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أخواني في الله أحضرت لكم كتاب Strength of Materials [For Engineering Degree, Diploma and A.M.I E. Students] By S. Ramamrutham B.E., (Civilf M.l.C.E. Principal, Modern College of Engineering, New Delhi Author of Design of Reinforced Concrete Structures, Design of Steel Structutes, Theory of Structures, Applied Mechanics etc.
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CONTENTS Chapter * Pages 1. Simple Stresses and Strains * Introduction - Definitions, stress, strain, tensile and compres¬ sive stresses - Sheaf stress - Plastic limit - Hooke’s law poisson’s ratio - Modulus of Elasticity - Modulus of Rigidity, Bulk Modulus - Bars of varying section - Extension of a tapering rod - Composite section -modular ratio- Bar of uniform strength - Equivalent area of composite sections - Temjierature stresses - Hoop stress-Stresses on oblique sections - State of simple shear - Relation between the Elastic constants - Volumetric Strain - Rectangular block subject to normal stresses - Diagonal tensile and diagonal compressive stresses - Solved problems I to 71 - Problems for exercise. 1 - 100 2. Strain Energy - Impact Leading Strain Energy - Elastic, plastic and rigid members - Stresses due to different types of axial loading - Gradually applied loads - Suddenly applied load) - Impact loads - Solved pro¬ blems 72 to 84 - Problems for exercise. 101 - 118 3- Centre of Gravity and Moment of Inertia Centre of Gravity - Definition - Lamina - Moment of an area - Centroid of a uniform lamina - Centroids of laminae of various shapes - Triangle, circle, semicircle, trapeziumBuilt-in sections - Analytical and graphical methods - Moment of Inertia of a lamina - Definition - Parallel axes theoremPerpendicular axes theorem - Moment of Inertia of laminae of different shapes- Rectangalar, ciicular, triangular and com¬ posite sections - Solved problems 85 to 104 - Problems for exercise. 119 - 157 4. Shear Forces and Bending Moments Definitions -Cantilevers, simply supported beam, fixed beam, continuous beams -Conception of Shear Force and Bending Moment - Sign conventions - shear force and Bending Mo¬ ment diagrams for cantilevers, beams supported at ends. Beams with overhangs - Point of contraffexure-Member sub¬ jected to couples - Members subjected to Oblique loading - Miscellaneous types of members and corresponding S.F. and B.M. diagrams - Inter-relation between S F. and B. M^ diagrams - To obtain the B.M. diagrams from S.F. dia¬ gram-Solved problems 105 to 130 -Problems for exercise. 158-227 5. Stresses in Beams Definition - Pure or simple bending - Theory of simple bend¬ ing-Netural layer - Neutral axis - Bending Stress distribu¬ tion-moment of resistance - Assumptions in the theory ofan Chapter Pages simple binding - Practical application of bending equation Section modulus - Section moduli for different shapesRectangular, triangular, circular, I-section, T-section - Normal force on a partial area of a beam section - Moment of resis¬ tance of a partial area of a btam section -Flitched beams - Equivalent section - Beams of uniform strength - Shear stress distribution on a beam section - Shear stress distribution on rectangular, circular, triangular, 1 and T sections - Shear stresses in bolts connecting components in laminated beams. Proportion of B M and S F. resisted by flange and web of anI section - Shrar centre - Solved problems 131 to 199 - Problems for exercise. 228 - 337 6. Direct and Bending Stresses Stress distribution of the section of an eccentrically loaded rectangular column. The middle third rule - Core or kernel of a section - Circular section - Hollow section - Structural section - Walls and pillars - Solved Problems 200 to 223 - Problems for exercise. 338 - 370 7. Masonary Dams Forces acting on a dam - Stress distribution on the base of a dam, Stability of a dam - Minimum bottom width of a dam section. Solved Problems 224 to 228. 