Mechanics of Solids

Description

Mechanics of Solids provides an introduction to the behaviour of solid materials under various loading conditions, focusing upon the fundamental concepts and principles of statics and stress analysis. As the primary recommended text of the Council of Engineering Institutions for university undergraduates studying mechanics of solids it is essential reading for mechanical engineering undergraduates and also students on many civil, structural, aeronautical and other engineering courses. The mathematics in this book has been kept as straightforward as possible and worked examples are used to reinforce key concepts. Practical stress and strain scenarios are covered, including simple stress and strain, torsion, bending, elastic failure and buckling. Many examples are given of thin-walled structures, beams, struts and composite structures. This third edition includes new chapters on matrix algebra, linear elastic fracture mechanics, material property considerations and more on strain energy methods. The companion website www.routledge.com/cw/bird provides full solutions to all 575 further problems in the text, multiple-choice tests, a list of essential formulae, resources for adopting course instructors, together with several practical demonstrations by Professor Ross. Cover Half Title Title Page Copyright Page Table of Contents Preface 1 Revisionary mathematics 1.1 Introduction 1.2 Radians and degrees 1.3 Measurement of angles 1.4 Trigonometry revision 1.5 Brackets 1.6 Fractions 1.7 Percentages 1.8 Laws of indices 1.9 Simultaneous equations Revision Test 1 Revisionary mathematics Multiple-Choice Questions Test 1 2 Further revisionary mathematics 2.1 Units, prefixes and engineering notation 2.2 Metric–US/Imperial conversions 2.3 Straight line graphs 2.4 Gradients, intercepts and equation of a graph 2.5 Practical straight line graphs 2.6 Introduction to calculus 2.7 Basic differentiation revision 2.8 Revision of integration 2.9 Definite integrals 2.10 Simple vector analysis Revision Test 2 Further revisionary mathematics Multiple-Choice Questions Test 2 Mathematics help – some references Notation used in Mechanics of Solids 3 Statics 3.1 Plane pin-jointed trusses 3.2 Criterion for sufficiency of bracing 3.3 Mathematics used in statics 3.4 Equilibrium considerations 3.5 Bending moment and shearing force 3.6 Loads 3.7 Types of beam 3.8 Bending moment and shearing force diagrams 3.9 Point of contraflexure 3.10 Relationship between bending moment (M), shearing force (F) and intensity of load (w) 3.11 Cables 3.12 Suspension bridges 4 Stress and strain 4.1 Introduction 4.2 Hooke’s Law 4.3 Load-extension relationships 4.4 Proof stress 4.5 Ductility 4.6 Shear stress and shear strain 4.7 Poisson’s ratio (v) 4.8 Hydrostatic stress 4.9 Relationship between the material constants E, G, K and v 4.10 Three-dimensional stress 4.11 Composite materials 4.12 Thermal strain 4.13 Compound bars 4.14 Failure by fatigue 4.15 Failure due to creep 5 Geometrical properties of symmetrical sections 5.1 Introduction 5.2 Centroid 5.3 Second moment of area 5.4 Polar second moment of area 5.5 Parallel axis theorem 5.6 Perpendicular axis theorem 5.7 Calculation of I through numerical integration 5.8 Computer program for calculating ӯ and I[sub(XX)] 5.9 Use of EXCEL spreadsheet in calculating geometrical properties of beams 6 Bending stresses in beams 6.1 Introduction 6.2 Proof of σ/y = M/I = E/R 6.3 Sectional modulus (Z) 6.4 Anticlastic curvature 6.5 Composite beams 6.6 Flitched beams 6.7 Composite ship structures 6.8 Composite structures 6.9 Combined bending and direct stress 7 Beam deflections due to bending 7.1 Introduction 7.2 Repeated integration method 7.3 Macaulay’s method 7.4 Statically indeterminate beams 7.5 Moment-area method 7.6 Slope-deflection equations 8 Torsion 8.1 Introduction 8.2 Torque (T) 8.3 Assumptions made in circular shaft theory 8.4 Proof of τ/r =T/J = Gθ/l 8.5 Flanged couplings 8.6 Keyed couplings 8.7 Compound shafts 8.8 Tapered shafts 8.9 Close-coiled helical springs 8.10 Torsion of thin-walled non-circular sections 8.11 Torsion of thin-walled rectangular sections 8.12 Torsion of thin-walled open sections 8.13 Elastic-plastic torsion of circular-section shafts Multiple-Choice Questions Test 3 Revision Test 3 Specimen examination questions for Chapters 3 to 8 Multiple-Choice Questions Test 4 9 Complex stress and strain 9.1 Introduction 9.2 To obtain σ[sub(θ)] in terms of the co-ordinate stresses 9.3 Principal stresses (σ[sub(1)] and σ[sub(2)]) 9.4 Mohr’s stress circle 9.5 Combined bending and torsion 9.6 Two-dimensional strain systems 9.7 Principal strains (ε[sub(1)] and ε[sub(2)]) 9.8 Mohr’s circle of strain 9.9 Stress-strain relationships for plane stress 9.10 Stress-strain relationships for plane strain 9.11 Pure shear 9.12 Strain rosettes 9.13 Computer program for principal stresses and strains 9.14 The constitutive laws for a lamina of a composite in global co-ordinates 10 Membrane theory for thin-walled circular cylinders and spheres 10.1 Introduction 10.2 Is it possible for humans to inhabit the moon? 10.3 Circular cylindrical shells under uniform internal pressure 10.4 Thin-walled spherical shells under uniform internal pressure 10.5 Bending stresses in circular cylinders under uniform pressure 10.6 Circular cylindrical shell