Mechanics of Solids

✍ Scribed by Carl Ross, John Bird, Andrew Little

• Publisher: Routledge
• Year: 2021
• Tongue: English
• Leaves: 519
• Edition: 3
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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