371 - 388 8. Deflection of beams Member bending into a circular are - slope, deflection and ladius of curvature - Derivation of formulae for slope and deflection - Cantilever - Propped cantilevers- Beams - Macau¬ lay’s Method - Beams subjected to couples - Moment area method - Mohr’s theorems - Relations between maximum bending stress and maximum deflection - Beams of varying . section - Strain energy stored due to bending - Law of reci¬ procal deflections -Bette's law - The first theorem of Castigliano - Impact loading on beams - Laminated SpringsConjugate beam method - Solved problems 229 to 312 Pro^ blems for exercise. 389 - 527 9. Fixed and Continuous Beams Fixed beam -Relation between the free B.M. diagram and the fixed B.M. diagram-slope and deflection - Effect of sinking of supports - Fixed beam subjected to couple - Degree of fixing - Advantages and disadvantages of fixing beams - Continuous beam - Clapyron’s theorm of three moments - Solved problems 3)3 to 324 - Problems for exercise. 528 - 581 10. Torsion of Shafts Pure Torsion - Theory of Pure Torsion - Torsional mement of resistance. Assumptions in the theory of pure Torsion - Polar modulus - H.P. transmitted by a shaft - Torsional Rigidity - Stepped shafts - Composite shafts - Keys - Couplings - Shear and Torsional resilience - Shaftsof non-circular section - Close(fit) coiled helical springs - Torsion of a tapering rod. Solved Problems 325 to 361 - Problems for exercise. ’582 - 632 11. Principal stresses and strains Normal stresses - Tangential or shear streses - Principal stresses - Principal planes - Graphical and analytical methods - Ellipse of stress - Determination of principal stresses and strains - Obliquity - Mohr’s circle of stress - Combined bending and Torsion - Strain energy in terms of principal stresses - Equivalent bending moment and equivalent torque - Principal strains - Criterion for failure - Ellipse of strain - Solved prob¬ lems 362 to 388. Problems for exercise. 633 - 682 12- Thin Cylinders and Spheres Thin cylinders - circumferential ond longitudinal Stresses - Riveted cylinderical boilers - Wire bound pipes. Thin spherical shells - Biaxial stresses in doubly curved walls of pressure vessels - Stresses in a conical tank. Solved problems 342 to 349. Problems for exercise. 683 - 705 13. Thick cylinders and Spheres Thick cylinders -Derivation of formulae - Lamme’s equations - Hoop stresses and radial pressure distribution - compound cylinders - Thick spherical Shells- Solved problems 350 to 413 - Problems for exercise. 706 - 726 14. Columns and Struts Introduction - Axially loaded compression members - Crush¬ ing load - Buckling or critical load or crippling load - Euler’s theory of long columns - Different end conditions - Effective length of colums - Assumptions made in Euler’s theoryLimitations of Euler's formula - Empirical formulae - Rankine’s formula - Straight line formula - Johnson's para¬ bolic formula - Formula given by the I S. code - Column •objected to eccentric loading - Euler’s method - Rankine’s method - Prof Perry’s formula - Columns with initial curva¬ ture - Laterally loaded struts - Solved problems 413 to 429. Problems for exercise. 727 - 768 15. Riveted Joints Types of joints - Lap and butt joints - Failure of a riveted joint - Tearing strength, shearing strength, bearing strength - Efficiency of a joint - Riveted joints in structural steel work - Chain riveting and diamond riveting - Eccentric Riveted connections - Resistance of a rivet against translation and rotation. Solved problems 430 to 442. Problems for exercise. 769 - 798 16. Welded Connections The welding process - Advantages of welded connection - Disadvantages of welded connection - Types of weld - Mini¬ mum sizes of weld - Effective length - Minimum length - Fillet(iv) weld applied tp the edge of a plate-Angle between fusion faces - Throat thickness-Intermittent fillet welds - Lap joints - Fillet welds in slots or holes - End returns - Bending about a single fillet -Permissible stresses in welds - Combined stresses in welds -Eccentric welded connections, Solved problems 443 to- 462 799 - 830 17. Analysis of Framed Structures Perfect frame -Deficient frame - Redundant frame-Reactions at supports - Analysis of a truss - Method of joints-Method of section - Graphical method. Solved problems 463 to 489. 