Solid Mechanics in Engineering

ISBN-10: 0471493007

ISBN-13: 9780471493006

Edition: 2001

Authors: Raymond Parnes

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This text is a systematic treatment of solid mechanics related to everyday applications in engineering.
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Book details

List price: $102.95
Copyright year: 2001
Publisher: John Wiley & Sons, Incorporated
Publication date: 11/28/2001
Binding: Paperback
Pages: 748
Size: 7.75" wide x 10.25" long x 1.55" tall
Weight: 3.586
Language: English

Basic concepts
Introductory concepts of solid mechanics
Forces, loads and reactions - idealisations
Types of loads
Representation of forces and loads
Reactions and constraints - idealisations
Intensity of internal forces - average stresses
Intensity of a normal force acting over an area - refinement of the concept: normal stress at a point
Average stresses on an oblique plane
Variation of internal forces and stresses with position
Strain as a measure of intensity of deformation
Mechanical behaviour of materials
Internal forces and stress
Internal force resultants
State of stress at a point: traction
Sign convention
The stress tensor
Equality of the conjugate shear stresses
Stress equations of motion and equilibrium
Relations between stress components and internal force resultants
Stress transformation laws for plane stress
Remarks on the transformation laws (stress as a tensor; invariants of a tensor)
Transformation law of a vector: the vector as a tensor
Principal stresses and stationary shear stress values
Principal stresses: stationary values of [sigma subscript n]
Maximum and minimum shear stress components
Summary of results
Parametric representation of the state of stress: the Mohr circle
Cartesian components of traction in terms of stress components: traction on the surface of a body
Deformation and strain
Types of deformation
Extensional or normal strain
Shear strain
Strain-displacement relations
Some preliminary instructive examples
Strain-displacement relations for infinitesimal strains and rotations
State of strain
Two-dimensional transformation law for infinitesimal strain components
Geometric derivation
Analytic derivation of the transformation laws
The infinitesimal strain tensor - two-dimensional transformation laws
Principal strains and principal directions of strain: the Mohr circle for strain
The strain rosette
Volumetric strain - dilatation
Behaviour of materials: constitutive equations
Some general idealisations (definitions: 'micro' and 'macro' scales)
Classification of materials: viscous, elastic, visco-elastic and plastic materials
Elastic materials
Constitutive equations for elastic materials: general elastic and linear elastic behaviour, Hooke's law
Elastic strain energy
Mechanical properties of engineering materials
Behaviour of ductile materials
Behaviour of brittle materials
Behaviour of rubber-like materials
Plastic behaviour: idealised models
Summary of basic results and further idealisations: solutions using the 'mechanics-of-materials' approach
Superposition principles
Superposition of infinitesimal strains
Basic principle of superposition for linear elastic bodies
The principle of de Saint Venant
Applications to simple elements
Axial loadings
Elastic behaviour of prismatic rods: basic results
Some general comments
Extension of results: approximations for rods having varying cross-sections
Statically indeterminate axially loaded members
Temperature problems: thermal stresses
Elastic-plastic behaviour: residual stresses
Torsion of circular cylindrical rods: Coulomb torsion
Basic relations for elastic members under pure torsion
Deformation analysis: conclusions based on axi-symmetry of the rod
Basic relations
Some comments on the derived expressions: extension of the results and approximations
Comments on the solution
An approximation for thin-wall circular tubular cross-sections
Extension of the results: engineering approximations
Some practical engineering design applications of the theory
Circular members under combined loads
Statically indeterminate systems under torsion
Elastic-plastic torsion
Symmetric bending of beams - basic relations and stresses
Resultant shear and bending moments - sign convention
Some simple examples
Sign convention
Differential relations for beams
Some further examples for resultant forces in beams
Integral relations for beams
Symmetrical bending of beams in a state of pure bending
Some preliminary definitions and limitations - deformation analysis
Moment-curvature relations and flexural stresses in an elastic beam under pure bending: Euler-Bernoulli relations
Axial displacements of beams under pure bending
Comments on the solution - exactness of the solution
Methodology of solution - the methodology of 'mechanics of materials'
Flexure of beams due to applied lateral loads - Navier's hypothesis
Shear stresses in beams due to symmetric bending
Limitations on the derived expression
Shear effect on beams - warping of the cross-sections due to shear
Re-examination of the expression for flexural stress [sigma subscript x] = My/I: further engineering approximations
Examination of equilibrium state
Flexural stress in a non-prismatic beam - an engineering approximation
Engineering design applications for beams
Bending of composite beams
Combined loads
Elastic-plastic behaviour
Fully plastic moments - location of the neutral axis
Moment-curvature relation for beams of rectangular cross-section in the plastic range
Symmetric bending of beams: deflections, fundamental solutions and superposition
Linearised beam theory
Accuracy of the linearised beam theory
Elastic curve equations for some 'classical' cases
Axial displacements due to flexure of a beam under lateral loads
Deflections due to shear deformation
Singularity functions and their application
Definition of singularity functions
