Engineering Mechanics

Engineering Mechanics
K. L. Kumar
CONTENTS
Preface to the Third Revised Editio
Terminal Objectives
1 ENGINEERING MECHANICS; WHAT AXD WHY? 1
1.1 Engineering and Engineering Sciences J
1.2 Mechanics and Its Relevance to Engineering 2
L3 Different Formulations of Mechanics 3
1.4 Foundational Concepts 4
1.5 Frames of Reference: Inertial and Moving 5
ft Idealisation of Bodies 5
1.7 Internal and F.xternaI Forces R
1.8 Principle of Transmissibility of Force 9
1.9 Concept of Free-Body Diagram 11
I 10 I
-aws nf Merhanirs 17
1.11 Law of Gravitation
—Weight of Bodies 17
Concept Review Questions 18
Multiple-Choice Questions 18
REVIEW SECTION 21
R1 RF.VfF.W OF SI UNITS 22
R I I 5sT Rnst» IlniK 7 ?
R 1.7 £1 Dgriv*H Units with New Namgs 7 ? R1.3 Units of Some Common Physical Quantities 24 R1.4 Multiples and Submultiples 25 R 1.5 Some Conversion Factors 25 P ) (\ VphifS nf .9nme TTsefiil Constants R1.7 Properties of Water. Mercury and Air 26 Test Your SI Power 27 R2 REVIEW OF VECTORS 28 R2.1 Numbers. Scalars and Vectors 28 R2.2 R2.7 Resolution of Vectors JJ R2.4 Concept of Products 40wiii Omlcnls R2.5 Dcrivalivcs and Integrals of Vectors 47 R2.6 Gradient, Divergence and Curl 51 R2.7 Some Vector Operations 52 R ? X Vector Rlt-ntilipx 55 R2.9 Position Vcclor. Displacement. Velocity and Acceleration 57 R2.10 Some Other Vcclor Ouanlitics 61 i Concept Review Questions 69 Tutorial Problems 70 Multiple-Choice Questions 73 2 FORCES AND FORCF. SYSTEMS 75 2.1 Force and Moment Concepts 75 2.2 Force Fields: Linear, Plane and Spatial 77 2 L Dtslrihufril Forty T-iolfR 70 2.4 Force System Acting on a Body 80 2.5 Resultant of a Force System SI 2.6 Principle of Parallel Transfer of a Force 82 2.7 Resultant of a Concurrent Force System 87 2.X Resultant of a Parallel Force System 90 2.9 Resultant of a Cpplanar Force System 97 2.10 Resultant of u Spatial Force System 102 2.1 I firnvitntinnal Force Field 10.1 2.12 Hydrostatic Force Field 106 Conccpl Review Questions 107 Tutorial Prohlcmx IQS Multiple-Choice Questions III5 3 EQUILIBRIUM ANALYSIS OF STATIC SYSTEMS 117 3.1 Equilibrium Concept in Mechanics 117 3.2 Frcc-Body Diagram in Statics 120 3.3 Reactions by Supports 122 3.4 Equilibrium of a Particle /25 experiment EI: Equilibrium under Coplan.tr Forces 129 3.5 Equilibrium of a Rigid Body /35 3.6 Ettuilibrium of a System of Particles 138 Experiment E2: Equilibrium under Spatial Forces /5/ Concept Review Questions 15.1 Tutorial Problems / 54 Multiple-Choice Questions /59 ABELICAHONS 161 -IN-SXAIICSSt SIMPLE STRUCTURES 163 SI . I Types of Structures 163 SI.2 Internal Forces: Tension and Compression 167Onitenis xix SI.3 Analysis by the Method of Joints 167 Experiment E3: Forces in a Plane Truss 174 SI.4 Analysis by the Method of Sections /77 Experiment E4: Forces in a Space Frame 1X4 Concept Review Questions 1X7 Tutorial Prohlcms 1X7 Multiple-Choice Questions 192 S2 THIN ttlfiin BEAMS 193 52.1 Beams and Loading 193 52.2 Shear Force and SF Diagram / 94 52.3 Bending Moment and BM Diagram /97 52.4 Relationship between Bending Moment, Shear Force and Loading /99 Experiment E5: Shear Force and Bending Moment in a Beam 2/6 Concept Review Questions 2/9 Tutorial Prohlems 219 Multiple-Choice Questions 221 S3 FRICTION 223 53.1 Friction and Impending Motion 223 Experiment E6: Coefficient of Static Friction 230 53.2 Rolling Resistance 237 53.3 Sliding and Rolling of Cylinders 238 53.4 Band-Brake and Belt Friction 244 S4.5 Lifting by a Screw Jack 25 / 53.6 Disc and Bearing Friction 256 53.7 Input/Output of Simple Machines 261 Experiment E7: Performance of Simple Lifting Machines 26X Concept Review Questions 27/ Tutorial Prohlems 272 Multiple-Choice Questions 27X 4 CENTRAL POINTS: CENTROID, CENTRE OF MASS AND CF.NTRK OF GRAVITY 28» 4 I Inlrtnliiclinn 7X0 4.2 Concept of First Moment 280 4 3 Central Points: Definitions of Centroid. Centre of Mass and Centre of Gravity 282 4.4 Centroid of a Length 283 4.5 Centroids of a Composite Length 2X4 4.6 Centroid of an Area 7XX 4.7 Theorems of Pappus-Guldinus 299 4.9 Centre of Mass 707 4.10 Centre of Gravity .?/.?XX Contents Concept Review Questions 3 / 8 Tutorial Problems 319 Multiple-Choice Questions 322 5 KINF.MATICS OF A PARTICLE AND OF A POINT IN C;KNKRAI 323 5.1 Kinematic Concepts 323 5.2 Motion Referred to Fixed Rectangular Coordinates 324 5 1 Rectilinear Motion of a Point 126 5.4 Motion Referred to Cylindrical Polar Coordinates 330 5.5 Motion Referred to Path Coordinates 339 5.6 Plane Motion of a Point’ Gravitational Field 343 5.7 Motion Referred to Moving Frames of Reference 355 Concept Review Questions 374 Tutorial Problems 375 Multiple-Choice Questions 38/ 6 DYNAMICS OF A PARTICLE AND OF THE MASS CENTRE OF ANY SYSTEM 583 Introduction INI 6.2 Equation of Motion 383 6.3 DAlembert Principle: Inertia Forces 399
