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9780471493006

Solid Mechanics in Engineering

by
  • ISBN13:

    9780471493006

  • ISBN10:

    0471493007

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2001-11-28
  • Publisher: WILEY
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Summary

This book provides a systematic, modern introduction to solid mechanics that is carefully motivated by realistic Engineering applications. Based on 25 years of teaching experience, Raymond Parnes uses a wealth of examples and a rich set of problems to build the reader's understanding of the scientific principles, without requiring 'higher mathematics'. Highlights of the book include * The use of modern SI units throughout * A thorough presentation of the subject stressing basic unifying concepts * Comprehensive coverage, including topics such as the behaviour of materials on a phenomenological level. * Over 600 problems, many of which are designed for solving with MATLAB, MAPLE or MATHEMATICA. Solid Mechanics in Engineering is designed for 2-semester courses in Solid Mechanics or Strength of Materials taken by students in Mechanical, Civil or Aeronautical Engineering and Materials Science and may also be used for a first-year graduate program.

Author Biography

<B>RAYMOND PARNES </B>is a Professor in the Department of Solid Mechanics, Materials and Structures in Tel-Aviv University. A graduate of Columbia University, he has over 25 years experience of teaching the subject in the United States, Europe and Israel and has published extensively in a variety of subjects in Solid Mechanics.

