كتاب Mechanics of Materials I

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Mechanics of Materials I

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Simple Stress and Strain
Load
Direct or normal stress (a)
Direct strain ( E )
Sign convention for direct stress and strain
Elastic materials - Hooke’s law
Modulus of elasticity - Young’s modulus
Tensile test
Ductile materials
Brittle materials
Poisson’s ratio
Application of Poisson’s ratio to a two-dimensional stress system
Shear stress
Shear strain
Modulus of rigidity
Double shear
Allowable working stress -factor of safety
Load factor
Temperature stresses
Stress concentrations -stress concentration factor
Toughness
Creep and fatigue
Examples
Problems
Bibliography
Compound Bars
Summary
Compound bars subjected to external load
vi Contents
Compound bars - ‘equivalen”t or “combined” modulus
Compound bars subjected to temperature change
Compound bar (tube and rod)
Compound bars subjected to external load and temperature effects
Compound thick cylinders subjected to temperature changes
Examples
Problems
Shearing Force and Bending Moment Diagrams
Summary
Shearing force and bending moment
Shearing force (SF) sign convention
Bending moment (BM) sign convention
SF and BM diagrams for beams carrying concentrated loads only
SF and BM diagrams for uniformly distributed loads
SF and BM diagrams for combined concentrated and uniformly
distributed loads
Points of contrafexure
Relationship between SF Q BM M and intensity of loading w
SF and BM diagrams for an applied couple or moment
SF and BM diagrams for inclined loa&
Graphical construction of SF and BM diagrams
SF and BM diagrams for beams carrying distributed loads of
increasing value
SF at points of application of concentrated loads
Examples
Problems
Bending
Summary
Introduction
Simple bending theory
Neutral axis
Section modulus
Second moment of area
Skew loading
Bending of composite or fitched beams
Reinforced concrete beams -simple tension reinforcement
Combined bending and direct stress -eccentric loading
Shear stresses owing to bending
Strain energy in bending
Limitations of the simple bending theory
“Middle-quarter ” and “middle-third ” rules
Examples
Problems
Slope and Deflection of Beams
Summary
Introduction
Direct integration method
MacaulayS method
Macaulay’s method for udls
Macaulay’s method for beams with ud applied over part of the beam
Macaulay’s method for couple applied at a point
Mohr’s “area-moment” method
Principle of superposition
Energy method
Maxwell’s theorem of reciprocal displacements
Continuous beams - CIapeyron’s “three-moment ” equation
Finite difference method
Defections due to temperature effects
Relationship between loading SF BM slope and akfection
Examples
Problems
Built-in Beams
Summary
Introduction
Built-in beam carrying central concentrated load
Built-in beam carrying uniformly distributed load across the span
Built-in beam carrying concentrated load offset from the centre
Built-in beam carrying a non-uniform distributed load
Advantages and disadvantages of built-in beams
Effect of movement of supports
Contents
Vlll
Shear Stress Distribution
Summary
Introduction
Distribution of shear stress due to bending
Application to rectangular sections
Application to I-section beams
Vertical shear in the web
Vertical shear in the flanges
Horizontal she& in the flanges
Application to circular sections
Limitation of shear stress distribution theory
Shear centre
Examples
Problems
Torsion
Summary
Simple torsion theory
Polar second moment of area
Shear stress and shear strain in shafts
Section modulus
Torsional rigidity
Torsion of hollow shafts
Torsion of thin-walled tubes
Composite shafts -series connection
Composite shafts -parallel connection
Principal stresses
Strain energy in torsion
Variation of data along shaft length -torsion of tapered shafts
Power transmitted by shafts
Combined stress systems -combined bending and torsion
Combined bending and torsion - equivalent bending moment
Combined bending and torsion -equivalent torque
Combined bending torsion and direct thrust
Combined bending torque and internal pressure
Thin Cylinders and Shells
Summary
Thin cylinders under internal pressure
Hoop or circumferential stress
Longitudinal stress
Changes in dimensions
Thin rotating ring or cylinder
Thin spherical shell under internal pressure
