Ziegler Mechanics of Solids and Fluids

Erscheinungsjahr 2012
ISBN: 978-1-4684-0512-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 735 Seiten, eBook

Reihe: Mechanical Engineering Series

This book offers a unified presentation of the concepts and most of the practicable principles common to all branches of solid and fluid should be appealing to advanced undergraduate mechanics. Its design students in engineering science and should also enhance the insight of both graduate students and practitioners. A profound knowledge of applied mechanics as understood in this book may help to cultivate the versatility that the engineering community must possess in this modern world of high-technology. This book is, in fact, a reviewed and extensively improved second edition, but it can also be regarded as the first edition in English, translated by the author himself from the original German version, "Technische Mechanik der festen und flOssigen Korper," published by Springer-Verlag, Wien, in 1985. Although this book grew out of lecture notes for a three semester course for advanced undergraduate students taught by the author and several colleagues during the past 20 years, it contains sufficient material for a subsequent two-semester graduate course. The only prerequisites are basic algebra and analysis as usually taught in the first year of an undergraduate engineering curriculum. Advanced mathematics as it is required in the progress of mechanics teaching may be taught in parallel classes, but also an introduction into the art of design should be offered at that stage.

Zielgruppe

Research

Autoren/Hrsg.

Ziegler, Franz

Inhaltsverzeichnis

1. Kinematics.- 1.1. Point Kinematics.- 1.1.1. Example: The Trajectory in a Homogeneous Gravity Field Above a “Flat Planet”.- 1.1.2. Example: Guided Motion of a Point.- 1.1.3. The Natural Coordinates of the Trajectory.- 1.2. Kinematics of Rigid Bodies.- (§) Show ? to be a Free Vector.- (§) Reduction of Angular Velocity Vectors.- 1.2.1. Special Motions of a Rigid Body.- (§) Pure Translation.- (§) Rotation About a Fixed Point.- (§) Plane Motion of Rigid Bodies.- (§) Example: The Wheel in a Straight Rolling Motion.- (§) Acceleration.- 1.3. Kinematics of Deformable Bodies.- 1.3.1. Elongation and Shear.- 1.3.2. Dilatation and Strain Deviations.- 1.3.3. Streamlines and Streamtubes: Local and Convective Acceleration.- 1.3.4. Kinematic (Geometric) Boundary Conditions.- 1.4. Supplements to and Applications of Point and Rigid-Body Kinematics.- 1.4.1. The Velocity Diagram of Plane Motion.- 1.4.2. Kinematics of the Planetary Gear Train.- 1.4.3. The Universal Joint (after Kardan).- 1.4.4. Central Motion (The Kepler Problem): Polar Coordinates.- 1.5. Supplements to and Applications of Deformation Kinematics.- 1.5.1. The Uniaxial Homogeneous Deformation.- 1.5.2. The Natural Coordinates of the Streamline.- 1.5.3. The Strain Tensor. The Plane Strain State.- (§) The Tensor Property of the Strain Matrix.- (§) The Principal Axes Transformation, Mohr’s Circle.- 1.6. Conservation of Mass: The Continuity Equation.- 1.6.1. Stationary Flow Through a Conical Pipe: Eulerian and Lagrangean Representations.- 1.7. Exercises A 1.1 to A 1.8 and Solutions.- 2. Statics, Systems of Forces, Hydrostatics.- 2.1. Forces, Body-Forces, Tractions, Stresses, Equilibrium.