CONTENTS UNIT-I INTRODUCTION CHAPTER 1 INTRODUCTION 3-17 1.1 Mechanics 4 1.2 BasicTerminologies 4 1.3 Idealisation of Bodies 6 1.4 Mechanics of Fluid 7 1.5 Mechanics of Solids 7 1.5.1. Mechanics of Rigid Bodies (Engineering Mechanics) 7 1.5.2. Mechanics of Deformable Bodies (Strength of Materials) 8 1.6 Fundamental Principles of Mechanics 8 1.7 Units 9 1.8 Vectors 13 1.8.1. Vector Components 15 1.8.2. Dot product of Vectors 15 1.8.3. Cross Product of Vectors 16 Review Exercises 18 UNIT - 2 FUNDAMENTAL OF STATICS CHAPTER 2 COPLANAR CONCURRENT FORCES. 21-105 2.1 Force 22 2.1.1. Types of Forces 22 2.1.2. Characteristics of a Force 23 2.2 System of Forces 23 2.2.1. Resultant of Force System 26 2.3 Coplanar Concurrent Forces 27 ii MECHANICS OF SOLIDS 2.4. Resultant of Coplanar Concurrent Force System 27 2.4.1. Law of Parallelogram of Forces 27 2.4.1.1.Graphical Solution 28 2.4.1.2.Analytical Solution28 2.4.2. Triangle Law of Forces43 2.4.2.1.Graphical Method 44 2.4.2.2.Analytical Method 44 2.5 Resolution of Forces or Component of Forces 48 2.5.1. Principal of Resolution 50 2..6. Law of Polygon of Forces56 2.6.1. Graphical Method 57 2.6.2. Analytical Method 57 2.7. Equilibrium Conditions for Coplanar Concurrent Forces74 2.8 Equilibrant 75 2.9, Free body Diagram81 2.10. Lami's Theorem 87 CHAPTER-3 COPLANAR NON-CONCURRENT FORCES 107-173 3.1.Introduction 108 3.2.Moment of Force 109 3.2.1. Direction of Moment 110 3.3.Couple 120 3.3.1. Magnitude of Couple 121 3.3.1 Direction of Couple 121 3.4.Characteristics of Moment and Couple 122 3.5.Equivalent Couples 122 3.6.Force couple System 123 3.7.Varignon's Theorem 124 3.8.Parallel Forces 125 3.9. Resultant of Non-Concurrent Forces 127 3.10. Equilibrium of Coplanar Non-Concurrent Force System 136 3.11. Support Conditions 137 Review Exercises 174 UNIT-3 TRUSS CHAPTER 4 TRUSS195-264 4.1. Introduction 196 4.2. Trusses and Frames 196 4.2.1. Frame 196 4.2.2. Truss 198 4.3. Plane truss 199 4.4. Analysis of Plane Truss 199 4.5.Static Determinacy of Plane Truss 200 4.6. Methods of Analysis of Truss 202 4.7.Zero Force Members 202 4.8. Representation of Forces in Truss Member 207 4.9. Method of Joints 208 4.10. Method of Section 244 Review Exercises 265 UNIT - 4 CENTER OF GRAVITY AND MOMENT OF INERTIA CHAPTER 5 CENTER OF GRAVITY, CENTER OF MASS & CENTROID 271-352 5.1. Introduction 272 5.2. Center of Gravity 272 5.3. Center of Mass 274 5.4. Centroid 275 5.5. Centroid of a Line Segment 276 5.6. Centroid of Area 297 5.7. Pappus Guldinus Theorems 331 5.7.1. Pappus Guldinus First Theorem 333 5.7.2. Pappus Guldinus Second Theorem 334 5.8 Centerof Gravity of Three Dimensional Bodies 346 CHAPTER 6 MOMENT OF INERTIA 353-400 6.1. Introduction 354 6.2. Theorem of Parallel Axes 356 6.3. Theorem of Perpendicular Axes 357 6.4. Radius of Gyration 358 Review Exercises 401 UNIT-5 FRICTION CHAPTER 7 FRICTION 409-481 7.1.Introduction 410 7.2. Impending Motion . 410 7.3.Types of Friction 410 7.4.Dry Friction 411 7.5.Static Friction or Friction at Rest 412 7.6. Kinetic Friction or Friction During Motion 413 7.7.Friction Angles 413 7.8. Cone of Friction 414 7.9.Angle of Repose 414 7.10. Laws of Friction 415 7.11. Ladder Friction 437 7.12. Wedge Friction 452 7.13. Belt and Rope Friction 467 Review Exercises 482 UNIT-6 SIMPLE MACHINE CHAPTER 8 SIMPLE LIFTING MACHINE 487-531 8.1. Introduction 488 8.2. Reversible Machine 491 8.2.1. Condition of Irreversibility of Machine 492 8.3.Law of Machine 492 8.4. Maximum Efficiency 495 8.5. Types of Simple Lifting Machine 501 8.6. Pulleys and Pulley Blocks 504 8.7. Multiple Grooved Pulleys 509 8.8. Wheel and Axles 515 8.9. Geared or Toothed Simple Lifting Machines 518 8.10. Simple Screw Jack 521 8.11. Self-Locking Machines , 525 8.12. Compound Screw Jack 525 Review Exercises . 532 UNIT - 7 PHYSICAL & MECHANICAL PROPERTIES CHAPTER 9 MECHANICAL PROPERTIES OF MATERIALS. 