831-914 18. Simple Mechanical Properties of Metals Yield or flow of material - Tensile stress - Stress - Strain diagrams for Mild Steel Specimen - Limit of proportionality - Ultimate stress-Working stress - Factor of safety - Measure¬ ment of ductility -Unwin’s Method based on reduction of sectional area - Hardness - Scratch test - Indentation test - Brinnel’s method-Impact testing - Fatigue of metals - Endurance limit. Solved problems 449 to 491. 915 - 922 19. Elements of reinforced Concrete General principles of design - Assumptions - Singly reinforced beams-Netural axis -Lever arm - Moment of resistanceBalanced or economic or critical sections - Unbalanced sections - Under-reinforced and over-reinforced sections - Doubly reinforced beams-Shear in beams- Shear stresses - Diagonal tensile and diagonal compressive stresses in concrete-Stirrups-Diagonal reinforcement - Bond stresses - End anchora.e -Standard hook - Reinforcement-T and L beams-Axially Loaded Columns-Combined bending and direct stresses. Solved problems 492 to 520. Problems for exercises. 923 - 998 Appendix Useful tables. 999-1035 Index 1036 - 1038INDEX A Analysis of frames, 831 Analysis of dams. 371 Assumptionsin theory of bending, 228 Axis, neutral, 229, 230 ' B Balanced section, 928 Bar of composite section, 27 Bar of uniform stren th, 47 Bar of varying section, 11 Beams, 158 Beams-deflection, 389 Beams of uniform strength, 295 Beams of varying section, 469 Bearing value of rivets, 773 Bending, 228 Bending moment, >58, 160 Beltrami theory, 678 Bending stress, 228 Bet'e’s law, 484 Bond stress, 966, 967 Boom, 727 Bow’s notation, 891 Brinnel's method. 921 Buckling load, 72k Built-m-beams, 158, 528 Bulk m< dulus, 86 Butt-joint, 769 Butt weld, 801 C Cantilevers, 158 Cantilever-propped, 400 Carriage springs, 5<)0 Castigliano’s theorem, 485 Centre of gravity, 119 Centroid, t <9 Cham riveting, 787 Circum’erential stress, 72. 684 Clapeyron's theorem, 561 Clear span, 158 Close coiled springs, 620 Columns, 727 Combined stresses, 338 Complementary shear stress, 81 Composite sections, 27 Composite shafts, 610 Compound cylinders, 713 Compoon stresses and strains, 633 Compressive siress, 31 Compressive strain, 31 Cbmpound section,27 Conjugate beam method, 505 Continuous beam, 158, 528, 560 Continuous columns, 987 Contraflexure-point of, 186 Core of a section, 342 Couples, 203 Couplings, 616 Cover, 973 CripplingI ad, 728 Critical load, 728 Critical section, 928 Crushing load, 727 Crushing s'ress, 727 D Dams, 371 Deficient frame, 832 Deflection of beams, 381 Deformation, 1 Diagonal compres ion, 84 Diagonal tension, 84 Diamond riveting, 787 Direct stress, 338 Direct and bending stresses, 338 Direct bond, 967 Doubly curved walls, 701 Doubly reinforced beams, 949 Ductility, 917 E Eccentricity, 339 Eccentric riveted connection, 791 Eccentric welded connections, 815 Economic section, 928 , Effective length of column, 735 Effective length of weld, 802 Effective span. 158 Efficiency of joints, 774 Elastic instability, 728 Elasic limit, 6 Elastic material, 1, 102 Elastic modulus, 102 Elapse of strain, 679 Ellipse of stress, 642 Encastred beams, 528 End Anchorage, 969 End returns, 804 Endurance limit, 922 Energy, strain, 47, 101, 102 Equivalent ana, 38 1036INDEX 1037 Euler’s theory, 728 F Factor of safety, 916 Failure of a riveted joint, 770 Fatigue of metals, 922 Fillet weld, 800 Fixed beam, 158, 52* Fixed ei d moment, 528 Flexural rigidity, 586 Flitched beams, 278 1rained structures, 831 Freely supported beams, 158 French formula, 774 G German formula, 774 Gradually applied loads, 103 Graphical methods, 838 Graphic statics, 891 Guest theory, <>77 Gusset plate, 785 Gyration-radius of, 137 H Haigh's theory, 678 Hardness, 920 Helical springs 620 Hogging moment, 161 Homogeneity, 23.' Hook's law, 6 Hoop stress, 72, 684 I Impact loading, 101 Impact testing. 