Mechanics of solids

Description

Cover Title Copyright 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 Iₓₓ 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 σθ in terms of the co-ordinate stresses 9.3 Principal stresses (σ₁ and σ₂) 9.4 Mohr’s stress circle 9.5 Combined bending and torsion 9.6 Two-dimensional strain systems 9.7 Principal strains (ε₁ and ε₂) 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 Suddenly applied and impact loads 11.12 Resilience 11.13 Unit load method 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 Unsymmetrical bending of beams 15.1 Introduction 15.2 Symmetrical-section beams loaded asymmetrically 15.3 Unsymmetrical sections 15.4 Calculation of Ixy 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 Revision Test 4 Specimen examination questions for Chapters 9 to 16 17 Composites 17.1 A comparison of mechanical properties of materials 17.2 Matrix equations for composites 17.3 Derivation of the stiffness matrix (Q) and (S)¯¹ for isotropic materials 17.4 Compliance matrix (S) for an orthotropic ply or sheet or layer 17.5 Derivation of the stiffness matrix (Q) for orthotropic materials 17.6 An orthotropic ply with off-axis loading 17.7 A laminate or ply based on orthotropic plies with off-axis loading 17.8 Failure criteria for composite materials 18 The matrix displacement method 18.1 Introduction 18.2 The matrix displacement method 18.3 The structural stiffness matrix (K) 18.4 Elemental stiffness matrix for a plane rod 18.5 Continuous beams 18.6 Analysis of pin-jointed trusses on SmartPhones, tablets and Microsoft computers 18.7 Analysis of continuous beams on SmartPhones, tablets and Microsoft computers 18.8 Analysis of rigid-jointed plane frames on SmartPhones, tablets and Microsoft computers 19 The finite element method 19.1 Introduction 19.2 Stiffness matrix for the in-plane triangular element 19.3 Stiffness matrix for a three node rod element Revision Test 5 Specimen examination questions for Chapters 9 to 19 20 Experimental strain analysis 20.1 Introduction 20.2 Electrical resistance strain gauges 20.3 Types of electrical resistance strain gauge 20.4 Gauge material 20.5 Gauge adhesives 20.6 Water-proofing 20.7 Other strain gauges 20.8 Gauge circuits 20.9 Photoelasticity 20.10 Moire fringes 20.11 Brittle lacquer techniques 20.12 Semi-conductor strain gauges 20.13 Acoustical gauges A revisionary list of formulae for Mechanics of Solids Answers to multiple-choice questions References Index