كتاب Mechanics of Material Vol 2

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Mechanics of Material Vol 2
An introduction to the Mechanics of Elastic and
Plastic Deformation of Solids and Structural Materials
THIRD EDITION
E. J. HEARN
PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE
University of Warwick
United Kingdom

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1 Unsymmetrical Bending 1
Summary
Introduction
1.7 Momenta1 ellipse
1.8 Stress determination
1.9 Alternative procedure for stress determination
1.10 Alternative procedure using the momenta1 ellipse
1.1 1 Dejections
Examples
Problems
Product second moment of area
Principal second moments of area
Mohr’s circle of second moments of area
Land’s circle of second moments of area
Rotation of axes: determination of moments of area in terms of the
principal values
The ellipse of second moments of area
2 Struts
Summary
Introduction
2.1 Euler’s theory
2.2 Equivalent strut length
2.4 Euler “validity limit”
2.5 Rankine or Rankine-Gordon formula
2.6 Perry- Robertson formula
2.8 Struts with initial curvature
2.9 Struts with eccentric load
2.10 Laterally loaded struts
Comparison of Euler theory with experimental results
British Standard procedure (BS 449)
Alternative procedure for any strut-loading condition
2.1 2 Struts with unsymmetrical cross-section
Examples
Problems
3 Strains Beyond the Elastic Limit
Summary
Introduction
Plastic bending of rectangular-sectioned beams
Shape factor - symmetrical sections
Application to I-section beams
Partially plastic bending of unsymmetrical sections
Shape factor - unsymmetrical sections
Dejections of partially plastic beams
Length of yielded area in beams
Collapse loads - plastic limit design
Residual stresses after yielding: elastic-perfectly plastic material
Torsion of shafts beyond the elastic limit - plastic torsion
Angles of twist of shafts strained beyond the elastic limit
Plastic torsion of hollow tubes
Plastic torsion of case-hardened shafts
Residual stresses after yield in torsion
Plastic bending and torsion of strain-hardening materials
(a) Inelastic bending
(b) Inelastic torsion
Residual stresses - strain-hardening materials
Influence of residual stresses on bending and torsional strengths
Plastic yielding in the eccentric loadirzg of rectangular sections
Plastic yielding and residual stresses under axial loading with stress
concentrations
Plastic yielding of axially symmetric components
(a) Thick cylinders - collapse pressure
(b) Thick cylinders - “auto-frettage ’’
(c) Rotating discs
Examples
Problems
4 Rings, Discs and Cylinders Subjected to Rotation
and Thermal Gradients
Summary
4.2 Rotating solid disc
Thin rotating ring or cylinder
Rotating disc with a central hole
Rotating thick cylinders or solid shafs
Rotating disc of uniform strength
4.6 Combined rotational and thermal stresses in uniform discs and
thick cylinders
Examples
Problems
5 Torsion of Non-Circular and Thin- Walled Sections
Summary
Rectangular sections
Narrow rectangular sections
Thin-walled open sections
Thin-walled split tube
Other solid (non-tubular) shafts
Thin-walled closed tubes of non-circular section (Bredt-Batho theory)
Use of “equivalent J” for torsion of non-circular sections
Thin-walled cellular sections
Torsion of thin-walled stifSened sections
Membrane analogy
EfSect of warping of open sections
Examples
Problems
6 Experimental Stress Analysis
Introduction
Brittle lacquers
Strain gauges
Unbalanced bridge circuit
Null balance or balanced bridge circuit
Gauge construction
Gauge selection
Temperature compensation
Installation procedure
Basic measurement systems
D.C. and A.C. systems
Other types of strain gauge
Photoelasticity
Plane-polarised light - basic polariscope arrangements
Temporary birefringence
Production of fringe patterns
Interpretation of fringe patterns
Calibration
Fractional fringe order determination - compensation techniques
Isoclinics-circular polarisation
Stress separation procedures
Three-dimensional photoelasticity
6.22 Rejective coating technique
6.23 Other methods of strain measurement
Bibliography
7 Circular Plates and Diaphragms
Summary
A. CIRCULAR PLATES
Stresses
Bending moments
General equation for slope and dejection
General case of a circular plate or diaphragm subjected to
combined uniformly distributed load q (pressure) and central
