƵƚƚŚĞƉĞƌŵŝƐƐŝŽŶŽĨƚŚĞƉƵďůŝƐŚĞƌĐŽŶƐƟƚƵƚĞƐƵŶůĂǁĨƵůƉŝƌĂĐLJĂŶĚƚŚĞŌŽĨƚŚĞĐŽƉLJƌŝŐŚƚŚŽůĚĞƌ͛ƐŝŶƚĞůůĞĐƚƵĂůƉƌŽƉĞƌƚLJ͘/Ĩ LJŽƵǁŽƵůĚůŝŬĞƚŽƵƐĞŵĂƚĞƌŝĂůĨƌŽŵƚŚĞŬ;ŽƚŚĞƌƚŚĂŶĨŽƌƌĞǀŝĞǁƉƵƌƉŽƐĞƐͿ͕ƉƌŝŽƌǁƌŝƩĞŶƉĞƌŵŝƐƐŝŽŶŵƵƐƚďĞŽďƚĂŝŶĞĚĨƌŽŵƚŚĞ ƉƵďůŝƐŚĞƌƐ͘
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Contents Chapters
Pages
UNIT-I: FORCE SYSTEMS AND FRICTION 1.
2.
Basic Concepts of Engineering Mechanics 1.1.
Definitions
...
3
1.2.
Scalar and Vector Quantities
...
3
1.3.
Free, Forced and Fixed Vectors
...
4
1.4.
Law of Parallelogram of Forces
...
4
1.5.
Lami’s Theorem
...
7
1.6.
System of Units
...
7
1.7.
Resolution of a Force
...
17
1.8.
Moment of a Force
...
20
1.9.
Laws of Mechanics
...
22
1.10.
The Principle of Transmissibility of Forces
...
24
Highlights
...
25
Exercise 1
...
25
Force System and Classification
28–48
2.1.
Coplanar Collinear and Concurrent Forces
...
28
2.2.
Classification of a Force System
...
28
2.3.
Resultant of Several Forces
...
29
2.4.
Resultant of Coplanar Forces
...
30
2.5.
Resultant of Collinear Coplanar Forces
...
30
2.6.
Resultant of Concurrent Coplanar Forces
...
31
2.7.
3.
3–27
Resultant of Non-concurrent Coplanar Forces
...
42
Highlights
...
46
Exercise 2
...
46
Moment of a Force and Varignon’s Theorem
49–66
3.1.
Parallel Forces
...
49
3.2.
Moment of a Force
...
49
3.3.
Varignon’s Theorem (or Principle of Moments)
...
50
3.4.
Types of Parallel Forces
...
53
3.5.
Resultant of Two Parallel Forces
...
53
3.6.
Resolution of a Force into a Force and a Couple
...
58
3.7.
General Case of Parallel Forces in a Plane
...
61
Highlights
...
63
Exercise 3
...
63
(v)
( vi ) Chapters
4.
Equilibrium of Coplanar Force System and Free Body Diagram
6.
67–102
4.1.
Equilibrium of Coplanar Force System
...
67
4.2.
Action and Reaction
...
78
4.3.
Free Body Diagrams
...
79
4.4.
Equilibrium of a Body Under Three Forces
...
97
4.5.
5.
Pages
Lami’s Theorem
...
98
Highlights
...
100
Exercise 4
...
100
Determination of Support Reactions
103–127
5.1.
Introduction
...
103
5.2.
Types of Supports
...
103
5.3.
Types of Loading
...
104
5.4.
Determination of Reactions of a Beam
...
105
Highlights
...
125
Exercise 5
...
125
Friction
128–173
6.1.
Introduction
...
128
6.2.
Co-efficient of Friction (P)
...
128
6.3.
Angle of Friction (I)
...
129
6.4.
Cone of Friction
...
130
6.5.
Types of Friction
...
130
6.6.
Coulomb’s Laws of Friction
...
130
6.7.
Angle of Repose
...
135
6.8.
Equilibrium of a Body Lying on a Rough Inclined Plane
...
136
6.9.
Applications of Friction
...
148
6.10.
Wedge Friction
...
149
6.11.
Belt Friction
...
153
6.12.
Brakes and Screws Friction
...
160
6.13.
Friction in a Square Threaded Screw
...
164
Highlights
...
171
Exercise 6
...
172
UNIT-II: BASIC STRUCTURAL ANALYSIS 7.
Plane Truss
177–214
7.1.
Difference between Truss and Frame
...
177
7.2.
Perfect and Imperfect Truss
...
178
7.3.
Assumptions and Analysis of Plane Truss
...
