THE ELEMENTS OF GRAPHIC STATICS
Unit I FUNDAMENTAL CONCEPTS 1 Force System and Equilibrium 3 11 Introduction 3 12 Basic Concepts 4 13 Quantities 6 14 Reference Frame of Axes 6 15 Principles of Mechanics 7 16 Forces 8 17 System of Forces 8 18 Resultant of a Force System 10 19 Law of Triangle of Forces 26 110 Force Polygon 26 Objective Type Questions 27 Exercise 28 2 Engineering Properties of Materials 31 21 Introduction 31 22 Classification of Properties 32 23 Important Mechanical Properties of Metals 32 24 Summary 41 Exercise 43 3 Concepts in Structural Analysis, Loads, Supports and Free Body Diagrams (FBD) 45 30 Introduction 45 31 Type of Structures 45 32 Loads on Structure 47 Contents 33 Structural Supports 49 34 Classification of Structures 51 35 Internal Resistance, Stress and Deformation 53 36 Summary 62 Exercise 63 Unit II AXIAL FORCE STRUCTURES 4 Internal Forces in Axial Force Structures: Plane Trusses 67 41 Introduction 67 42 Axial Forces in Single Bar Structure 69 43 Determining Internal Forces in Members of Trussed Structures 72 44 Graphical Method 84 45 Determination of Internal Forces in Truss Members 89 46 Summary 110 Exercise 113 5 Axial Force Members, Stress, Strain and Elasticity 125 51 Introduction 125 52 Stress 126 53 Elasticity 129 54 Linear and Lateral Strains—Poisson’s Ratio 130 55 Tensile Test on Ductile Materials 134 56 Working Stress and Factor of Safety 136 57 Variable X-section Bars under Axial Forces 140 58 Axial Stress and Strain due to Self Weight 143 59 Axial Force Elements of Composite Materials 146 510 Stresses on Inclined Planes due to Axial Stress 150 511 Complementary Shear at any Point in Stressed Body 151 512 Stresses on Inclined Planes due to Simple Shear Stresses 152 513 Relations between Various Elastic Modulii (E, G and K) 153 514 Temperature Stresses in Single Material Axial Force Members 159 515 Temperature Stresses in Composite Material Axial Force Members 160 516 Temperature Stress in the Circular Rings 162 517 Summary 165 Exercise 168 Unit III BENDING STRUCTURES (BEAMS) 6 Shear Force, Axial Force and Bending Moments in Bending Structures 177 61 Introduction 178 62 Bending 178 63 Support or Base of Members 179 64 Type of Beams 180 65 Type of Loads 184 66 External Equilibrium of Beams and Support Reactions 186 67 Support Reactions 187 68 Shear Force and Bending Moments 190 69 Axial Force in Beam 192 610 Sign Conventions of SF and BM 193 611 Shear Force, Bending Moment and Axial Force Diagrams 194 612 Relationship of Loading, Shear Force and Bending Moment 221 613 Graphical Method for SF and BMD 224 614 Summary 226 Exercise 231 7 Centroid, Area and Moment of Inertia in Bending Structures 241 71 Introduction 241 72 Areas and Centroids of Plane Sections 243 73 Moment of Inertia (Second Moment of Area) 244 74 Theorems of Moment of Inertia 245 75 Areas, Centroids and Moment of Inertia of Regular Sections 247 76 Summary 262 Exercise 265 8 Bending Stresses in Bending Structures (Beams) 270 80 Entry Behaviour Test 272 81 Introduction 275 82 Assumptions in Theory of Simple Bending 277 83 Theory of Simple Bending 279 84 Position of Neutral Axis 283 85 Evaluation and Explanation of Moment of Resistance of Flexural Section 284 86 Units of Quantities in Bending Equation 285 87 Application of Bending Equation in Solution of Problems of Bending Stress Analysis and Simple Design 287 88 Beams of Composite Sections (Flitched Beam Sections) 297 89 Summary 304 Exercise 305 9 Shear Stresses in Bending Structures (Beams) 313 91 Introduction 313 92 Horizontal and Vertical Shear Stresses 313 93 Shear Stress Variation Across Depth 314 94 Shear Stress Distribution Across Different Shape of Sections 316 95 Summary 329 Exercise 331 Unit IV BENDING STRUCTURES: DEFORMATIONS 10 Slope and Deflections 336 101 Introduction 336 102 The Equation of Deflection Curve 337 103 Double Integration Method for Slope and Deflection in Beams 341 104 Macaulay’s Method (Discontinuity Function) 357 105 The Area-Moment Method 388 106 Conjugate Beam Method (Mohr’s Theorem III and IV) 404 107 Deflections by Strain Energy Method 423 108 Deflection by Fictitious Load Method (Castigliano’s First Theorem) 435 109 Deflection due to Shear 450 1010 Deflection due to Impact Loading 454 1011 Summary 464 Exercise 469 Unit V TORSION IN SHAFTS 11 Torsional Elements (Shafts) 479 111 Introduction 479 112 Torsion Equation 480 113 Power Transmission and Design of Shafts 486 114 Shafts of Variable and Stepped Sections 495 115 Flanged Couplings and Keys 498 116 Combined Bending and Torsion 503 117 Summary 508 Exercise 509 Unit VI LONG AND SHORT COLUMNS: LOAD CAPACITY ANALYSIS 12 Long and Short Columns in Structures 515 121 Introduction 515 122 Definitions 516 123 End Conditions 517 124 Euler’s Buckling Load 518 125 Limitations of Euler’s Formula 521 126 Rankine’s Hypothesis 526 127 Eccentric Loading on Long Columns and Secant Formula 533 128 Emperical Formula for Critical Loads on Column 541 129 Summary 549 Exercise 551 Unit VII COMBINED STRESSES AND PRINCIPAL STRESSES 13 Principal Planes and Principal Stresses 561 131 Introduction 561 132 Two Dimensional Plane Stress System 562 133 Sign Convention 563 134 Stresses along Inclined Plane 563 135 Two Dimensional Principal Stresses and Planes 567 136 Mohr Circle (Graphical) Approach 570 136 Summary 585 Exercise 586