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| موضوع: كتاب A Textbook of Strength of Materials - Mechanics of Solids الخميس 27 أكتوبر 2022, 1:46 am | |
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أخواني في الله أحضرت لكم كتاب A Textbook of Strength of Materials - Mechanics of Solids (In S.I. Units) For Degree, U.P.S.C. (Eng g. Services), GATE and Other Competitive Examinations By Dr. R.K. BANSAL B.Sc. Engg. (Mech.), M. Tech., Hons. (I.I.T., Delhi) Ph.D., M.I.E. (India) Formerly Professor and Head Department of Mechanical Engineering, (University of Delhi) Delhi College of Engineering, Delhi
و المحتوى كما يلي :
CONTENTS Chapters Pages Chapter 1. Simple Stresses and Strains 1—58 1.1. Introduction 1 1.2. Stress 1 1.3. Strain 2 1.4. Types of Stresses 2 1.5. Elasticity and Elastic Limit 5 1.6. Hooke’s Law and Elastic Modulii 6 1.7. Modulus of Elasticity (or Young’s Modulus) 6 1.8. Factor of Safety 6 1.9. Constitutive Relationship between Stress and Strain 6 1.10. Analysis of Bars of Varying Sections 14 1.11. Analysis of Uniformly Tapering Circular Rod 24 1.12. Analysis of Uniformly Tapering Rectangular Bar 27 1.13. Analysis of Bars of Composite Sections 30 1.14. Thermal Stresses 42 1.15. Thermal Stresses in Composite Bars 44 1.16. Elongation of a Bar Due to its Own Weight 50 1.17. Analysis of Bar of Uniform Strength 51 Highlights 53 Exercise 54 Chapter 2. Elastic Constants 59—84 2.1. Introduction 59 2.2. Longitudinal Strain 59 2.3. Lateral Strain 59 2.4. Poisson’s Ratio 60 2.5. Volumetric Strain 62 2.6. Volumetric Strain of a Cylindrical Rod 68 2.7. Bulk Modulus 70 2.8. Expression for Young’s Modulus in Terms of Bulk Modulus 70 2.9. Principle of Complementary Shear Stresses 73 2.10. Stresses on Inclined Sections when the Element is Subjected to Simple Shear Stresses 74 2.11. Diagonal Stresses Produced by Simple Shear on a Square Block 76 2.12. Direct (Tensile and Compressive) Strains of the Diagonals 77 2.13. Relationship between Modulus of Elasticity and Modulus of Rigidity 78 Highlights 81 Exercise 82 Chapter 3. Principal Stresses and Strains 85—142 3.1. Introduction 85 3.2. Principal Planes and Principal Stresses 85 3.3. Methods of Determining Stresses on Oblique Section 85 3.4. Analytical Method for Determining Stresses on Oblique Section 85x Chapters Pages 3.5. Mohr’s Circle 123 3.6. Strain on an Oblique Plane 133 3.7. Mohr’s Strain Circle 137 Highlights 137 Exercise 139 Chapter 4. Strain Energy and Impact Loading 143—170 4.1. Introduction 143 4.2. Some Definitions 143 4.3. Expression for Strain Energy Stored in a Body when the Load is Applied Gradually 143 4.4. Expression for Strain Energy Stored in a Body when the Load is Applied Suddenly 145 4.5. Expression for Strain Energy Stored in a Body when the Load is Applied with Impact 152 4.6. Expression for Strain Energy Stored in a Body due to Shear Stress 165 Highlights 166 Exercise 167 Chapter 5. Centre of Gravity and Moment of Inertia 171—236 5.1. Centre of Gravity 171 5.2. Centroid 171 5.3. Centroid or Centre of Gravity of Simple Plane Figures 171 5.4. Centroid (or Centre of Gravity) of Areas of Plane Figures by the Method of Moments 171 5.5. Important Points 173 5.6. Area Moment of Inertia 195 5.7. Radius of Gyration 196 5.8. Theorem of the Perpendicular Axis 196 5.9. Theorem of Parallel Axis 197 5.10. Determination of Area Moment of Inertia 198 5.11. Mass Moment of Inertia 212 5.12. Determination of Mass Moment of Inertia 213 5.13. Product of Inertia 219 5.14. Principal Axes 220 