6.4 Work, Power and Energy 402
6.5 Work-Energy Principle 4 / 9
6.6 Conservation of Mechanical Energy 42/
6.7 Impulse of a Force 424
6.8 Impulse-Momentum Principle 425
6A) Conservation of Momentum
6 I
426
6 10 Moment of Momentum 434
6.11 Moment of Momentum Equation 435
6.12 Conservation of Moment of Momentum 4.16
Concept Review Questions 438
Tutorial Problems 419
Multiple-Choice Questions 445
7 KINEMATICS OF A RIGID BODY 447
1 I Introduction 447
7.2 Types of Motion 447
7.3 Fixed-Axis Rotation 454
7.4 Plane Motion of a Rigid Body 454
7.5 Rigid-Body Motion of Fluids 458
7 6 Instantaneous Centre of Rotation
7.7 Relative Velocity and Acceleration for Points
on a Rigid Body 465
Concept Review Questions 485
Tutorial Problems 486
Multiple-Choice Questions 491
459a,minis xxl
8 MOMENT OF INKRTIA: ARI A AND MASS 492
8.1 Introduction 492
8.2 Inertial Concepts: Area 492
SJ. Parallel-Axis Theorem- Arrn -TAX’
5.4 Moment <if Inertia of Composite Sections 499
8.5 Principal Axes and Principal Moments of Inertia: Area SOS
8.6 Inertial Concepts: Mass 510
8 7 Moments of Inertia of Thin Plates 5/6
8.8 Parallel-Axis Theorem (Mass Moment of Inertia) 5/8
8.9 Moment of Inertia of Composite Bodies 522
Experiment E8: Moment of Inertia of a Body 524
Concept Review Questions 534
Tutorial Problems 535
MullipIc-CItoiec Questions 538
9 nviMAVtirs OF ninin Romps 540
‘7.1 Introduction Ull
9.2 Translation of a Rigid Body 540
9.3 Rotation of a Rigid Body About a Fixed Principal Axis .545
9.4 Plane Motion of a Rigid Body 550
Experiment E9: Looping the Loop 557
9.5 Work-Energy Formulation for Plane Motion 561
9.6 Impulse-Momentum Formulation for Plane Motion 576
Experiment EI0; Conservation of Angular Momentum—
A Human Experience 5/12
9.7 General Motion of a Rigid Body 588
9.8 Gyroscopic Action 594
Experiment Ell: Principle and Action of a Gyroscope—
A Human Experience 597
Concept Review Questions 599
Tutorial Problems 601
Multiple-Choice Questions 608
APPLICATIONS IN DYNAMICS 611
D1 IMPACT OF TWO BODIES 613
Dl . l Introductory Concepts 613
Ol 7 Coefficient of Restitution 616
Experiment El 2: Coefficient of Restitution 617
013 Plane Central Collision 620
PI.4 Collision of a Small Body with a Massive Body 623
Concept Review Questions 641
Tutorial Problems 641
Multiple-Choice Questions 645xxii Coii fenIs
D2 CENTRA!. FORCE MOTION 646
D2.I Iniroduclory Concepts 646
D2.2 Acceleration Due to Gravity 648
D2.3 Trajectories for Central Force Motion 65/
D2.4 Energy Expended for Different Trajectories 658
D2.5 Launching of Satellites at an Angle 660
D2.6 Astronomical Facts and Laws of Kepler 665
Concept Review Questions 677
Tutorial Problems 677
Multiple-Choice Questions 678
10 VIRTUAL WORK AND POTENTIAL
ENERGY PRINCIPLES 679
10 I Introduction 67V
10.2 Principle of Virtual Work 679
10.3 Principle of Potential Energy 687
10.4 Generalised Coordinates W6
Concept Review Questions 697
Tutorial Problems 698
Multiple-Choice Questions 701
11 VIBRATIONS OF SIMPLE MECHANICAL SYSTEMS 703
11.1 Elements of Mechanical Systems 703
11.2 Simple Mechanical Systems 706
11.3 Features of Vibrating Systems 709
11
-4 f -inear Free Vibrations 714
Experiment El 3: Oscillation of a Simple Pendulum 720
Experiment El 4: Multiple Elastic Impacts 722
11.5 Angular Free Vibrations 727
11.6 Pendulum Motions 732
Experiment El 5: Oscillation of a Compound Pendulum 742
Concept Review Questions 749
Tutorial Problems
Multiple-Choice Questions 754
250.
APPENDICES 151
Appendix I Rules for Differentiation and Integration 759
Properties of Plane Figures
Properties of Solid Bodies
Appendix 2 762
Appendix 3 76«
Hints in Tularial Prnfflt’ nis 774
Indf r 796

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