- 2.1.1. Stresses in a Tensile Rod: Mohr’s Circle.- 2.1.2. Plane State of Stress: Mohr’s Circle.- 2.1.3. General State ofStress.- 2.1.4. Mean Normal Stress and Stress Deviations.- 2.2. Systems of Forces.- 2.2.1. The Plane Force System: Computational and Graphic Reduction, Conditions of Equilibrium.- (§) Example: Support Reactions of an In-Plane Loaded Structure.- 2.2.2. Symmetry of the Stress Tensor.- 2.2.3. The Parallel Force System: Center of Forces, Center of Gravity (Centroids), Static Moments.- 2.3. Hydrostatics.- 2.3.1. Fluid Under Gravity.- (§) Incompressible Fluid.- (§) A Linear Compressive Spring.- (§) A Nonlinear Spring.- 2.3.2. Pressurized Fluids.- (§) Principle of the Hydraulic Pump.- (§) Vessels and Pipes.- 2.3.3. The Gravitational Hydrostatic Pressure in Open Containers.- (§) A Flat Horizontal Base of Area A.- (§) A Plane Retaining Wall of Area A.- (§) Circular Cylindrical Surface (Fig. 2.23).- (§) Hydrostatic Pressure on a Spherical Surface (Fig. 2.24).- (§) Hydrostatic Loading of a Doubly Curved Surface.- (§) Illustrative Example: Uplift.- 2.3.4. The Hydrostatic Buoyancy.- (§) The Upright Floating Cylinder: Stability (Fig. 2.26).- (§) Floating Cylinder with Horizontal Axis: Stability.- (§) Buoyancy.- 2.4 Moments of Inertia of a Plane Area A and Their Rules of Transformation.- (§) Moments of Inertia About Parallel Axes.- (§) Moments of Inertia About Rotated Axes (Mohr’s Circle).- (§) The Ellipse of Inertia.- (§) Example: The Central Ellipse of a Rectangle, A= B × H.- 2.5. Statics of Simple Structures.- 2.5.1. Beams and Frames.- 2.5.1.1. Local Equilibrium of a Plane Arch and Plane Beam Element (Fig. 2.31).- 2.5.1.2. Straight Beams, Force and Funicular Polygon.- (§) The Cantilever Beam.- (§) The Hinged-Hinged Beam.- (§) Illustrative Example: Eccentrical Axial Force.- (§) The Graphic Solution by Means of the Force and Funicular Polygon.- (§)Continuous (Multispan) Beams.- 2.5.1.3. Influence Lines.- 2.5.1.4. Plane Frames and the Three-Hinged Arch.- 2.5.1.5. Two Statically Determinate Stress States.- (§) Bending Stresses in a Sandwich Cross-Section.- (§) Torsional Shear Stresses in a Thin-Walled Tube.- 2.5.2. Trusses.- 2.5.2.1.Planar Trusses.- 2.5.3. Statics of Flexible Cables (and Chains).- 2.6. Exercises A 2.1 to A 2.15 and Solutions.- 3. Mechanical Work, Power, Potential Energy.- 3.1. Work and Power of Single Forces and Couples.- 3.1.1. Example: The Work of Gravity Forces.- 3.1.2. Example: The Work of a Couple.- 3.2. Power Density, Stationary and lrrotational Forces, Potential Energy.- 3.3. Potential Energy of External Forces.- 3.3.1. Homogeneous and Parallel Gravity, Potential of the Dead Weight.- 3.3.2. Central Force Field with Point Symmetry.- 3.4. Potential Energy of Internal Forces.- 3.4.1. The Elastic Potential of the Hookean Solid (Linear Spring).- (§) Example: A Simple Truss.- 3.4.2. The Barotropic Fluid.- 3.5. Lagrangean Representation of the Work of Internal Forces, Kirchhoff’s Stress Tensor.- 3.6. Exercises A 3.1 to A 3.2 and Solutions.- 4. Constitutive Equations.- 4.1. The Elastic Body, Hooke’s Law of Linear Elasticity.- 4.1.1. The Linear Elastic Body, Hooke’s Law.- (§) The Bending Test.- (§) The Torsional Test.- 4.1.2. A Note on Anisotropy.- (§) Plane Stress State.- (§) Transverse Isotropy Lateral to the X Axis.