5.15. Principal Moments of Inertia 221 Highlights 229 Exercise 230 Chapter 6. Shear Force and Bending Moment 237—294 6.1. Introduction 237 6.2. Shear Force and Bending Moment Diagrams 237 6.3. Types of Beams 237 6.4. Types of Load 238 6.5. Sign Conventions for Shear Force and Bending Moment 239 6.6. Important Points for Drawing Shear Force and Bending Moment Diagrams 240 6.7. Shear Force and Bending Moment Diagrams for a Cantilever with a Point Load at the Free End 241 6.8. Shear Force and Bending Moment Diagrams for a Cantilever with a Uniformly Distributed Load 244xi 6.9. Shear Force and Bending Moment Diagrams for a Cantilever Carrying a Gradually Varying Load 252 6.10. Shear Force and Bending Moment Diagrams for a Simply Supported Beam with a Point Load at Mid-point 254 6.11. Shear Force and Bending Moment Diagrams for a Simply Supported Beam with an Eccentric Point Load 256 6.12. Shear Force and Bending Moment Diagrams for a Simply Supported Beam Carrying a Uniformly Distributed Load 258 6.13. Shear Force and Bending Moment Diagrams for a Simply Supported Beam Carrying a Uniformly Varying Load from Zero at Each End to w Per Unit Length at the Centre 266 6.14. Shear Force and B.M. Diagrams for a Simply Supported Beam Carrying a Uniformly Varying Load from Zero at one End to w Per Unit Length at the Other End 268 6.15. Shear Force and Bending Moment Diagrams for Over-hanging Beams 272 6.16. S. F. and B. M. Diagrams for Beams Carrying Inclined Load 281 6.17. Shear Force and Bending Moment Diagrams for Beams Subjected to Couples 286 6.18. Relations between Load, Shear Force and Bending Moment 289 Highlights 290 Exercise 291 Chapter 7. Bending Stresses in Beams 295—344 7.1. Introduction 295 7.2. Pure Bending or Simple Bending 295 7.3. Theory of Simple Bending with Assumptions Made 296 7.4. Expression for Bending Stress 297 7.5. Neutral Axis and Moment of Resistance 298 7.6. Bending Stresses in Symmetrical Sections 300 7.7. Section Modulus 303 7.8. Section Modulus for Various Shapes or Beam Sections 303 7.9. Bending Stress in Unsymmetrical Sections 315 7.10. Strength of a Section 323 7.11. Composite Beams (Flitched Beams) 330 Highlights 340 Exercise 341 Chapter 8. Shear Stresses in Beams 345—380 8.1. Introduction 345 8.2. Shear Stress at a Section 345 8.3. Shear Stress Distribution for Different Sections 351 Highlights 376 Exercise 377 Chapter 9. Direct and Bending Stresses 381—412 9.1. Introduction 381 9.2. Combined Bending and Direct Stresses 381 9.3. Resultant Stress when a Column of Rectangular Section is Subjected to an Eccentric Load 382 9.4. Resultant Stress when a Column of Rectangular Section is Subjected to a Load which is Eccentric to both Axes 390 Chapters Pagesxii 9.5. Resultant Stress for Unsymmetrical Columns with Eccentric Loading 397 9.6. Middle Third Rule for Rectangular Sections (i.e., Kernel of Section) 402 9.7. Middle Quarter Rule for Circular Sections (i.e., Kernel of Section) 404 9.8. Kernel of Hollow Circular Section (or Value of Eccentricity for Hollow Circular Section) 405 9.9. Kernel of Hollow Rectangular Section (or Value of Eccentricity for Hollow Rectangular Section) 406 Highlights 409 Exercise 410 Chapter 10. Dams and Retaining Walls 413—468 10.1. Introduction 413 10.2. Types of Dams 413 10.3. Rectangular Dams 413 10.4. Stresses Across the Section of a Rectangular Dam 417 10.5. Trapezoidal Dam having Water Face Inclined 428 10.6. Stability of a Dam 434 10.7. Retaining Walls 447 10.8. Rankine’s Theory of Earth Pressure 449 10.9. Surcharged