535-570 9.1. Introduction 536 9.2. Modes of Failure 537 9.3.Static Tension Test 538 9.3.1. Test Procedure 542 9.3.2. Observation to be Made for Tensile Test 543 9.3.3. Characteristic Stress-Strain Curves 544 9.3.4. Factors Affecting Tension Test . 546 9.4.Static Compression Test 547 9.4.1.Test Procedure 548 9.5.ShearTest 550 9.5.1. Direct ShearTest 551 9.5.2. PunchingShearTest 553 9.5.3. Torsion Test 553 9.6.Bending or Flexure or Transverse Test 557 9.7. Impact Test 560 9.7.1. Izod Impact Test 562 9.7.2. Charpy Impact Test 563 9.8. Hardness Test 563 9.8.1. BrinellHandnessTest 564 9.8.2. Vicker's Hardness Test 566 9.83. RockwelfTest 567 9.9 Fatigue Test 567 Review Exercises 571 UNIT - 8 SIMPLE STRESSES & STRAIN CHAPTER 10 SIMPLE STRESSES AND STRAIN 575-664 10.1. Introduction 576 10.2. Assessment of Engineering Strength 577 10.3. Axial Load or Normal Force 578 lO.B.l.Tension 578 10.3.2. Compression 579 10.4. Concept of Stress 580 10.4.1.Axial or Normal Stress 580 10.4.2. Unit of Stress 581 10.5. Deformation Due to Applied Load 585 10.6. Axial Deformation Parameters 585 10.7. Compound Bars 595 10.8. Bars in Series 596 10.9. Extension of Tapered Rod Under Axial Load 626 10.10. Extension of Tapered Bar Under Axial Load . 627 10.11. Bars in Parallel 628 10.11.1. Bars in Parallel Type-1 Problems 630 10.11.2. Bars in Parallel Type-2 Problems 649 CHAPTER 11 TEMPERATURE OR THERMAL STRESSES IN MATERIAL. 665-696 11.1. Introducion 666 11.2. Temperature Effect on Bars in Series 674 11.3. Temperature Effect on Bars in Parallel 683 11.4. Hoop Stress in Cart Wheel Tyre 695 CHAPTER 12 ELASTIC CONSTANTS697-744 12.1Introduction 698 12.2. Modulus of Elasticity 698 12.3. Lateral Strain and Poisson's Ratio 701 12.4. Volumetric Strain 705 12.5. Effect of Multidirectional Axial Forces 711 12.6. Shear Stress and Modulus of Rigidity 723 12.7. Complementary Shear 724 12.8. Element Under State of Pure Shear 725 12.9. Relation Between Modulus of Elasticity and Modulus of Rigidity 726 12.10. Bulk Modulus 728 Review Exercises 745 UNIT-9 BEAMS CHAPTER 13 SHEAR FORCE & BENDING MOMENT761-919 13.1. Introductions 762 13.2. Types of Load 763 13.3. Types of Supports o 768 13.4. Types of Beam 768 13.5. Determination of Reactions 769 13.6. Direction of Moments 770 13.7. Method to Determine Reactions 770 13.8. Shear Force in Beams 783 13.9. Bending Moment 797 13.10. Point of Contraflexure or Point of Inflexion 804 13.11. Shapes of Shear Force and Bending Moment Diagram 812 13.12. Relationship Between Loading, Shear Force & Bending Moment 812 13.13. Maximum or Minimum Bending Moment 815 13.14. Derivation of Bending Moment Diagram From Shear Force Diagram 897 13.15. Beam With Inclined Loads 901 13.16. Beams with Levers 909 Review Exercises 920 UNIT -10 STRESS IN BEAMS CHAPTER 14 BENDING STRESSES IN BEAMS 929-983 14.1. Introduction 930 14.2. Pure Bending ' 932 14.3. Theory of Pure Bending 933 14.4. Moment of Resistance 933 14.5. Theory of Simple Bending 935 14.5.1. Relationship Between Bending Stress and Radius of Curvature 935 14.5.2. Neutral Axis 937 14.5.3. Relationship Between Moment of Resistance & Bending Stress 938 14.6. Selection Modulus 969 CHAPTER 15 FLITCHED OR COMPOSITE BEAMS985-1022 15.1. Introduction 986 15.2. Assumptions 986 CHAPTER 16 SHEAR STRESS IN BEAMS 1023-1082 16.1. Introduction 1024 16.2. Horizontal Shear Stress 1028 16.3. Horizontal Shear Stress Distribution Across Beam Section 1029 16.4. Vertical Shear Stress 1031 16.5. Shear Connectors in Beams 1066 Review Exercises 1083 UNIT -11 PRINCIPAL STRESSES AND STRAINS CHAPTER 17 PRINCIPAL PLANES AND PRINCIPAL STRESSES.1095-1179 17.1. Introduction 1096 17.2. Normal and Tangential Stress on Given Plane 1097 17.3. Resultant Stress on Plane Under Consideration 1099 17.4. Load Cases 1100 17.5. Graphical Solution by Mohr's Circle 1128 17.6. Mohr circle Method (when no shear stress) 1129 17.7. Mohr circle Method (when there is shear force) 1142 17.8. Principal Stress and Principal Planes 1156 17.9. Maximum Tangential or Shear Stress 1159 17.10. Principal Stress in Various Stress Conditions 1160 Review Exercises 1180