Strength of Materials and Structures
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Table of contents
- Cover
- Contentsv
- Prefacex
- Acknowledgementsxi
- Principal notationxii
- Note on SI unitsxiii
- Introduction1
- 1.1 Introduction1
- 1.2 Trigonometrical definitions1
- 1.3 Vectors and scalars2
- 1.4 Newton's laws of motion2
- 1.5 Elementary statics3
- 1.6 Couples6
- 1.7 Equilibrium8
- Chapter 1. Tension and compression: direct stresses12
- 1.1 Introduction12
- 1.2 Stretching of a steel wire12
- 1.3 Tensile and compressive stresses14
- 1.4 Tensile and compressive strains17
- 1.5 Stress–strain curves for brittle materials18
- 1.6 Ductile materials20
- 1.7 Proof stresses31
- 1.8 Ductility measurement31
- 1.9 Working stresses32
- 1.10 Load factors33
- 1.11 Lateral strains due to direct stresses33
- 1.12 Strength properties of some engineering materials36
- 1.13 Weight and stiffness economy of materials36
- 1.14 Strain energy and work done in the tensile test39
- 1.15 Initial stresses41
- 1.16 Composite bars in tension or compression42
- 1.17 Temperature stresses45
- 1.18 Temperature stresses in composite bars45
- 1.19 Circular ring under radial pressure48
- 1.20 Creep of materials under sustained stresses52
- 1.21 Fatigue under repeated stresses53
- Chapter 2. Pin-jointed frames or trusses55
- 2.1 Introduction55
- 2.2 Statically determinate pin-jointed frames56
- 2.3 The method of joints57
- 2.4 The method of sections62
- 2.5 A statically indeterminate problem63
- Chapter 3. Shearing stress67
- 3.1 Introduction67
- 3.2 Measurement of shearing stress68
- 3.3 Complementary shearing stress71
- 3.4 Shearing strain73
- 3.5 Strain energy due to shearing actions73
- Chapter 4. Joints and connections76
- 4.1 Importance of connections76
- 4.2 Modes of failure of simple bolted and riveted joints76
- 4.3 Efficiency of a connection81
- 4.4 Group-bolted and -riveted joints82
- 4.5 Eccentric loading of bolted and riveted connections83
- 4.6 Welded connections86
- 4.7 Welded connections under bending actions89
- Chapter 5. Analysis of stress and strain94
- 5.1 Introduction94
- 5.2 Shearing stresses in a tensile test specimen94
- 5.3 Strain figures in mild steel; Lüder's lines96
- 5.4 Failure of materials in compression96
- 5.5 General two-dimensional stress system97
- 5.6 Stresses on an inclined plane98
- 5.7 Values of the principal stresses100
- 5.8 Maximum shearing stress101
- 5.9 Mohr's circle of stress103
- 5.10 Strains in an inclined direction109
- 5.11 Mohr's circle of strain111
- 5.12 Elastic stress–strain relations112
- 5.13 Principal stresses and strains114
- 5.14 Relation between E, G and v115
- 5.15 Strain 'rosettes'118
- 5.16 Strain energy for a two-dimensional stress system126
- 5.17 Three-dimensional stress systems127
- 5.18 Volumetric strain in a material under hydrostatic pressure129
- 5.19 Strain energy of distortion130
- 5.20 Isotropic, orthotropic and anisotropic132
- 5.21 Fibre composites132
- 5.22 In-plane equations for a symmetric laminate or composite139
- 5.23 Equivalent elastic constants for problems involving bending and twisting142
- 5.24 Yielding of ductile materials under combined stresses144
- 5.25 Elastic breakdown and failure of brittle material149
- 5.26 Failure of composites150
- Chapter 6. Thin shells under internal pressure152
- 6.1 Thin cylindrical shell of circular cross-section152
- 6.2 Thin spherical shell162
- 6.3 Cylindrical shell with hemispherical ends163
- 6.4 Bending stresses in thin-walled circular cylinders164
- Chapter 7. Bending moments and shearing forces169
- 7.1 Introduction169
- 7.2 Concentrated and distributed loads170
- 7.3 Relation between the intensity of loading, the shearing force, and bending moment in a straight170
- 7.4 Sign conventions for bending moments and shearing forces172
- 7.5 Cantilevers173
- 7.6 Cantilever with non-uniformly distributed load177
- 7.7 Simply-supported beams178
- 7.8 Simply-supported beam carrying a uniformly distributed load and end couples183
- 7.9 Points of inflection185
- 7.10 Simply-supported beam with a uniformly distributed load over pad of a span187
- 7.11 Simply-supported beam with non-uniformly distributed load188
- 7.12 Plane curved beams189
- 7.13 More general case of bending of a curved bar192
- 7.14 Rolling loads and influence lines194
- 7.15 A single concentrated load traversing a beam194
- 7.16 Influence lines of bending moment and shearing force196
- Chapter 8. Geometrical properties of cross-sections200
- 8.1 Introduction200
- 8.2 Centroid200
