Mechanics of solids

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