Retaining Wall 459 10.10. Chimneys 462 Highlights 464 Exercise 466 Chapter 11. Analysis of Perfect Frames 469—514 11.1. Introduction 469 11.2. Types of Frames 469 11.3. Assumptions Made in Finding Out the Forces in a Frame 470 11.4. Reactions of Supports of a Frame 470 11.5. Analysis of a Frame 471 Highlights 508 Exercise 508 Chapter 12. Deflection of Beams 515—558 12.1. Introduction 515 12.2. Deflection and Slope of a Beam Subjected to Uniform Bending Moment 515 12.3. Relation between Slope, Deflection and Radius of Curvature 517 12.4. Deflection of a Simply Supported Beam Carrying a Point Load at the Centre 519 12.5. Deflection of a Simply Supported Beam with an Eccentric Point Load 523 12.6. Deflection of a Simply Supported Beam with a Uniformly Distributed Load 530 12.7. Macaulay’s Method 535 12.8. Moment Area Method 550 12.9. Mohr’s Theorems 552 12.10. Slope and Deflection of a Simply Supported Beam Carrying a Point Load at the Centre by Mohr’s Theorem 553 12.11. Slope and Deflection of a Simply Supported Beam Carrying a Uniformly Distributed Load by Mohr’s Theorem 554 Highlights 555 Exercise 556 Chapters Pagesxiii Chapter 13. Deflection of Cantilevers 559—582 13.1. Introduction 559 13.2. Deflection of a Cantilever with a Point Load at the Free End by Double Integration Method 559 13.3. Deflection of a Cantilever with a Point Load at a Distance ‘a’ from the Fixed End 561 13.4. Deflection of a Cantilever with a Uniformly Distributed Load 562 13.5. Deflection of a Cantilever with a Uniformly Distributed Load for a Distance ‘a’ from the Fixed End 566 13.6. Deflection of a Cantilever with a Uniformly Distributed Load for a Distance ‘a’ from the Free End 566 13.7. Deflection of a Cantilever with a Gradually Varying Load 572 13.8. Deflection and Slope of a Cantilever by Moment Area Method 576 Highlights 580 Exercise 581 Chapter 14. Conjugate Beam Method, Propped Cantilevers and Beams 583—618 14.1. Introduction 583 14.2. Conjugate Beam Method 583 14.3. Deflection and Slope of a Simply Supported Beam with a Point Load at the Centre 583 14.4. Simply Supported Beam Carrying an Eccentric Point Load 585 14.5. Relation between Actual Beam and Conjugate Beam 597 14.6. Deflection and Slope of a Cantilever with a Point Load at the Free End 597 14.7. Propped Cantilevers and Beams 602 14.8. S.F. and B.M. Diagrams for a Propped Cantilever Carrying a Point Load at the Centre and Propped at the Free End 603 14.9. S.F. and B.M. Diagrams for a Propped Cantilever Carrying a Uniformly Distributed Load and Propped at the Free End 604 14.10. S.F. and B.M. Diagrams for a Simply Supported Beam with a Uniformly Distributed Load and Propped at the Centre 610 14.11. Yielding of a Prop 614 Highlights 615 Exercise 616 Chapter 15. Fixed and Continuous Beams 619—678 15.1. Introduction 619 15.2. Bending Moment Diagram for Fixed Beams 620 15.3. Slope and Deflection for a Fixed Beam Carrying a Point Load at the Centre 624 15.4. Slope and Deflection for a Fixed Beam Carrying an Eccentric Point Load 628 15.5. Slope and Deflection for a Fixed Beam Carrying a Uniformly Distributed Load Over the Entire Length 644 15.6. Fixed End Moments of Fixed Beam Due to Sinking of a Support 654 15.7. Advantages of Fixed Beams 657 15.8. Continuous Beams 658 15.9. Bending Moment Diagram for Continuous Beams 658 Highlights 675 Exercise 676 Chapters Pagesxiv Chapter 16. Torsion of Shafts and Springs 679—746 16.1. Introduction 679 16.2. Derivation of Shear Stress Produced in a Circular Shaft Subjected to