Change in internal volume
Vessels subjected to JIuid pressure
Cylindrical vessel with hemispherical end
Effects of end plates and joints
Examples
Problems
Wire-wound thin cylinders
Thick cylinders
Summary
Longitudinal stress
Maximum shear stress
Change of cylinder dimensions
Compound cylinders
Compound cylinders -graphical treatment
Shrinkage or interference allowance
Hub on solid shaji
Force fits
Compound cylinder -different materials
Uniform heating of compound cylinders of different materials
Failure theories -yield criteria
Plastic yielding - “auto-frettage”
Wire-wound thick cylinders
Difference in treatment between thin and thick cylinders -basic
assumptions
Development of the Lame theory
Thick cylinder - internal pressure only
Comparison with thin cylinder theory
Graphical treatment - Lame line
X Contents
Strain Energy
Summary
Introduction
Strain energy -shear
Strain energy -bending
Strain energy - torsion
Strain energy of a three-dimensional principal stress system
Volumetric or dilatational strain energy
Shear or distortional strain energy
Suddenly applied loads
Impact loads -axial load application
Impact loads -bending applications
Castigliano’s first theorem for deflection
“Unit-load ” method
Application of Castigliano ’s theorem to angular movements
Shear deflection
Examples
Problems
Strain energy - tension or compression
Springs
Summary
Introduction
Close-coiled helical spring subjected to axial load W
Close-coiled helical spring subjected to axial torque T
Open-coiled helical spring subjected to axial load W
Open-coiled helical spring subjected to axial torque T
Springs in series
Springs in parallel
Allowable stresses
Leaf or carriage spring: semi-elliptic
Leaf or carriage spring: quarter-elliptic
Spiral spring
Limitations of the simple theory
Extension springs - initial tension
Con tents
Complex Stresses
Summary
Stresses on oblique planes
Material subjected to pure shear
Material subjected to two mutually perpendicular direct stresses
Material subjected to combined direct and shear stresses
Principal plane inclination in terms of the associated principal stress
Graphical solution - Mohr 's stress circle
Alternative representations of stress distributions at a point
Three-dimensional stresses -graphical representation
Examples
Problems
Complex Strain and the Elastic Constants
Summary
Linear strain for tri-axial stress state
Principal strains in terms of stresses
Principal stresses in terms of strains -two-dimensional stress system
Bulk modulus K
Volumetric strain
Effect of lateral restraint
Strains on an oblique plane
Principal strain - Mohr s strain circle
Mohr 's strain circle -alternative derivation from the
Relationship between Mohr 's stress and strain circles
Construction of strain circle from three known strains
Analytical determination of principal strains from rosette readings
Alternative representations of strain distributions at a point
I Strain energy of three-dimensional stress system
Volumetric strain for unequal stresses
Change in volume of circular bar
Relationship between the elastic constants E G K and v
general stress equations
(McClintock method) -rosette analysis
Theories of Elastic Failure
Summary
Introduction
Maximum principal stress theory
Maximum shear stress theory
Maximum principal strain theory
Maximum total strain energy per unit volume theory
Maximum shear strain energy per unit volume (or distortion energy)
theory
Mohr 's modijied shear stress theory for brittle materials
Graphical representation of failure theories for two-dimensional
stress systems (one principal stress zero)
Graphical solution of two-dimensional theory of failure problems
Graphical representation of the failure theories for three-dimensional
stress systems
Ductile materials
Brittle materials
Limitations of the failure theories
Eflect of stress concentrations
Safety factors
Modes of failure
Examples
Problems
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
DC and AC 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
Reflective coating technique
Other methods of strain measurement
Bibliography
Appendix Typical mechanical and physical pro'prties for engineering
materials
Appendix Typical mechanical properties of non-metals
Appendix Other properties of non-metals
Index

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كتاب Mechanics of Materials I 4276