Table of Contents

Preface xvii
PART A Basic concepts
Introductory concepts of solid mechanics
3(18)
Introduction
3(2)
Forces, loads and reactions - idealisations
5(3)
Types of loads
5(1)
Representation of forces and loads
6(1)
Reactions and constraints - idealisations
7(1)
Intensity of internal forces-average stresses
8(3)
Intensity of a normal force acting over an area - refinement of the concept: normal stress at a point
11(1)
Average stresses on an oblique plane
12(1)
Variation of internal forces and stresses with position
13(1)
Strain as a measure of intensity of deformation
14(2)
Mechanical behaviour of materials
16(2)
Summary
18(3)
Problems
18(3)
Internal forces and stress
21(53)
Introduction
21(1)
Internal force resultants
21(6)
State of stress at a point: traction
27(8)
Traction
27(3)
Sign convention
30(1)
The stress tensor
30(1)
Equality of the conjugate shear stresses
31(4)
Stress equations of motion and equilibrium
35(3)
Relations between stress components and internal force resultants
38(4)
Stress transformation laws for plane stress
42(6)
Derivation
42(4)
Remarks on the transformation laws (stress as a tensor; invariants of a tensor)
46(1)
Transformation law of a vector: the vector as a tensor
47(1)
Principal stresses and stationary shear stress values
48(13)
Principal stresses: stationary values of σn
48(3)
Maximum and minimum shear stress components
51(2)
Summary of results
53(1)
Parametric representation of the state of stress: the Mohr circle
53(8)
Cartesian components of traction in terms of stress components: traction on the surface of a body
61(13)
Problems
64(10)
Deformation and strain
74(45)
Introduction
74(1)
Types of deformation
74(1)
Extensional or normal strain
75(3)
Shear strain
78(3)
Strain-displacement relations
81(11)
Some preliminary instructive examples
81(4)
Strain-displacement relations for infinitesimal strains and rotations
85(7)
State of strain
92(1)
Two-dimensional transformation law for infinitesimal strain components
93(7)
Geometric derivation
93(3)
Analytic derivation of the transformation laws
96(2)
The infinitesimal strain tensor-two-dimensional transformation laws
98(2)
Principal strains and principal directions of strain: the Mohr circle for strain
100(5)
The strain rosette
105(2)
Volumetric strain - dilatation
107(12)
Problems
108(11)
Behaviour of materials: constitutive equations
119(26)
Introduction
119(1)
Some general idealisations (definitions: 'micro' and 'macro' scales
119(2)
Classification of materials: viscous, elastic, viscous-elastic and plastic materials
121(2)
Elastic materials
123(11)
Constitutive equations for elastic materials: general elastic and linear elastic behaviour Hooke's law
123(7)
Elastic strain energy
130(4)
Mechanical properties of engineering materials
134(7)
Behaviour of ductile materials
134(5)
Behaviour of brittle materials
139(1)
Behaviour of rubber-like materials
140(1)
Plastic behaviour: idealised models
141(4)
Problems
142(3)
Summary of basic results and further idealisations: solutions using the mechanics-of-materials' approach
145(10)
Introduction
145(2)
Superposition principles
147(3)
Superposition of infinitesimal strains
147(1)
Basic principle of superposition for linear elastic bodies
148(2)
The principle of de Saint Venant
150(5)
PART B Applications to simple elements
Axial loadings
155(35)
Introduction
155(1)
Elastic behaviour of prismatic rods: basic results
155(4)
Some general comments
159(3)
Extension of results: approximations for rods having varying cross-sections
162(2)
Statically indeterminate axially loaded members
164(6)
Temperature problems: thermal stresses
170(4)
Elastic-plastic behaviour: residual stresses
174(16)
Problems
179(11)
Torsion of circular cylindrical rods: Coulomb torsion
190(35)
Introduction
190(1)
Basic relations for elastic members under pure torsion
190(7)
Deformation analysis: conclusions based on axi-symmetry of the rod
190(3)
Basic relations
193(4)
Some comments on the derived expressions: extension of the results and approximations
197(7)
Comments on the solution
197(3)
An approximation for thin-wall circular tubular cross-sections
200(1)
Extension of the results: engineering approximations
201(3)
Some practical engineering design applications of the theory
204(2)
Circular members under combined loads
206(1)
Statically indeterminate systems under torsion
207(3)
Elastic-plastic torsion
210(15)
Problems
213(12)
Symmetric bending of beams - basic relations and stresses
225(88)
Introduction
225(1)
Resultant shear and bending moments - sign convention
225(5)
Some simple examples
225(4)
Sign convention
229(1)
Differential relations for beams
230(1)
Some further examples for resultant forces in beams
231(6)
Integral relations for beams
237(5)
Symmetrical bending of beams in a state of pure bending
242(13)
Some preliminary definitions and limitations - deformation analysis
242(2)
Moment-curvature relations and flexural stresses in an elastic beam under pure bending: Euler-Bernoulli relations
244(8)
Axial displacements of beams under pure bending
252(2)
Comments on the solution - exactness of the solution
254(1)
Methodology of solution -the methodology of `mechanics of materials'
254(1)
Flexure of beams due to applied lateral loads - Navier's hypothesis
255(4)
Shear stresses in beams due to symmetric bending
259(6)
Derivation
259(5)
Limitations on the derived expression
264(1)
Shear effect on beams-warping of the cross-sections due to shear
265(1)
Re-examination of the expression for flexural stress σx=My/l: further engineering approximations
265(4)
Examination of equilibrium state
265(2)
Flexural stress in a non-prismatic beam - an engineering approximation
267(2)
Engineering design applications for beams
269(3)
Bending of composite beams
272(4)
Combined loads
276(2)
Elastic-plastic behaviour
278(35)
Fully plastic moments - location of the neutral axis
278(4)
Moment-curvature relation for beams of rectangular cross-section in the plastic range
282(4)
Problems
286(27)
Symmetric bending of beams: deflections, fundamental solutions and superposition
313(79)
Introduction
313(1)
Linearised beam theory
314(2)
Accuracy of the linearised beam theory
316(2)
Elastic curve equations for some 'classical' cases
318(6)
Axial displacements due to flexure of a beam under lateral loads
324(2)
Deflections due to shear deformation
326(3)
Singularity functions and their application
329(8)
Definition of singularity functions
329(1)
Applications
330(7)
Solutions for statically indeterminate beams by integration of the differential equation
337(2)
Application of linear superposition in beam theory
339(3)
Analysis of statically indeterminate beams: the force method
342(7)
Development of the force method
342(6)
Comments on the force method
348(1)