- 8.3 Centroidal axes201
- 8.4 Second moment of area (I)201
- 8.5 Parallel axes theorem202
- Chapter 9. Longitudinal stresses in beams212
- 9.1 Introduction212
- 9.2 Pure bending of a rectangular beam212
- 9.3 Bending of a beam about a principal axis216
- 9.4 Beams having two axes of symmetry in the cross-section218
- 9.5 Beams having only one axis of symmetry221
- 9.6 More general case of pure bending222
- 9.7 Elastic section modulus228
- 9.8 Longitudinal stresses while shearing forces are present229
- 9.9 Calculation of the principal second moments of area230
- 9.10 Elastic strain energy of bending239
- 9.11 Change of cross-sectlon in pure bending241
- Chapter 10. Shearing stresses in beams245
- 10.1 Introduction245
- 10.2 Shearing stresses in a beam of narrow rectangular cross-section245
- 10.3 Beam of any cross-section having one axis of symmetry248
- 10.4 Shearing stresses in an I-beam250
- 10.5 Principal stresses in beams256
- 10.6 Superimposed beams258
- 10.7 Shearing stresses in a channel section; shear centre259
- Chapter 11. Beams of two materials266
- 11.1 Introduction266
- 11.2 Transformed sections266
- 11.3 Timber beam with reinforcing steel flange plates270
- 11.4 Ordinary reinforced concrete272
- Chapter 12. Bending stresses and direct stresses combined283
- 12.1 Introduction283
- 12.2 Combined bending and thrust of a stocky strut283
- 12.3 Eccentric thrust285
- 12.4 Pre-stressed concrete beams289
- Chapter 13. Deflections of beams295
- 13.1 Introduction295
- 13.2 Elastic bending of straight beams295
- 13.3 Simply-supported beam carrying a uniformly distributed load300
- 13.4 Cantilever with a concentrated load301
- 13.5 Cantilever with a uniformly distributed load303
- 13.6 Propped cantilever with distributed load304
- 13.7 Simply-supported beam carrying a concentrated lateral load307
- 13.8 Macaulay's method310
- 13.9 Simply-supported beam with distributed load over a portion of the span313
- 13.10 Simply-supported beam with a couple applied at an intermediate point316
- 13.11 Beam with end couples and distributed load320
- 13.12 Beams with non-uniformly distributed load322
- 13.13 Cantilever With irregular loading324
- 13.14 Beams of varying section324
- 13.15 Non-uniformly distributed load and terminal couples; the method of moment-areas327
- 13.16 Deflections of beams due to shear333
- Chapter 14. Built-in and continuous beams339
- 14.1 Introduction339
- 14.2 Built-in beam with a single concentrated load339
- 14.3 Fixed-end moments for other loading conditions342
- 14.4 Disadvantages of built-in beams344
- 14.5 Effect of sinking of supports345
- 14.6 Continuous beam346
- 14.7 Slope-deflection equations for a single beam347
- Chapter 15. Plastic bending of mild-steel beams350
- 15.1 Introduction350
- 15.2 Beam of rectangular cross-section351
- 15.3 Elastic-plastic bending of a rectangular mild-steel beam352
- 15.4 Fully plastic moment of an I-section; shape factor355
- 15.5 More general case of plastic bending357
- 15.6 Comparison of elastic and plastic section moduli359
- 15.7 Regions of plasticity in a simply-supported beam361
- 15.8 Plastic collapse of a built-in beam364
- Chapter 16. Torsion of circular shafts and thin-walled tubes367
- 16.1 Introduction367
- 16.2 Torsion of a thin circular tube367
- 16.3 Torsion of solid circular shafts368
- 16.4 Torsion of a hollow circular shaft370
- 16.5 Principal stresses in a twisted shaft374
- 16.6 Torsion combined with thrust or tension375
- 16.7 Strain energy of elastic torsion378
- 16.8 Plastic torsion of a circular shaft379
- 16.9 Torsion of thin tubes of non-circular cross-section382
- 16.10 Torsion of a fiat rectangular strip385
- 16.11 Torsion of thin-walled open sections387
- Chapter 17. Energy methods390
- 17.1 Introduction390
- 17.2 Principle of virtual work390
- 17.3 Deflections of beams391
- 17.4 Statically indeterminate beam problems396
- 17.5 Plastic bending of mild-steel beams397
- 17.6 Plastic design of frameworks401
- 17.7 Complementary energy413
- 17.8 Complementary energy in problems of bending415
- 17.9 The Raleigh-Ritz method419
- Chapter 18. Buckling of columns and beams424
- 18.1 Introduction424
- 18.2 Flexural buckling of a pin-ended strut424
- 18.3 Rankine-Gordon formula428
- 18.4 Effects of geometrical imperfections430
- 18.5 Effective lengths of struts431
- 18.6 Pin-ended strut with eccentric end thrusts432
- 18.7 Initially curved pin-ended strut436
- 18.8 Design of pin-ended struts440
- 18.9 Strut with uniformly distributed lateral loading441