with hemispherical ends 11 Energy methods 11.1 Introduction 11.2 The method of minimum potential (Rayleigh-Ritz) 11.3 The principle of virtual work 11.4 The principle of complementary virtual work 11.5 Castigliano’s first theorem 11.6 Castigliano’s second theorem 11.7 Strain energy stored in a rod under axial loading 11.8 Strain energy stored in a beam subjected to couples of magnitude M at its ends 11.9 Strain energy due to a torque T stored in a uniform circular-section shaft 11.10 Deflection of thin curved beams 11.11 Unit load method 11.12 Suddenly applied and impact loads 11.13 Resilience 11.14 Plastic collapse of beams 11.15 Residual stresses in beams 12 Theories of elastic failure 12.1 Introduction 12.2 Maximum principal stress theory (Rankine) 12.3 Maximum principal strain theory (St Venant) 12.4 Total strain energy theory (Beltrami and Haigh) 12.5 Maximum shear stress theory (Tresca) 12.6 Maximum shear strain energy theory (Hencky and von Mises) 12.7 Yield loci 12.8 Conclusions 13 Thick cylinders and spheres 13.1 Introduction 13.2 Derivation of the hoop and radial stress equations for a thick-walled cylinder 13.3 Lamé line 13.4 Compound cylinders 13.5 Plastic yielding of thick tubes 13.6 Thick spherical shells 13.7 Rotating discs 13.8 Plastic collapse of discs 13.9 Rotating rings 13.10 Design of the ‘Trieste’ to conquer the Mariana Trench 14 The buckling of struts 14.1 Introduction 14.2 Axially loaded struts 14.3 Elastic instability of very long slender struts 14.4 Struts with various boundary conditions 14.5 Limit of application of Euler theory 14.6 Rankine-Gordon formula for struts buckling inelastically 14.7 Effects of geometrical imperfections 14.8 Eccentrically loaded struts 14.9 Struts with initial curvature 14.10 Perry-Robertson formula 14.11 Dynamic instability 15 Asymmetrical bending of beams 15.1 Introduction 15.2 Symmetrical-section beams loaded asymmetrically 15.3 Asymmetrical sections 15.4 Calculation of I[sub(xy)] 15.5 Principal axes of bending 15.6 Mohr’s circle of inertia 15.7 Stresses in beams of asymmetrical section 16 Shear stresses in bending and shear deflections 16.1 Introduction 16.2 Vertical shearing stresses 16.3 Horizontal shearing stresses 16.4 Shear centre 16.5 Shear centre positions for closed thin-walled tubes 16.6 Shear deflections 16.7 Warping 17 Experimental strain analysis 17.1 Introduction 17.2 Electrical resistance strain gauges 17.3 Types of electrical resistance strain gauge 17.4 Gauge material 17.5 Gauge adhesives 17.6 Water-proofing 17.7 Other strain gauges 17.8 Gauge circuits 17.9 Photoelasticity 17.10 Moire fringes 17.11 Brittle lacquer techniques 17.12 Semiconductor strain gauges 17.13 Acoustical gauges Revision Test 4 Specimen examination questions for Chapters 9 to 17 18. An introduction to matrix algebra 18.1 Introduction 18.2 Elementary matrix algebra 18.3 Addition and subtraction of matrices 18.4 Matrix multiplication 18.5 Two by two determinants 18.6 Three by three determinants Multiple-Choice Questions Test 5 19 Composites 19.1 A comparison of mechanical properties of materials 19.2 Matrix equations for composites 19.3 Derivation of the stiffness matrix (Q) and (S)[sup(-1)] for isotropic materials 19.4 Compliance matrix (S) for an orthotropic ply or sheet or layer 19.5 Derivation of the stiffness matrix (Q) for orthotropic materials 19.6 An orthotropic ply with off-axis loading 19.7 A laminate or ply based on orthotropic plies with off-axis loading 19.8 Failure criteria for composite materials 20 The matrix displacement method 20.1 Introduction 20.2 The matrix displacement method 20.3 The structural stiffness matrix (K) 20.4 Elemental stiffness matrix for a plane rod 20.5 Continuous beams 20.6 Analysis of pin-jointed trusses on SmartPhones, tablets and Microsoft computers 20.7 Analysis of continuous beams on SmartPhones, tablets and Microsoft computers 20.8 Analysis of rigid-jointed plane frames on SmartPhones, tablets and Microsoft computers 21. The finite element method 21.1 Introduction 21.2 Stiffness matrix for the in-plane triangular element 21.3 Stiffness matrix for a three node rod element Revision Test 5 Specimen examination questions for Chapters 19 to 21 22. An introduction to linear elastic fracture mechanics 22.1 Introduction 22.2 Basis of fracture mechanics theory 22.3 Strain energy release and crack propagation 22.4 Energy balance approach 22.5 The stress intensity approach 22.6 Plane stress and plane strain 22.7 Plane stress and plain strain behaviour 22.8 Allowance for small scale yielding at crack tip 22.9 Fracture toughness crack tip opening displacement (CTOD) 22.10 Application of fracture mechanics to fatigue crack growth 22.11 The J-Integral 22.12 Crack extension resistance curves (R-curves) 23. Material property considerations 23.1 Introduction 23.2 Fatigue and the effects of cyclic loading 23.3 Design against fatigue 23.4 Mean stress and fatigue 23.5 Further applications of Goodman diagrams 23.6 Varying stress amplitudes and fatigue 23.7 The effects of surface treatment and surface finish on fatigue 23.8 Corrosion and fatigue 23.9 Creep – the effects of high temperature 23.10 Creep testing 23.11 Extrapolation of creep data 23.12 Effect of restraint – creep relaxation A revisionary list of formulae for Mechanics of Solids Answers to multiple-choice questions References Index