Table of Contents

Preface Notation CHAPTER I. TORSION 1. Non-circular Prisms 2. Saint-Venant's Theory 3. Prandtl's Membrane Analogy 4. Kelvin's Fluid-flow Analogy 5. Hollow Sections 6. Warping of the Cross Sections 7. Round Shafts of Variable Diameter 8. Jacobsen's Electrical Analogy CHAPTER II. ROTATING DISKS 9. Flat Disks 10. Disks of Variable Thickness 11. Disks of Uniform Stress CHAPTER III. MEMBRANE STRESSES IN SHELLS 12. General Theory 13. Applications 14. Shells of Uniform Strength 15. Non-symmetrical Loading CHAPTER IV. BENDING OF FLAT PLATES 16. General Theory 17. Simple Solutions; Saint-Venant's Principle 18. Circular Plates 19. Catalogue of Results 20. Large Deflections CHAPTER V. BEAMS ON ELASTIC FOUNDATION 21. General Theory 22. The Infinite Beam 23. Semi-infinite Beams 24. Finite Beams 25. Applications; Cylindrical Shells CHAPTER VI. TWO-DIMENSIONAL THEORY OF ELASTICITY 26. The Airy Stress Function 27. Applications to Polynomials in Rectangular Coordinates 28. Polar Coordinates 29. "Kirsch, Boussinesq, and Michell" 30. Plasticity CHAPTER VII. THE ENERGY METHOD 31. The Three Energy Thereoms 32. Examples on Least Work 33. Proofs of the Theorems 34. Bending of Thin-walled Curved Tubes 35. Flat Plates in Bending CHAPTER VIII. BUCKLING 36. Rayleigh's Method 37. Coil Springs; Beams on Elastic Foundation 38. Proof of Rayleigh's Theorem 39. Vianello's or Stodola's Method 40. "Rings, Boiler Tubes, and Arches" 41. Twist-bend Buckling of Beams 42. Buckling of Shafts by Torsion 43. Twist Buckling of Columns 44. Thin Flat Plates CHAPTER IX. MISCELLANEOUS TOPICS 45. Mohr's Circle for Three Dimensions 46. Torsion of Pretwisted Thin-walled Sections 47. The Theorems of Biezeno and Spielvogel Problems Answers to Problems Index

About the Author

J. P. Den Hartog: The Reprint Engineer J. P. Den Hartog (1901-1989), who taught for most of his career at MIT, was one of the founders of the Dover reprint program in engineering. As the author of several books that Dover reprinted and still has in print, and as an advisor from the 1950s until just a few years before his death in 1989, Professor Den Hartog gave invaluable advice concerning books of lasting interest and importance in his field. Not many books in engineering have a productive shelf life spanning several decades. Among the exceptions are these four books of Professor Den Hartog, which Dover reprinted and occasionally revised in later printings from 1961 through 1987: Mechanics, 1961, Strength of Materials, 1961, Mechanical Vibrations, 1985, and Advanced Strength of Materials, 1987. Still widely read and cited by authors in these areas, Den Hartog's books are a tribute to his gift for exposition and clarity. The J. P. Den Hartog Award, established in 1987, is presented in recognition of lifetime contributions to the teaching and practice of vibration engineering.