Torsion 679 16.3. Maximum Torque Transmitted by a Circular Solid Shaft 681 16.4. Torque Transmitted by a Hollow Circular Shaft 683 16.5. Power Transmitted by Shafts 684 16.6. Expression for Torque in Terms of Polar Moment of Inertia 694 16.7. Polar Modulus 695 16.8. Strength of a Shaft and Torsional Rigidity 695 16.9. Flanged Coupling 702 16.10. Strength of a Shaft of Varying Sections 705 16.11. Composite Shaft 713 16.12. Combined Bending and Torsion 717 16.13. Expression for Strain Energy Stored in a Body Due to Torsion 720 16.14. Springs 728 Highlights 741 Exercise 743 Chapter 17. Thin Cylinders and Spheres 747—788 17.1. Introduction 747 17.2. Thin Cylindrical Vessel Subjected to Internal Pressure 747 17.3. Stresses in a Thin Cylindrical Vessel Subjected to Internal Pressure 748 17.4. Expression for Circumferential Stress (or Hoop Stress) 748 17.5. Expression for Longitudinal Stress 749 17.6. Efficiency of a Joint 753 17.7. Effect of Internal Pressure on the Dimensions of a Thin Cylindrical Shell 757 17.8. A Thin Cylindrical Vessel Subjected to Internal Fluid Pressure and a Torque 768 17.9. Wire Winding of Thin Cylinders 772 17.10. Thin Spherical Shells 777 17.11. Change in Dimensions of a Thin Spherical Shell Due to an Internal Pressure 778 17.12. Rotational Stresses in Thin Cylinders 780 Highlights 783 Exercise 784 Chapter 18. Thick Cylinders and Spheres 789—816 18.1. Introduction 789 18.2. Stresses in a Thick Cylindrical Shell 789 18.3. Stresses in Compound Thick Cylinders 797 18.4. Initial Difference in Radii at the Junction of a Compound Cylinder for Shrinkage 802 18.5. Thick Spherical Shells 808 Highlights 813 Exercise 814 Chapter 19. Columns and Struts 817—880 19.1. Introduction 817 19.2. Failure of a Column 817 19.3. Assumptions Made in the Euler’s Column Theory 818 Chapters Pagesxv 19.4. End Conditions for Long Columns 818 19.5. Expression for Crippling Load When Both the Ends of the Column are Hinged 819 19.6. Expression for Crippling Load When One End of the Column is Fixed and the Other End is Free 820 19.7. Expression for Crippling Load When Both the Ends of the Column are Fixed 822 19.8. Expression for Crippling Load When One End of the Column is Fixed and the Other End is Hinged (or Pinned) 825 19.9. Effective Length (or Equivalent Length) of a Column 827 19.10. Limitation of Euler’s Formula 829 19.11. Rankine’s Formula 844 19.12. Straight Line Formula 856 19.13. Johnson’s Parabolic Formula 856 19.14. Factor of Safety 857 19.15. Formula by Indian Standard Code (I.S. Code) for Mild Steel 857 19.16. Columns with Eccentric Load 858 19.17. Columns with Initial Curvature 862 19.18. Strut with Lateral Load (or Beam Columns) 867 Highlights 875 Exercise 877 Chapter 20. Riveted Joints 881—910 20.1. Introduction 881 20.2. Types of Riveted Joints 881 20.3. Chain Riveted Joint 882 20.4. Zig-Zag Riveted Joint 882 20.5. Diamond Riveted Joint 882 20.6. Failure of a Riveted Joint 886 20.7. Strength of a Riveted Joint 889 20.8. Efficiency of a Riveted Joint 890 20.9. Design of a Riveted Joint 902 Highlights 905 Exercise 907 Chapter 21. Welded Joints 911—930 21.1. Introduction 911 21.2. Advantages and Disadvantages of Welded Connections 911 21.3. Types of Welded Joints 912 21.4. Analysis of a Compound Weld 916 21.5. Analysis of Unsymmetrical Welded Sections which are Loaded Axially 918 Highlights 925 Exercise 927 Chapter 22. Rotating Discs and Cylinders 931—968 22.1. Introduction 931 22.2. Expression for Stresses in a Rotating Thin Disc 931 22.3. Disc of