Superposition - integral formulation: the fundamental solution and Green's functions
349(8)
Development and applications
349(3)
Generalisation: Green's functions for shears, moments, etc. in beams
352(4)
Some general comments
356(1)
The fourth-order differential equation for beams
357(8)
Development and applications
357(2)
The fourth-order differential equation for concentrated force and couple loadings
359(6)
Moment-area theorems
365(27)
Problems
375(17)
Thin-wall pressure vessels: thin shells under pressure
392(12)
Introduction
392(1)
Thin cylindrical shells
392(5)
Thin spherical shells
397(1)
Comments and closure
398(6)
Problems
399(5)
Stability and instability of rods under axial compression: beam-columns and tie-rods
404(43)
Introduction
404(1)
Stability and instability of mechanical systems
405(1)
Stability of rigid rods under compressive loads: the concept of bifurcation
406(5)
Stability of an elastic rod subjected to an axial compressive force - Euler buckling load
411(4)
Elastic buckling of rods under various boundary conditions
415(5)
Rods under eccentric axial loads - the 'secant formula
420(3)
Rods under combined axial and lateral loads: Preliminary remarks
423(1)
Differential equations of beams subjected to combined lateral loads and axial forces
424(2)
Stability analysis using the fourth-order differential equation
426(2)
Beam-column subjected to a single lateral force F and an axial compressive force P
428(4)
Some comments on the solution: use of linear superposition
432(1)
Tie-rods
433(2)
General comments and conclusions
435(12)
Problems
436(11)
Torsion of elastic members of arbitrary cross-section: de Saint Venant torsion
447(49)
Introduction
447(1)
Semi-inverse methods: uniqueness of solutions
448(1)
The general de Saint Venant torsion solution
449(9)
Torsion of a member of elliptic cross-section
458(4)
Torsion of a member of rectangular cross-section
462(6)
The membrane analogy
468(4)
Torsion of a member having a narrow rectangular cross-section
472(3)
Derivation of membrane analogy solution
472(2)
Comparison of exact solution with membrane analogy for narrow rectangular sections
474(1)
Torsion of thin-wall open-section members
475(3)
Shear stress at a re-entrant corner: approximate solution
478(3)
Torsion of closed-section members: thin-wall sections
481(6)
Torsion of multi-cell closed thin-wall sections
487(2)
Closure
489(7)
Problems
490(6)
General bending theory of beams
496(41)
Introduction
496(1)
Moment-curvature relation for elastic beams in flexure
497(3)
Sign convention and beam equations for bending about two axes
500(2)
Sign convention
500(1)
Differential beam equations
501(1)
General expression for stresses due to flexure
502(6)
Derivation: stresses in beams under pure bending
502(2)
Extension of expression for flexural stress in beams due to applied lateral loads
504(1)
Some particular cases
504(2)
General case
506(2)
Shear stresses due to bending of beams
508(5)
Derivation
508(3)
Comments on the expressions
511(2)
Distribution of shear stresses in a thin-wall section: shear centers
513(5)
Shear stress distribution
513(1)
The shear center
514(3)
Some remarks and comments
517(1)
Deflections and rotations of a beam under applied loads
518(2)
Shear stresses in closed thin-wall sections
520(17)
Problems
525(12)
PART C Energy methods and virtual work
Basic energy theorems, principles of virtual work and their applications to structural mechanics
537(109)
Introduction
537(1)
Elastic strain energy
537(5)
Review of results for the uniaxial state of stress
538(1)
General stress state
539(2)
Examples of strain energy for linear elastic bodies
541(1)
The Principle of conservation of energy for linear elastic bodies
542(4)
Derivation of the principle
542(3)
Application of the principle
545(1)
Betti's law and Maxwell's reciprocal relation: flexibility coefficients
546(4)
Castigliano's second theorem
550(6)
Geometric representation (complementary strain energy and Castigliano's first theorem)
556(2)
The principle of virtual work
558(42)
Introduction
558(1)
Definitions of external and internal virtual work: virtual displacements
558(4)
Proof of the principle of virtual work: comments on the principle
562(5)
The principle of virtual work for flexure of beams
567(3)
Application of the principle of virtual work to evaluate reactions and internal stress resultants: the 'method of virtual displacements'
570(18)
Influence lines for reactions, shears and moments in beams by the principle of virtual work
588(12)
The principle of complementary virtual work
600(23)
Introduction
600(1)
Development and derivation of the principle
600(5)
Comparison and analogues between the two principles
605(2)
Expressions for internal complementary virtual work in terms of internal stress resultants: generalised forces and displacements
607(6)
Internal complementary virtual work in linear elastic rods and beams: explicit expressions (some generalisations)
613(2)
Application of the principle of complementary virtual work to evaluate displacements of linear elastic bodies: the 'method of virtual forces'
615(8)
The principle of stationary potential energy
623(11)
Derivation of the principle and some applications
623(6)
Approximate solutions - the Rayleigh-Ritz method
629(5)
Summary and conclusions
634(12)
Problems
634(12)
Stability of mechanical systems by energy considerations: approximate methods
646(41)
Introduction
646(1)
Classification of equilibrium states according to energy criteria
646(2)
Stability of a rigid rod subjected to a compressive axial force
648(7)
Determination of critical loads using a small deflection analysis-pseudo-neutral equilibrium
655(4)
The total potential for small displacements: reconsideration of the stability criteria
659(2)
Systems having several degrees-of-freedom - small displacement analysis
661(5)
Two-degree-of-freedom system
661(4)
n-Degree-of-freedom systems
665(1)
Stability of an elastic rod: the Rayleigh quotient
666(5)
The Ravleigh method for critical loads
671(8)
Development of the method
671(6)
Proof of the upper boundedness of the Rayleigh load (restricted proof)
677(2)
The Rayleigh-Ritz method for critical loads
679(8)
Problems
682(5)
Appendix A: Properties of areas 687(7)
A.1 General properties: centroids, first and second moments of areas
687(5)
A.2 Properties of selected areas
692(2)
Appendix B: Some mathematical relations 694(4)
B.1 Curvature of a line y=y(x)
694(1)
B.2 Green's theorem
695(1)
B.3 The divergence theorem (Gauss' theorem)
696(2)
Appendix C: The membrane equation 698(3)
Appendix D: Material properties 701(2)
Appendix E: Table of structural properties 703(7)
Appendix F: Reactions, deflections and slopes of Selected beams 710(5)
Answers to selected problems 715(8)
Index 723

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