Solutions for statically indeterminate beams by integration of the differential equation
Application of linear superposition in beam theory
Analysis of statically indeterminate beams: the force method
Development of the force method
Comments on the force method
Superposition - integral formulation: the fundamental solution and Green's functions
Development and applications
Generalisation: Green's functions for shears, moments, etc. in beams
Some general comments
The fourth-order differential equation for beams
Development and applications
The fourth-order differential equation for concentrated force and couple loadings
Moment-area theorems
Thin-wall pressure vessels: thin shells under pressure
Thin cylindrical shells
Thin spherical shells
Comments and closure
Stability and instability of rods under axial compression: beam-columns and tie-rods
Stability and instability of mechanical systems
Stability of rigid rods under compressive loads: the concept of bifurcation
Stability of an elastic rod subjected to an axial compressive force-Euler buckling load
Elastic buckling of rods under various boundary conditions
Rods under eccentric axial loads-the 'secant formula'
Rods under combined axial and lateral loads: preliminary remarks
Differential equations of beams subjected to combined lateral loads and axial forces
Stability analysis using the fourth-order differential equation
Beam-column subjected to a single lateral force F and an axial compressive force P
Some comments on the solution: use of linear superposition
General comments and conclusions
Torsion of elastic members of arbitrary cross-section: de Saint Venant torsion
Semi-inverse methods: uniqueness of solutions
The general de Saint Venant torsion solution
Torsion of a member of elliptic cross-section
Torsion of a member of rectangular cross-section
The membrane analogy
Torsion of a member having a narrow rectangular cross-section
Derivation of membrane analogy solution
Comparison of exact solution with membrane analogy for narrow rectangular sections
Torsion of thin-wall open-section members
Shear stress at a re-entrant corner: approximate solution
Torsion of closed-section members: thin-wall sections
Torsion of multi-cell closed thin-wall sections
General bending theory of beams
Moment-curvature relation for elastic beams in flexure
Sign convention and beam equations for bending about two axes
Sign convention
Differential beam equations
General expression for stresses due to flexure
Derivation: stresses in beams under pure bending
Extension of expression for flexural stress in beams due to applied lateral loads
Some particular cases
General case
Shear stresses due to bending of beams
Comments on the expressions
Distribution of shear stresses in a thin-wall section: shear centers
Shear stress distribution
The shear center
Some remarks and comments
Deflections and rotations of a beam under applied loads
Shear stresses in closed thin-wall sections
Energy methods and virtual work
Basic energy theorems, principles of virtual work and their applications to structural mechanics
Elastic strain energy
Review of results for the uniaxial state of stress
General stress state
Examples of strain energy for linear elastic bodies
The principle of conservation of energy for linear elastic bodies
Derivation of the principle
Application of the principle
Betti's law and Maxwell's reciprocal relation: flexibility coefficients
Castigliano's second theorem
Geometric representation (complementary strain energy and Castigliano's first theorem)
The principle of virtual work
Definitions of external and internal virtual work: virtual displacements
Proof of the principle of virtual work: comments on the principle
The principle of virtual work for flexure of beams
Application of the principle of virtual work to evaluate reactions and internal stress resultants: the 'method of virtual displacements'
Influence lines for reactions, shears and moments in beams by the principle of virtual work
The principle of complementary virtual work
Development and derivation of the principle
Comparison and analogues between the two principles
Expressions for internal complementary virtual work in terms of internal stress resultants: generalised forces and displacements
Internal complementary virtual work in linear elastic rods and beams: explicit expressions (some generalisations)
Application of the principle of complementary virtual work to evaluate displacements of linear elastic bodies: the 'method of virtual forces'
The principle of stationary potential energy
Derivation of the principle and some applications
Approximate solutions-the Rayleigh-Ritz method
Summary and conclusions
Stability of mechanical systems by energy considerations: approximate methods
Classification of equilibrium states according to energy criteria
Stability of a rigid rod subjected to a compressive axial force
Determination of critical loads using a small deflection analysis-pseudo-neutral equilibrium
The total potential for small displacements: reconsideration of the stability criteria
Systems having several degrees-of-freedom-small displacement analysis
Two-degree-of-freedom system
n-Degree-of-freedom systems
Stability of an elastic rod: the Rayleigh quotient
The Rayleigh method for critical loads
Development of the method
Proof of the upper boundedness of the Rayleigh load (restricted proof)
The Rayleigh-Ritz method for critical loads
Properties of areas
General properties: centroids, first and second moments of areas
Properties of selected areas
Some mathematical relations
Curvature of a line y = y(x)
Green's theorem
The divergence theorem (Gauss' theorem)
The membrane equation
Material properties
Table of structural properties
Reactions, deflections and slopes of selected beams
Answers to selected problems
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