179
7.4.
Method of Joints
...
179
7.5.
Method of Sections
...
200
( vii ) Chapters 7.6.
8.
Pages Zero Force Members
...
207
Highlights
...
208
Exercise 7
...
208
Beams (Shear Force and Bending Moment)
215–265
8.1.
Types of Beams
...
215
8.2.
Types of Load
...
216
8.3.
Statically Determinate Beams
...
216
8.4.
Shear Force and Bending Moment in Beams
...
217
8.5.
Shear Force and Bending Moment Diagrams
...
217
8.6.
Shear Force and Bending Moment Diagrams for a Cantilever
...
219
8.7.
Shear Force and Bending Moment Diagrams for a Simply Supported Beam...
234
8.8.
Shear Force and Bending Moment Diagrams for Overhanging Beams
...
247
8.9.
Shear Force and Bending Moment Diagrams for Beams Subjected to Couples
...
255
8.10.
Relations between Load, Shear Force and Bending Moment
...
259
8.11.
Support Reactions from given Shear Force Diagram or given Bending Moment Diagram
...
260
Highlights
...
262
Exercise 8
...
263
UNIT-III: CENTROID AND MOMENT OF INERTIA 9.
Centroid and Moment of Inertia 9.1.
Centre of Gravity
269–325 ...
269
9.2.
Centre of Mass
...
269
9.3.
Centroid or Centre of Gravity of Simple Plane Figures
...
269
9.4.
Centroid (or Centre of Gravity) of Areas of Plane Figures by the Method of Moments
...
269
9.5.
Centroid of Composite Bodies
...
271
9.6.
Determination of Centroid by Integration
...
278
9.7.
Centroid of Volume
...
290
9.8.
Definition of Moment of Inertia of Area
...
293
9.9.
Perpendicular Axis Theorem and Polar Moment of Inertia
...
295
9.10.
Parallel Axis Theorem
...
295
9.11.
Moment of Inertia of Simple Areas by Integration
...
296
9.12.
Moment of Inertia of Composite Areas
...
304
9.13.
Polar Moment of Inertia of Masses
...
311
9.14.
Parallel Axis Theorem for Mass Moment of Inertia
...
312
9.15.
Mass Moment of Inertia of Simple Bodies by Integration
...
312
9.16.
Mass Moment of Inertia of Composite Bodies
...
318
Highlights
...
319
Exercise 9
...
321
( viii ) Chapters
Pages
UNIT-IV: KINEMATICS AND KINETICS OF RIGID BODIES 10.
Kinematics of Rigid Bodies 10.1.
11.
329–394
Introduction
...
329
10.2.
Absolute Motion
...
329
10.3.
Plane Rectilinear Motion of Rigid Body
...
329
10.4.
Plane Curvilinear Motion of Rigid Body
...
347
10.5.
Rotation of Rigid Bodies
...
350
10.6.
x – y and n – t Components
...
358
10.7.
Relative Motion
...
362
10.8.
Plane Motion of Rigid Bodies
...
366
10.9.
Instantaneous Centre of Zero Velocity
...
382
Highlights
...
390
Exercise 10
...
391
Kinetics of Rigid Bodies
395–468
11.1.
Introduction
...
395
11.2.
Force, Mass and Acceleration
...
395
11.3.
Newton’s Laws of Motion
...
396
11.4.
D’ Alembert’s Principle and Dynamic Equilibrium
...
401
11.5.
Laws of Motion Applied to Planer Translation
...
407
11.6.
Momentum and Angular Momentum (or Moment of Momentum)
...
428
11.7.
Laws of Motion Applied to Rotary Motion
...
432
11.8.
Laws of Motion Applied to Plane Motion
...
441
11.9.
Work and Energy
...
442
11.10. Kinetic Energy
...
448
11.11. Principle of Work and Energy
...
449
11.12. Conservative Forces
...
451
11.13. Law of Conservation of Energy
...
451
11.14. Linear Impulse and Momentum
...
459
11.15. Conservation of Linear Momentum
...
462
Highlights
...
465
Exercise 11
...
466
UNIT-V: MECHANICS OF DEFORMABLE SOLIDS 12.
Simple Stresses and Strains 12.1.
Introduction
471–497 ...
471
12.2.
Simple Stress and Strain
...
471
12.3.
Normal and Shear Stresses
...
472
12.4.
Elasticity and Elastic Limit
...
475
12.5.
One Dimensional Loading
...
476
( ix ) Chapters 12.6.
13.
14.
Pages Stress on an Inclined Plane Members of Varying Cross-Sections
...
486
12.8.