concentrated load F
Uniformly loaded circular plate with edges clamped
Uniformly loaded circular plate with edges freely supported
Circular plate with central concentrated load F and edges clamped
Circular plate with central concentrated load F and edges freely
supported
Circular plate subjected to a load F distributed round a circle
Application to the loading of annular rings
Summary of end conditions
Stress distributions in circular plates and diaphragms subjected to
lateral pressures
Discussion of results - limitations of theory
Other loading cases of practical importance
B. BENDING OF RECTANGULAR PLATES
Rectangular plates with simply supported edges carrying uniformly
distributed loads
Rectangular plates with clamped edges carrying uniformly distributed
loads
Examples
Problems
8 Introduction to Advanced Elasticity Theory
8.1 Types of stress
The Cartesian stress components: notation and sign convention
8.2.1 Sign conventions
The state of stress at a point
Direct, shear and resultant stresses on an oblique plane
Line of action of resultant stress
Line of action of normal stress
Principal stresses and strains in three dimensions - Mohr 's circle
representation
Graphical determination of the direction of the shear stress r,, on an
inclined plane in a three-dimensional principal stress system
The combined Mohr diagram for three-dimensional stress and strain
systems
Application of the combined circle to two-dimensional stress systems
Graphical construction for the state of stress at a point
Construction for the state of strain on a general strain plane
State of stress-tensor notation
The stress equations of equilibrium
Principal stresses in a three-dimensional Cartesian stress system
8.13.1 Solution of cubic equations
Stress invariants - Eigen values and Eigen vectors
Stress invariants
Reduced stresses
Strain invariants
Alternative procedure for determination of principal stresses
8.1 8.1 Evaluation of direction cosines for principal stresses
Octahedral planes and stresses
Deviatoric stresses
Deviatoric strains
Plane stress and plane strain
8.22.1 Plane stress
8.22.2 Plane strain
The stress-strain relations
The strain-displacement relationships
The strain equations of transformation
Compatibility
The stress function concept
8.27.1 Forms of Airy stress function in Cartesian coordinates
8.27.2 Case 1 - Bending of a simply supported beam by a uniformly
8.27.3 The use of polar coordinates in two dimensions
8.27.4 Forms of stress function in polar coordinates
8.27.5 Case 2 - hi-symmetric case: solid shaft and thick cylinder
radially loaded with uniform pressure
8.27.6 Case 3 - The pure bending of a rectangular section
curved beam
8.27.7 Case 4 - Asymmetric case n = 1. Shear loading of a circular
arc cantilever beam
8.27.8 Case 5 - The asymmetric cases n >, 2 -stress concentration at
a circular hole in a tension$eld
8.27.9 Other useful solutions of the biharmonic equation
Examples
Problems
9 Introduction to the Finite Element Method
Introduction
Basis of the finite element method
Applicability of the finite element method
Formulation of the Jinite element method
General procedure of the Jinite element method
9.4.1 Identification of the appropriateness of analysis by the jinite
element method
9.4.2 Identification of the type of analysis
9.4.3 Idealisation
9.4.4 Discretisation of the solution region
9.4.5 Creation of the material model
9.4.6 Node and element ordering
9.4.7 Application of boundary conditions
9.4.8 Creation of a data file
9.4.9 Computer, processing, steps
9.4.10 Interpretation and validation of results
9.4.1 1 Modification and re-run
Fundamental arguments
9.5.1 Equilibrium
9.5.2 Compatibility
9.5.3 Stress-strain law
9.5.4 Forceldisplacement relation
The principle of virtual work
A rod element
9.7.1 Formulation of a rod element using fundamental equations
9.7.2 Formulation of a rod element using the principle of virtual work
equation
A simple beam element
9.8.1 Formulation of a simple beam element using fundamental
equations
93.2 Formulation of a simple beam element using the principle of
virtual work equation
A simple triangular plane membrane element
9.9.1 Formulation of a simple triangular plane membrane element
using the principle of virtual work equation
Formation of assembled stcfiess matrix by use of a dof.