- 4.1.3. A Note on Nonlinearity.- 4.2. The Visco-Elastic Body.- 4.2.1. Newtonian Fluid.- (§) Illustrative Example.- (§) The One-Dimensional Viscous Model.- 4.2.2. Linear Visco-Elasticity.- (§) The Kelvin-Voigt Body.- (§) Maxwell Fluid.- (§) The Multiple-Parameter Linear Visco-Elastic Body.- (§) General Linear Viscoelasticity.- 4.2.3. A Nonlinear Visco-ElasticMaterial.- (§) Example: The Creep Collapse of a Tensile Rod.- 4.3. The Plastic Body.- 4.3.1. The Rigid-Plastic Body.- 4.3.2. The Elastic-Plastic Body.- 4.3.3. The Visco-Plastic Body.- 4.4. Exercise A 4.1 and Solution.- 5. Principle of Virtual Work.- 5.1. Example: The Three-Hinged Arch.- 5.2. Influence Lines of Statically Determinate Structures.- 5.3. Conservative Mechanical Systems.- 5.3.1. Differential Equation of the Deflection of a Linear Elastic Beam.- 5.3.2. The von Karman Plate Equations.- 5.4. Principle of Complementary Virtual Work.- 5.4.1. Castigliano’s Theorem and Menabrea’s Theorem.- (§) The Linear Elastic, Thin, and Straight Rod.- (§) A Plane Truss with a Single Internal Static Indeterminacy (Fig. 5.7).- (§) A Double-Span Beam Loaded According to Fig. 5.9.- (§) Deflection of a Uniformly Loaded Cantilever.- (§) The Plane Snap Under the Action of Tip Forces.- 5.4.2. Betti’s Method.- (§) Thin-Walled Structures Free of Any Torsion..- (§) The Cantilever of Fig. 5.11.- (§) The Cantilever with an Additional Simple Support, Fig. 5.13.- 5.4.3. Transformation of the Principles of Minimum Potential and Complementary Energy.- 5.5. Exercises A 5.1 to A 5.4 and Solutions.- 6. Selected Topics of Elastostatics.- 6.1. Continuum Theory of Linearized Elastostatics.- (§) The One-Dimensional Problems of Linear Elasticity.- (§) Shrink Fit.- 6.1.1. Thermoelastic Deformations.- (§) The Complementary Energy of a Thermally Loaded Rod.- (§) Example: A Single-Span Redundant Beam.- (§) Maysel’s Formula of Thermoelasticity.- (§) A Hollow Sphere with Point Symmetry and a Thick-Walled Cylinder with Axial Symmetry, Maysel’s Formula.- 6.1.2. Saint Venant’s Principle.- 6.1.3. Stress and Strain Hypotheses.- (§) Principal Normal Stress Hypothesis.- (§) Hencky-vonMises Energy Hypothesis.- (§) Mohr-Coulomb Stress Hypothesis.- (§) The Concept of Allowable Stress.- 6.2. Rods and Beams with Straight Axes.- (§) Normal Force and Bending Moments.- 6.2.1. Shear Stresses and Deformations due to a Shear Force.- (§) Rectangular Cross-Section.- (§) Maximal Shear in an Elliptic or Circular Cross-Section.- (§) Equation (6.58) when Applied to the T Cross-Section.- (§) Example: Deflection of a Cantilever in Shear Bending.- 6.2.2. Mohr’s Method of Calculating Deflections.- (§) Mohr’s Analytic Method Applied to the Cantilever of Fig. 6.9.- (§) Mohr’s Graphic Method Applied to the Cantilever of Fig. 6.9.- (§) Influence Lines of Deformations by Mohr’s Method.- (§) Mohr’s Method.- (§) The Multispan Beam of Fig. 6.13.- 6.2.3. Thermal Stresses in Beams.- (§) The Single-Span, Simply Supported Beam.- (§) A Redundant Single-Span Beam.- 6.2.4. Torsion.- 6.2.4.1. Thin-Walled, Single- and Multiple-Cell Cross-Sections.- 6.2.4.2. Thin-Walled Open Cross-Sections.- (§) Torsion of a Thin-Walled Bar with Rectangular Cross-Section.- (§) Generalization of Eq. (6.134).- (§) Constrained Warping.- (§) The Cantilever with a C-Profile of Fig. 6.17.