Uniform Strength 948 22.4. Long Cylinders 952 Highlights 965 Exercise 967 Chapters Pagesxvi Chapters Pages Chapter 23. Bending of Curved Bars 969—1016 23.1. Introduction 969 23.2. Assumptions Made in the Derivation of Stresses in a Curved Bar 969 23.3. Expression for Stresses in a Curved Bar 969 23.4. Determination of Factor ‘h2’ for Various Sections 976 23.5. Resultant Stress in a Curved Bar Subjected to Direct Stresses and Bending Stresses 989 23.6. Resultant Stress in a Hook 990 23.7. Stresses in Circular Ring 999 23.8. Stresses in a Chain Link 1005 Highlights 1012 Exercise 1014 Chapter 24. Theories of Failure 1017—1050 24.1. Introduction 1017 24.2. Maximum Principal Stress Theory 1017 24.3. Maximum Principal Strain Theory 1018 24.4. Maximum Shear Stress Theory 1022 24.5. Maximum Strain Energy Theory 1026 24.6. Maximum Shear Strain Energy Theory 1030 24.7. Graphical Representation of Theories for Two Dimensional Stress System 1032 24.8. Important Points from Theories of Failures used in Design 1036 24.9. Energy of Distortion (or Shear Strain Energy) 1045 Highlights 1048 Exercise 1048 Chapter 25. Unsymmetrical Bending and Shear Centre 1051—1090 25.1. Introduction 1051 25.2. Properties of Beam Cross-section 1051 25.3. Stress in Unsymmetrical Bending 1053 25.4. Deflection of Beams in Unsymmetrical Bending 1055 25.5. Shear Centre 1073 25.6. Determination of Shear Centre for Channel Section 1073 25.7. Determination of Shear Centre for I-Section 1080 Highlights 1088 Exercise 1089 Chapter 26. Objective Type Questions 1091—1142 26.1. Objective Type Questions Generally Asked in Competitive Examinations 1091 26.2. Answers of Objective Type Questions 1118 26.3. Objective Type Questions from Competitive Examinations 1119 26.4. Answers with Explanations 1127 Subject Index 1143 SUBJECT INDEX 1143 A Analysis of bars of varying sections, 14 – of composite sections, 30 Analysis of a compound weld, 916 Area moment method, 550 Assumption made in the theory of simple bending 296 B Bar of uniform strength, 51 – composite sections, 30 – varying sections, 14 Beams, continuous, 658 – fixed, 619 – deflection of beams, 515 – propped, 609 – columns, 867 Bending, 291 – plane, 296 – moment, 237 – moment and shear force, 237 – stresses in beams, 295 – of curved bars, 969 Bulk modulus, 70 Buckling load, 818 Butt joint, 881 – weld 912 C Cantilever, 237 – propped, 602 – truss, 476 Centre of gravity, 171 Circumferential stress, 748 Centroid, 171 Chain riveting, 882 Chimneys, 462 – wind pressure, 462 Clapeyron’s equation, 659 Columns and struts, 817 – long, 817 – beams, 868 – with eccentric load, 858 – with initial curvature, 862 Combined direct and bending, 381 Composite shaft, 713 Composite sections, 30 Combined bending and torsion, 717 Complementary shear stresses, 73 Compressive stress, 3 – strain, 3 Conjugate beam method, 583 Continuous beams, 658 Coupling, 702 Crippling load, 818 Critical load, 818 Curved bars, 969 – Rectangular, 977 – Triangular, 978 – Circular, 981 – Trapezoidal, 980 Cylinders, thin, 747 – thick, 786 D Dams, 413 Deflection of beams, 515 – in unsymmetrical bending, 1055 – of cantilever, 559 Thin cylindrical shell, 784 Riveted joint, 892 Diamond riveting, 882 Direct and bending stress combined, 381 Disc of uniform strength, 948 E Earth pressure, 449 Eccentric loading, 397 Elasticity, 5 Elastic constants, 59 Elastic limit, 5 Elastic modulii, 6 Efficiency of a joint, 753, 890 Energy of distortion, 1033 Effective length, 827 Euler’s theory, 818 – limitations of, 829 F