correspondence table
Amlieation of boundarv conditions and uartitioninn r , "
9.12 Solution for displacements and reactims
Bibliography
Examples
Problems
10 Contact Stress, Residual Stress and Stress Concentrations
Summary
10.1 Contact stresses
Introduction
10.1.1 General case of contact between two curved surfaces
10.1.2 Special case I - Contact of parallel cylinders
10.1.3 Combined normal and tangential loading
10.1.4 Special case 2 - Contacting spheres
10.1.5 Design considerations
10.1.6 Contact loading of gear teeth
10.1.7 Contact stresses in spur and helical gearing
10.1.8 Bearing failures
Introduction
10.2.1 Reasom for residual stresses
(a) Mechanical processes
(b) Chemical treatment
(c) Heat treatment
(d) Welds
(e) Castings
10.2 Residual stresses
10.2.2 The injuence of residual stress on failure
10.2.3 Measurement of residual stresses
The hole-drilling technique
X-ray difiaction
10.2.4 Summary of the principal effects of residual stress
Introduction
10.3.1 Evaluation of stress concentration factors
10.3.2 St. Venant 's principle
10.3.3 Theoretical considerations of stress concentrations due to
10.3 Stress concentrations
concentrated loads
(a) Concentrated load on the edge of an infinite plate
(b) Concentrated load on the edge of a beam in bending
10.3.4 Fatigue stress concentration factor
10.3.5 Notch sensitivity
10.3.6 Strain concentration - Neuber 's rule
10.3.7 Designing to reduce stress concentrations
(a) Fillet radius
(b) Keyways or splines
(e) Grooves and notches
(d) Gear teeth
(e) Holes
cf) Oil holes
(g) Screw threads
(h) Press or shrink Jit members
10.3.8 Use of stress concentration factors with yield criteria
10.3.9 Design procedure
References
Examples
Problems
11 Fatigue, Creep and Fracture
Summary
11.1 Fatigue
Introduction
11.1.1 The SIN curve
1 1.1.2 PISIN curves
1 1.1.3 Effect of mean stress
1 1.1.4 Effect of stress concentration
11.1.5 Cumulative damage
1 1.1.6 Cyclic stress-strain
1 1.1.7 Combating fatigue
1 1.1.8 Slip bands and fatigue
Introduction
1 1.2.1 The creep test
1 1.2.2 Presentation of creep data
11.2.3 The stress-rupture test
11.2.4 Parameter methods
1 1.2.5 Stress relaxation
1 1.2.6 Creep-resistant alloys
1 1.3 Fracture mechanics
Introduction
1 1.3.1 Energy variation in cracked bodies
(a) Constant displacement
(b) Constant loading
(a) Grifith 's criterion for fiacture
(b) Stress intensity factor
11.2 Creep
1 1.3.2 Linear elastic fracture mechanics (L.E.F.M.)
1 1.3.3 Elastic-plastic fracture mechanics (E.P.F.M.)
1 1.3.4 Fracture toughness
1 1.3.5 Plane strain and plane stress fracture modes
1 1.3.6 General yielding fracture mechanics
1 1.3.7 Fatigue crack growth
1 1.3.8 Crack tip plasticity under fatigue loading
11.3.9 Measurement of fatigue crack growth
References
Examples
Problems
12 Miscellaneous topics 509
12.1 Bending of beams with initial curvature
12.2 Bending of wide beams
12.3 General expression for stresses in thin-walled
pressure or selj-weight
12.4 Bending stresses at discontinuities in thin shells
1 2.5 Viscoelasticity
References
Examples
Problems
shells subjected to
Appendix 1. npical mechanical and physical properties for
engineering metals
Appendix 2. Typical mechanical properties of non-metals
Appendix 3. Other properties of non-metals
Index

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