Bars in Series
...
491
12.9.
Tensile Test Diagrams for Ductile and Brittle Materials
...
493
Highlights
...
494
Exercise 12
...
495
Elastic Constants
498–516
13.1.
Introduction
13.2.
Longitudinal Strain
...
498
13.3.
Lateral Strain
...
498
13.4.
Poisson’s Ratio
...
499
13.5.
Volumetric Strain
...
501
13.6.
Volumetric Strain of a Cylindrical Rod
...
507
13.7.
Bulk Modulus
...
508
13.8.
Expression for Young’s Modulus in Terms of Bulk Modulus
...
508
13.9.
Relationship between Modulus of Elasticity and Modulus of Rigidity
...
510
Highlights
...
513
Exercise 13
...
514
...
Strain Energy and Impact Loading
498
517–526
Introduction
...
517
14.2.
Some Definitions
...
517
14.3.
Expression for Strain Energy Stored in a Body when the Load is ...
517
14.4.
Expression for Strain Energy Stored in a Body when the Load is ...
519
Applied with Impact
...
521
Highlights
...
525
Exercise 14
...
525
Applied Gradually Applied Suddenly 14.5.
16.
481
12.7.
14.1.
15.
...
Expression for Strain Energy Stored in a Body when the Load is
Bending of Beams
527–543
15.1.
Introduction
...
527
15.2.
Theory of Pure Bending
...
527
15.3.
Neutral Surface and Neutral Axis
...
530
15.4.
Stresses in Beams of Different Cross-Sections
...
532
Highlights
...
541
Exercise 15
...
542
Theory of Torsion
544–559
16.1.
Torque and Twist
...
544
16.2.
Shear Stress Produced in a Circular Shaft Subjected to Torsion
...
544
(x) Chapters
Pages
16.3.
Maximum Torque Transmitted by a Circular Solid Shaft
...
546
16.4.
Torque Transmitted by a Hollow Circular Shafts
...
548
16.5.
Power Transmitted by Shafts
...
549
Highlights
...
557
Exercise 16
...
558
Objective Type Questions
561–593
Examination Paper with Solutions
595–605
Preface to the Eighth Edition The course contents of the eighth edition of the book entitled, ‘A Textbook of Engineering Mechanics’ are planned in such a way that the book covers the complete course of first year students of all disciplines of Gautam Buddh Technical University, Lucknow (Formerly known as U.P. Technical University, Lucknow) strictly as per the latest syllabus prescribed by G.B. Technical University, Lucknow. This edition has been thoroughly revised and made up-to-date. The book contains following five units: Unit I : Force Systems, Basic Concepts, Resultant of a Force System, Free Body Diagrams, Equilibrium and Equation of Equilibrium and Friction. Unit II : Basic Structural Analysis, Plane Truss and Beam (Shear Force and Bending Moment Diagrams). Unit III : Centroid and Moment of Inertia. Unit IV : Kinematics and Kinetics of Rigid Body. Unit V : Mechanics of Deformable Solids, Simple Stress and Strain, Bending of Beams and Theory of Torsion. The following additions have been made in this edition: 1. Free, Forced and Fixed Vectors. Application of Friction, Wedge, Belt, Brakes and Screws. 2. Zero Force Member and Statically determinate Beams. 3. Mass Moment of Inertia of Composite Bodies. 4. Relative Velocity, Plane Motion of Rigid Bodies and Conservative Forces. 5. Tensile Test Diagrams for Ductile and Brittle Materials. Also the latest solved papers of U.P. Technical University have been added at proper places. These additions makes the book more useful to the students. The book is written in a simple and easy-to-follow languages, so that even an average student can grasp the subject by self-study. At the end of each chapter, highlights, theoretical questions and many unsolved problems with answers are given for the students to solve them. Though every care has been taken in checking the manuscripts and proofreading, yet claiming perfection is very difficult. We shall be very grateful to the readers and users of this book for pointing any mistake that might have crept in. Suggestions for improvement are most welcome and would be incorporated in the next edition with a view to make the book more useful. —AUTHORS
( xi )
SYLLABUS B. Tech. Ist Year NME-102 : ENGINEERING MECHANICS UNIT I: FORCE SYSTEMS
L T P [310] 9
Basic concepts: Definitions, Basic assumptions, Scalar and Vector quantities, Free, Forced and fîxed vectors. x Force System; Force, Classification and Representation, Force as a Vector, Composition of forces, Parallelogram Law, Resolution, Principle of Transmissibility of forces. x Moment of a force, Vector representation, Moment for coplanar force system, Varignon’s theorem. x Couple, Vector representation, Resolution of a force into a force and a couple. x Force Systems: Coplanar Concurrent Force system and Coplanar Non-concurrent force systems, Resultant of coplanar force system. x Equilibrium of coplanar force system, Free body diagrams, Determination of reactions, Equilibrium of a body under three forces, Lami’s theorem. Friction x Introduction, Wet and Dry friction, Theory of Dry friction, Angle of friction, Angle of Repose, Cone of friction, Coulomb’s laws of friction, Applications of friction: Wedge, Belt, Brakes and Screws. x
UNIT II: BASIC STRUCTURAL ANALYSIS x
x
8
Plane Truss: Difference between truss and frame, Perfect and imperfect truss, Assumptions and Analysis of Plane Truss, Method of joints, Method of section, Zero force members. Beams, Types of beams, Statically Determinate Beams, Shear force and bending moment in beams, Shear force and bending moment diagrams, Relationships between load, shear and bending moment.