101, 105, 498, 921 I ‘ entation test, 921 Inertia-moment of, 136 1< lens ty of stress, 2 Isotropy, 233 Izod test, 921, 922 J Johnson’s parabolic formula, 749 Joints-riveted, 769 Joiots-weided. 799 K Kernel of a Section, 342 Keys, 616 L L-boams, 974 Lame's equatioa, 70* Laminated spriaM 900 Lap joint, 769. <04 Lateral strain, 74 Laterally loaded strata, 743 Leaf springs, *00 Lever arm, 927 Limit-elastic, 6 Load, I Loading-gradual, sudden, impact, 101 Local bond, 969 Long columns, 986 Longitudinal stress, 684 M Macaulay’s method, 423 Masonry dams, 371 Maxwell's law, 483 Mechanical properties of metals, 915 Membrane stresses 701 Meridional stress, 702 Method of joints, 838 Method of resolution, 838 Method of section, 838 864 Method of substitution, 903 Middle third rule, 341 Modular rati >, 27, 279,923 Modulus bulk, 86 Modulus of elasticity, 6 Modulus of rigidity, 6 Modulus ol section. 2M Mohr's Circle, 645 Mohr’s theorems, 459, 460 Moment area method, 459 Mou. nt of Inertia, 136, 928 MorneM of resistance, 231 N Neutral axis. 229, 230, 926 Neutral layer, 229 Neutral suifa^e, 229 Normal stresses, 83 O Oblique loading on beams, 210 Obliquity, 6 5 Over reinforced sectian, 951 P Parabolic formula, 749 Parallel axes the rem, 138 Perfect frame, 831 Perpendicular au« theorem, 137 P-rry's f. rmula, 758 PUUra, 364 Plastic member, 1, 102 Poet of contrafcxure, 186 Poiet of laflextion. 86 Pvkacw'a ami*, 741038 Polar modulus, ^84 Port, 727 . Principal planes, 633, 634 Principal strains, 613. 675 Principal stresses, 633, 634 Propp,d cantilevers, 400 Pure bending, 228 R Radius of curvature, 390 Radius of gyration, 137 Rankine’s formula, 740 Rankine’s theory, 677 Reinforced < oncrete, 923 Reciprocal deflection theorem, 482 Reinforcement, 970 Redundant frame, 833 Relation between elastic constants, Resistance, I, 101 Resistance-moment of, 231 Rigid material, ], 102 Rigidity modulus 6 Riveted boilers, 693 Riveted joints, 769 Roller support, 833 Safety-factor of, 916 Sagging moment, 160 Scratch test, 921 Second moment of area, 136 Section-composite, 27 Section-method of, 833, 864 Section modulus, 234 Shafts, 582 Shear centre, 330 Shear delormalion, 5, 6 Shear force, 158 Shear mo ulus, 6 Sheaf reinforcement, 944 Shear resistance, 618 Shear strain, 4 Shear stress, 4, 297, 954, 957 Shear stress distribution, Shear value of rivets, 773 Shells, 683 Simple bending. 228 Simple stresses and strains, 1 Simply supported beams, 158 Singly reinforced beams, 924 Sieucer* ess ratio, 736 Slope, 390 Span, 158 Spherical shells. 698 Spnngs-coiled, 620 Spr ngs-lamrnated, 500 Stability of dams, 373 Stannard book, 969 Stare of simple shear, 81 Strffnem.502 621 STRENGTH OF MATERIALS Stirrups, 960 Straight line formula, 749 Strain, 1, 2, 3 Strain energy, 47, 101, 102 Strength, i Stress, 1, 2, 3 Stress intensity, 2 Stresses in beams, 228 Struts, 727 St. Venant’s theory, 677 Subs itution method, 903 Suddenly applied loads, 104 T T-beams, 973 Tapering shafts, 628 Tearing strength, 771 Temperature stresses, 55 Tensile strain, 3 Tensile stress, 3 Theorem of three moments, 561 The ry of bending. 228 Thick cylindeis, 706 Thick sph-res, 7?t Thin cylinders, 683 Thin spheres, 698 Thr at of weld, 800, 802 Thrust diagram, 11,212 Torsion of shafts, 582 Torsion of non circular section, 619- Torsional resilience, 618 Torsional rigidity, 586 Twist of a shaft, 583 U U-Butt weld, 801 Ultimate stress, 9 6 Unbalanced setion, 931 Under reinforced section 931 Unit stress, 2 Unwin’s formula, 774 V V-Butt weld, 801 Volumetric strain, 7* W Walls, 364 Welded joints, 799 Wind pressure, 364 Wire bound pipes, 695 Wohler’s experiments, 922. Work, 101..481 Working stresses, 916 Y Yield point, 915 Young’s modulus, 6
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