- 6.2.4.3. Torsion of Elliptic and Circular, Full and Hollow Cylinders.- (§) Elliptic Cross-Section.- 6.2.4.4. Torsion of a Notched Circular Shaft.- 6.2.4.5. Prandtl’s Membrane and an Electric Analogy.- 6.3. Multispan Beams and Frames.- (§) The Force Method of the Multispan Beam.- (§) The Deformation Method.- (§) The Deformation Method Applied to Frames.- 6.3.1. The Planar Single-Story Frame.- 6.4. Plane-Curved Beams and Arches.- (§) The Complementary Energy of the Curved Beam.- 6.4.1. Slightly Curved Beams and Arches.- (§) The Slightly Curved Parabolic Arch of Fig. 6.27.- (§) The SlightlyCurved Ring.- (§) Spinning Rings.- 6.5. In-Plane Loaded Plates.- 6.5.1. The Semiinfinite Plate.- (§) The Boussinesq Problem.- (§) The Stress Function in the Case of a Tangential Single Force.- 6.5.2. Stationary Spinning Disks.- 6.5.3. The Infinite Plate with a Circular Hole: Kirsch’s Problem.- 6.5.4. Thermal Membrane Stresses in Plates.- 6.6. Flexure of Plates.- 6.6.1. Axisymmetric Flexure of Circular Kirchhoff Plates.- 6.6.2. The Infinite Plate Strip.- 6.6.3. The Rectangular Plate with Four Edges Simply Supported.- 6.6.4. Thermal Deflection of Plates.- (§) A Plate of Quadratic Planform.- (§) The Infinite Plate.- 6.7. Thin Shells of Revolution.- (§) Membrane Stresses.- (§) Bending Perturbation of the Membrane State.- 6.7.1. Thin Circular Cylindrical Shells.- (§) The Open Cylindrical Storage Tank.- 6.7.2. The Semispherical Dome of Fig. 6.39.- 6.7.3. Thermal Stresses in Thin Shells of Revolution.- (§) The Radial Thermal Expansion of a Circular Cylindrical Shell.- 6.8. Contact Problems (The Hertz Theory).- 6.9. Stress-Free Temperature Fields, Fourier’s Law of Heat Conduction.- 6.10. The Elastic-Visco-Elastic Analogy.- 6.10.1. The Creeping Simply Supported Single-Span Beam.- 6.10.2. The Heated Thick-Walled Pipe (Fig. 6.42).- 6.11. Exercises A 6.1 to A 6.22 and Solutions.- 7. Dynamics of Solids and Fluids, Conservation of Momentum of Material and Control Volumes.- 7.1. Conservation of Momentum.- 7.2. Conservation of Angular Momentum.- 7.3. Applications of Control Volumes.- 7.3.1. Stationary Flow Through an Elbow.- (§) The Plane Elbow.- (§) A Nozzle with a Straight Axis.- (§) Plane U-Shaped Elbow.- 7.3.2. Thrust of a Propulsion Engine.- 7.3.3. Euler”s Turbine Equation.- 7.3.4. Water Hammer in a Straight Pipeline.- 7.3.5. Carnot s Loss of Pressure Head.-7.4. Applications to Rigid-Body Dynamics.- 7.4.1. The Rolling Rigid Wheel.- 7.4.2. Cable Drive.- 7.4.3. Dynamics of the Crushing Roller (Fig. 1.3).- 7.4.4. Swing Crane with a Boom.- 7.4.5. Balancing of Rotors.- 7.4.6. The Gyro-Compass.- 7.4.7. The Linear Oscillator.- (§) Periodic Forcing Function, F(t) = F(t + Te).- (§) Excitation by a Nonperiodic Forcing Function.- (§) Representation of the Motion in the Phase Plane (?, d?/dt).- (§) Some Structural Models of the Linear Oscillator.- (§) Linear Torsional Vibrations.- 7.4.8. Nonlinear Vibrations.- (§) Motion of a Planar Pendulum.- (§) SDOF-System with Dry Friction.- 7.4.9. Linear Elastic Chain of Oscillators.- (§) The Residual Method of Holzer and Tolle.- (§) Dunkerly’s Formula.- (§) Natural Modes.- (§) The Amplitude Frequency Response Functions of the Two-Mass System.- 7.5. Bending Vibrations of Linear Elastic Beams.- (§) Natural and Forced Vibrations of a Slender, Hinged-Hinged, Single-Span Beam.