UNIT III: CENTROID AND MOMENT OF INERTIA x x
x
8
Center of Gravity, Center of Mass and Centroid of curves, areas, volumes, Determination of centroid by integration, Centroid of composite bodies. Definition of Moment of inertia of area, Perpendicular axis theorem and Polar moment of Inertia, Parallel axis theorem, Moment of inertia of simple areas by integration, Moment of Inertia of Composite Areas. Moment of Inertia of masses, Parallel axis theorem for mass moment of inertia, Mass moment of inertia of simple bodies by intégration, Mass moment of inertia of composite bodies.
UNIT IV: KINEMATICS OF RIGID BODY 9 x Introduction, Absolute motion, Plane rectilinear motion of rigid body, Plane curvilinear Motion of rigid body, x–y and n–t components, Rotation of rigid bodies, Relative Motion, Plane Motion of rigid bodies, Instantaneous center of zero velocity
( xii )
( xiii ) Kinetics of Rigid Body x Introduction, Force, Mass and Acceleration, Newton’s law of motion, D’ Alembert’s Principles and Dynamic Equilibrium, Laws of motion applied to planar translation, rotation and plane motion. x Work and Energy, Kinetic energy, Principle of work and energy, Conservative forces, Law of conservation of energy. x Linear Impulse and Momentum, Conservation of linear momentum. UNIT V: MECHANICS OF DÉFORMABLE SOLIDS 8 x Simple Stress and Strain: Normal and shear stresses. One Dimensional Loading; Stress on an inclined plane, members of varying cross-section, bars in series. Tensile Test diagram for ductile and brittle materials, Elastic constants, Strain energy, resilience. x Bending of Beams: Theory of pure bending, neutral surface and neutral axis, stresses in beams of different cross-sections. x Theory of Torsion: Torque and twist, Shear stress due to torsion circular sections.
UNIT I
FORCE SYSTEMS AND FRICTION
Chapters 1. 2. 3. 4. 5. 6.
Basic Concepts of Engineering Mechanics Force System and Classification Moment of a Force and Varignon’s Theorem Equilibrium of Coplanar Force System and Free Body Diagram Determination of Support Reactions Friction
ENGINEERING MECHANICS ABOUT THE BOOK The course contents of the revised eighth edition of the book entitled, 'A Textbook of Engineering Mechanics' are planned in such a way that the book covers the complete course of rst year students of all disciplines of Gautam Buddh Technical University, Lucknow according to the latest syllabus. This edition has been thoroughly revised and made up-to-date. Also the solved papers of Gautam Buddh Technical University upto May 2009 have been added at proper places. These additions makes the book more useful to the students. The book is written in a simple and easy-to-follow languages, so that even an average student can grasp the subject by self-study. At the end of each chapter, highlights, theoretical questions and many unsolved problems with answers are given for the students to solve them. ABOUT THE AUTHOR Dr. R. K. Bansal graduated in 1966. He obtained his Master's Degree in 1975 with honours from I.I.T., Delhi and Ph.D. in 1981 from University of Delhi. He joined Delhi College of Engineering as a Lecturer and became Assistant Professor in 1984. He was selected for the post of Professor in 1995. He also held the posts of Head of Mech. Engineering (Faculty of Technology, University of Delhi), Dean (P.G.) Studies and Dean (U.G.) Studies, Delhi College of Engineering. During his teaching career of about thirty ve years, he guided a large number of research students and got published many papers. Dr. Bansal is the author of many books, which are followed as textbooks.
ISBN: 978-81-318-0855-9
9 788131 808559
M.R.P. ` 499.00 EEM-0553-499-ENGG MECHANICS (UP)-BAN