- 18.10 Buckling of a strut with built-in ends444
- 18.11 Buckling of a strut with one end fixed and the other end free444
- 18.12 Buckling of a strut with one end pinned and the other end fixed445
- 18.13 Flexural buckling of struts with other cross-sectional forms448
- 18.14 Torsional buckling of a cruciform strut450
- 18.15 Modes of buckling of a cruciform strut452
- 18.16 Lateral buckling of a narrow beam454
- Chapter 19. Lateral deflections of circular plates458
- 19.1 Introduction458
- 19.2 Plate differential equation, based on small deflection elastic theory458
- 19.3 Large deflections of plates476
- 19.4 Shear deflections of very thick plates486
- Chapter 20. Torsion of non-circular sections492
- 20.1 Introduction492
- 20.2 To determine the torsional equation492
- 20.3 To determine expressions for the shear stress τ and the torque T496
- 20.4 Numerical solution of the torsional equation504
- 20.5 Prandtl's membrane analogy504
- 20.6 Varying circular cross-section507
- 20.7 Plastic torsion511
- Chapter 21. Thick circular cylinders, discs and spheres515
- 21.1 Introduction515
- 21.2 Derivation of the hoop and radial stress equations for a thick- walled circular cylinder515
- 21.3 Lamé line519
- 21.4 Compound tubes525
- 21.5 Plastic deformation of thick tubes531
- 21.6 Thick spherical shells540
- 21.7 Rotating discs543
- 21.8 Collapse of rotating rings548
- Chapter 22. Introduction to matrix algebra550
- 22.1 Introduction550
- 22.2 Definitions550
- 22.3 Matrix addition and subtraction552
- 22.4 Matrix multiplication554
- 22.5 Some special types of square matrix555
- 22.6 Determinants556
- 22.7 Cofactor and adjoint matrices557
- 22.8 Inverse of a matrix [A] -1559
- 22.9 Solution of simultaneous equations561
- Chapter 23. Matrix methods of structural analysis565
- 23.1 Introduction565
- 23.2 Elemental stiffness matrix for a rod565
- 23.3 System stiffness matrix [K]567
- 23.4 Relationship between local and global co-ordinates571
- 23.5 Plane rod element in global co-ordinates574
- 23.6 Pin-jointed space trusses587
- 23.7 Beam element598
- 23.8 Rigid-jointed plane frames607
- Chapter 24. The finite element method627
- 24.1 Introduction627
- 24.2 Stiffness matrices for some typical finite elements629
- Chapter 25. Structural vibrations643
- 25.1 Introduction643
- 25.2 Free vibrations of a mass on a beam643
- 25.3 Free vibrations of a beam with distributed mass646
- 25.4 Forced vibrations of a beam carrying a single mass649
- 25.5 Damped free oscillations of a beam652
- 25.6 Damped forced oscillations of a beam655
- 25.7 Vibrations of a beam with end thrust656
- 25.8 Derivation of expression for the mass matrix657
- 25.9 Mass matrix for a rod element659
- 25.10 Mass matrix for a beam element676
- 25.11 Mass matrix for a rigid-jointed plane frame element684
- 25.12 Units in structural dynamics686
- Answers to further problems691
- Index699
Engineers need to be familiar with the fundamental principles and concepts in materials and structures in order to be able to design structurers to resist failures. For 4 decades, this book has provided engineers with these fundamentals.
Thoroughly updated, the book has been expanded to cover everything on materials and structures that engineering students are likely to need. Starting with basic mechanics, the book goes on to cover modern numerical techniques such as matrix and finite element methods. There is also additional material on composite materials, thick shells, flat plates and the vibrations of complex structures. Illustrated throughout with worked examples, the book also provides numerous problems for students to attempt.
New edition introducing modern numerical techniques, such as matrix and finite element methods
Covers requirements for an engineering undergraduate course on strength of materials and structures
Thoroughly updated, the book has been expanded to cover everything on materials and structures that engineering students are likely to need. Starting with basic mechanics, the book goes on to cover modern numerical techniques such as matrix and finite element methods. There is also additional material on composite materials, thick shells, flat plates and the vibrations of complex structures. Illustrated throughout with worked examples, the book also provides numerous problems for students to attempt.
New edition introducing modern numerical techniques, such as matrix and finite element methods
Covers requirements for an engineering undergraduate course on strength of materials and structures