- 7.6. Body Waves in the Linear Elastic Solid.- (§) The Longitudinal Wave.- (§) The Shear Wave.- 7.7. Exercises A 7.1 to A 7.12 and Solutions.- 8 First Integrals of the Equations of Motion, Kinetic Energy.- 8.1. The Power Theorem and Kinetic Energy.- 8.2. Conservation of Mechanical Energy.- 8.3. Kinetic Energy of a Rigid Body.- 8.3.1. Pure Rotation of the Rigid Body About a Fixed Point 0.- 8.3.2. Rotation About an Axis ea Fixed in Space.- 8.4. Conservation of Energy in SDOF-Systems.- 8.4.1. Motion of a Linear Oscillator After Impact (Fig. 8.1).- 8.4.2. The Basic Vibrational Mode of a Linear Elastic Beam.- 8.4.3. Acceleration of a Motorized Vehicle.- 8.4.4. The Turning Points of a Nonlinear, Dry-Friction Oscillator.- 8.5. Bernoulli’s Equation of Fluid Mechanics.- 8.5.1. Stationary Flow with Power Charging orDischarging.- 8.5.2. Velocity of Efflux from a Small Aperture in an Open Vessel or a Pressurized Tank (Fig. 8.5).- 8.5.3. Stationary Flow Round an Immersed Rigid Body at Rest.- 8.5.4. Inviscid Flow Along a Rigid Wall.- 8.5.5. Pressure in a Pipe Measured by a Gully.- 8.5.6. Prandtl’s Tube and Pitot’s Tube.- 8.5.7. Transient Flow in a Drain Pipe Controlled by a Cock.- 8.5.8. Free Vibrations of a Fluid in an Open U-Shaped Pipe.- 8.5.9. Lossless Flow Through a Diffusor.- 8.5.10. A Bernoulli-Type Equation in a Rotating Reference System.- (§) Example: Segner’s Water Wheel.- 8.6. Remarks on the First Law of Thermodynamics (Conservation of Energy).- 8.7. Exercises A 8.1 to A 8.5 and Solutions.- 9. Stability Problems.- 9.1. Stability of an Equilibrium Configuration.- (§) Hanging Pendulum.- (§) Upright Position of the Pendulum.- 9.1.1. Example: The Balancing Problem of Heavy Rigid Cylinders.- 9.1.2. Example: A Simple Model of Buckling.- 9.1.3. Example: Stability of a Shallow Structure Under Lateral Load.- 9.1.4. Example: Buckling of Slender Elastic Columns (Euler Buckling).- 9.1.5. The Eccentrically Loaded Linear Elastic Column.- 9.1.6. Buckling of Thin Plates.- (§) Rectangular Simply Supported Plate.- 9.2. Stability of Motion.- 9.2.1. Example: The Centrifugal Governor.- 9.2.2. Stability of the Steady State of the Spinning Unsymmetric Gyroscope.- 9.3. Bounds of Stability of Equilibrium of Elastic-Plastic Structures: Limit Load Analysis.- 9.3.1. The Limit Load of the Single-Story Elastic-Plastic Frame.- 9.4. Stability of Motion of Elastic-Plastic Bodies (Cyclic Plasticity).- 9.5. Stability of the Flow in Dipping Open Channels, the Hydraulic Jump.- 9.6. Flutter Instability.- 9.7. Exercises A 9.1 to A 9.7 and Solutions.- 10. D’Alembert’s Principle and LagrangeEquations of Motion.- (§) A Point Mass m Carrying a Charge q, the Lorentz Force.- 10.1. Natural Vibrations of an Elastically Supported Foundation.- 10.2. Pendulum with Moving Support.- 10.2.1. Horizontal Motion of the Support.- 10.2.2. Vertical Motion of the Support.- 10.3. MDOF-Vibrational System of Point Masses Supported by a Mass-Less String.- 10.4. MDOF-Vibrational System of Point Masses Supported by a Mass-Less Beam.- 10.5. Planar Framed System with External Viscous Damping.- 10.6. Vibrational Testing by an Unbalanced Rotor.- 10.7. Exercises A 10.1 to A 10.3 and Solutions.- 11. Some Approximation Methods of Dynamics and Statics.- 11.1. The Rayleigh-Ritz-Galerkin Approximation Method.