Factor of safety, 6, 857 Failure of a column, 817 Failure of riveted joints, 886 SUBJECT INDEX Fixed beams, 619 Formula – Johnson’s, 856 – I.S.Code, 857 – straight line, 856 Frames, 469 Flanged coupling, 702 G Graphical method, 501 – principal stresses, 85 Guest’s theory, 1022 Gyration, radius, 196 H Haigh’s theory, 1026 Helical spring, 728 Hooke’s Law, 6 Hoop stress, 748 I Impact loading, 143 – load, 152 Inclined loads, 281 I-section, 359 J Johnson’s formula, 856 Joints, 881 – riveted, 881 – welded, 911 K Kernel, 408 – of hollow circular section, 408 – of hollow rectangular section, 408 L Lap joint, 881 – weld, 911 Lateral strain, 59 Leaf springs, 728 Long columns, 817 Longitudinal, strain, 59 – stress, 742 M Macaulay’s method, 535 Maximum principal stress theory, 1017STRENGTH OF MATERIALS 1144 – strain theory, 1018 – shear stress theory, 1022 – strain energy theory, 1026 – shear strain energy theory, 1030 Middle third rule, 402 Middle quarter rule, 404 Mises-Henky theory, 1030 Method of joints, 471 – sections, 492 Modulus, bulk, 70 – of elasticity, 6 – of rigidity, 6 Mohr’s circle, 123 Mohr’s strain circle, 137 Mohr’s theorem, 552 Moment area method, 550 Moment of inertia, 195 – resistances, 298 N Neutral axis, 297 – layer, 296 O Oblique, 85 Overhanging beams, 237 P Pitch of rivets, 902 Poisson’s ratio, 60 Polar moment of inertia, 694 Polar Modulus, 695 Power transmitted by shafts, 684 Principal planes, 85 – Strain, 85 – Stress, 85 Principle of complementary stresses, 73 Proof resilience, 143 Propped cantilevers and beams, 583 R Rankine’s formula, 844 Rankine theory, 449 Relationship between modulus of elasticity, 78 – S.F. and B.M. 286 Resilience, 143 – proof, 143 Resistance of moment, 299 Riveted joints, 881 – failure, 886 – strength, 889 – efficiency, 890 – design, 902 Rotational stress, 780 – in a thin cylinder, 780 – in a thin disc, 931 S Safety factor, 6 Simple bending, 295 Section modulus, 303 Shafts, torsion of, 679 Shafts, composite, 713 Shear centre, 1073 Shear force, 241 – for cantilevers, 241 – for a simply supported beam, 254 Shear in strain energy, 1033 Shear modulus, 6 Spherical shells, 771 Springs, 728 – leaf, 728 – helical, 728 Straight line formula, 856 Strain, 2 – types of, 2 – compressive, 2, 3 – shear, 2 – tensile, 2 Strain energy, 143 Stress, 1, 2 – in a curved bar, 969 – in unsymmetrical bending, 1053 – compressive, 3 – shear, 4 – principal, 85 – tensile, 2 – thermal, 42 – types of, 2 Strength of a shaft, 695 – riveted joint, 889, 892 Struts, 867 – with lateral load, 867 T Thermal stresses, 42 Tensile, 2 – strain, 2 – stress, 2 Thick cylinder, 789 Thick spherical shells, 808 Thin cylinder, 747 – spherical shells, 777 Theorem of – parallel axis, 197 – perpendicular axis, 196 Theories of failure, 1036 Theory of – maximum principal stress,1017 – maximum principal strain,1018 – maximum shear stress, 1022 – maximum strain energy, 1026 – maximum shear strain energy, 1036 Torsion of shafts, 679 Torsional rigidity, 695 Types of riveted joints, 881 – welded joints, 911 – beams, 237 – load, 237 U Uniform strength, 51 V Value of h2 for curved – rectangular bar, 977 – triangular bar, 978 – circular bar, 981 – trapezoidal bar, 980 Volumetric strain, 62 V-butt joint, 912 W Walls retaining, 447 Welded joints, 911 – butt weld joint, 912 – fillet weld joint, 912 – compound weld joint, 916 Winkler-Bach Formula, 964 Wind pressure on chimneys, 462 Y Young’s modulus, 6, 59 Z Zig-Zag riveted joint, 882
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