- 11.1.1. The Rayleigh-Ritz Method and the Lagrange Equations of the Equivalent MDOF-System.- 11.1.2. The Galerkin Procedure.- 11.1.3. Complete Algebraization of the Lagrange Equations of Motion.- 11.1.4. Forced Vibrations of a Nonlinear Oscillator.- 11.2. Illustrations of Linearized Elastic Systems with Heavy Mass and Soft Spring, SDOF Equivalent System.- 11.2.1. Longitudinal Vibrations.- 11.2.2. Bending Vibrations.- 11.2.3. Torsional Vibrations.- 11.2.4. Single-Story Frame.- 11.2.5. Thin Elastic Circular Plate with a Centrally Attached Heavy Mass.- 11.3. Examples of Elastic Structures with Abstract Equivalent Systems.- 11.3.1. Free Flexural Vibrations of a Prestressed Slender Beam.- 11.3.2. Buckling Load of the Euler Column on an Elastic Foundation.- 11.3.3. Torsional Rigidity of an Elastic Rod with a Rectangular Cross-Section.- 11.4. The Finite-Element Method (FEM).- 11.4.1. A Beam Element.- 11.4.2. The Planar Triangular Plate Element.- 11.5. Linearization of Nonlinear Equations of Motion.- (§) Linearization by Harmonic Balance.- (§) Transient Vibrations of Nonlinear Systems.-11.6. Numerical Integration of a Nonlinear Equation of Motion.- 11.7. Exercises A11.1 to A 11.11 and Solutions.- 12. Impact.- 12.1. Finite Relations of Momentum and Angular Momentum.- 12.1.1. Example: Impacting a Rigid-Plate Pendulum.- 12.1.2. Example: Axial Impact of a Deformable (Elastic) Column.- 12.2. Lagrange Equations of Idealized Impact.- 12.2.1. Example: Impacting a Chain-Type Pendulum (MDOF-S).- 12.2.2. Lateral Impact Loading of a Simply Supported (Elastic) Beam.- 12.3. Idealized Elastic and Inelastic Impact Processes.- 12.3.1. The Idealized Elastic Impact.- 12.3.2. The Idealized Inelastic Impact.- 12.3.3. Example: Collision of Two Point Masses.- (§) Idealized Elastic Impact.- (§) Idealized Inelastic Impact.- 12.4. The “Ballistic” Pendulum and the Center of Impact.- (§) Conservation of Energy.- (§) Inelastic Impact.- 12.5. Sudden Fixation of an Axis of Rotation.- 12.6. Dynamic Magnification Factor of Axial and Lateral Impact.- 12.7. Axial Impact of a Thin Elastic Rod, Wave Propagation.- 12.8. Water Hammer, Wave Propagation.- 12.9. Exercises A 12.1 to A 12.3 and Solutions.- 13. Elementary Supplements of Fluid Dynamics.- 13.1. Circulation and the Vortex Vector.- 13.2. The Hydrodynamic Lift Force.- 13.3. The Navier-Stokes Equations, Similarity Solutions.- 13.3.1. Viscous Pipe Flow.- 13.3.2. The Boundary Layer of a Plate.- 13.4. Potential Flow, the Singularity Method.- 13.4.1. Illustrative Examples.- (§) Two-Dimensional Potential Flow Toward a Rigid Wall.- (§) Two-Dimensional Flow in a Corner Space and Round a Sharp Edge.- (§) Singular Potential Flows.- 13.4.2. The Singularity Method.- (§) Superposition of a Line Source and a Parallel Main Stream.- (§) Superposition of Potential Vortex Lines and a Parallel Main Stream.- 13.4.3. Hydrodynamic Forces inTwo-Dimensional and Stationary Potential Flow, the Blasius Formula.- 13.4.4. von Karman Trail of Vortices, the Strouhal Number.- 13.4.5. The Hydrodynamic Pressure at the Face of a Moving Dam.- 13.4.6. Stationary Efflux of Gas from a Pressure Vessel.- 13.5. Momentum Integral Method of Boundary-Layer Analysis.- 13.6. Exercises A 13.1 to A 13.4 and Solutions.- Table A. Some Average Values of Mechanical Material Parameters.