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Strength of materials - For technical and industrial schools
STRENGTH OF MATERIALS
A TEXT BOOK FOR TECHNICAL AND INDUSTRIAL SCHOOLS
BY JOHN PAUL KOTTCAMP
Head of Department of Industrial Mechanical Engineering Pratt Institute, Brooklyn, N. Y.
NEW YORK;JOHN WILEY & SONS, INC; 1919
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PREFACE
This text is the result of over twelve years 7 experience in teaching the subject of strength of materials to the students at Pratt Institute. An attempt has been made to present the fundamental and underlying principles with a minimum of mathematics. These principles are applied by the introduction of a large number of examples which are worked out in detail. It is only by the working of original problems that the student is able to test his knowledge of the subject.
Many of the applications are made more particularly to mechanical lines of work, and yet the student who proposes to follow structural work will find the text of great help to him.
The text covers the application of strength of materials in the proportioning of beams, columns, shafting, riveted joints, and in problems dealing with simple stresses.
Chapter I has been made of an introductory nature, the desire being to present very briefly, but concisely, the simple laws of equilibrium, so that the student may be able quickly and accurately to analyze the forces acting in any machine or machine part.
A chapter is inserted dealing with the testing, and the production of the more common materials of construction.
It has been the experience of the author that only by the assigning of original problems in class is the instructor able to test the grasp of the subject the student is securing, and, therefore, recommends the use of 3X5 cards on which are placed problems which the student has not seen prior to entering class.
Many of the applications are made more particularly to mechanical lines of work, and yet the student who proposes to follow structural work will find the text of great help to him.
The text covers the application of strength of materials in the proportioning of beams, columns, shafting, riveted joints, and in problems dealing with simple stresses.
Chapter I has been made of an introductory nature, the desire being to present very briefly, but concisely, the simple laws of equilibrium, so that the student may be able quickly and accurately to analyze the forces acting in any machine or machine part.
A chapter is inserted dealing with the testing, and the production of the more common materials of construction.
It has been the experience of the author that only by the assigning of original problems in class is the instructor able to test the grasp of the subject the student is securing, and, therefore, recommends the use of 3X5 cards on which are placed problems which the student has not seen prior to entering class.
CONTENTS
CHAPTER I CONDITIONS OF EQUILIBRIUM
ART. 1. Definitions. ART. 2. Moments. ART. 3. Resultant Force, Graphical and Algebraic. ART. 4. General Conditions of Equilibrium as Applied to Systems of Coplanar Forces. Problems.
CHAPTER II SIMPLE STRESSES
ART. 5. Unit Stress, Kinds of Stresses. ART. 6. Elastic Limit, Table of Elastic Limits of Materials, Permanent Set. ART. 7. Ultimate Strength, Factor of Safety, Real and Apparent. Tables. ART. 8. Shear, Ultimate Shearing Strength. ART. 9. Design Problems, Rules for Solution of Problems and Recording of Calculations.
CHAPTER III MATERIALS OF CONSTRUCTION
ART. 10. Testing Machines, Construction and Operation. ART. 11. Tension and Compression Tests, Modulus of Elasticity. ART. 12. Cast Iron, its Manufacture and Properties. ART. 13. Wrought Iron, Puddling Furnace. ART. 14. Steel, Manufacture and Properties, Open-hearth Furnace. ART. 15. Timber, Stone, and Brick, Table of Properties. ART. 16. General Properties of Construction Materials. ART. 17. Practical Review Problems.
CHAPTER IV THEORY OF BEAMS
ART. 18. Beam Reactions, Method of Checking Results. ART. 19. Bending Moment. ART. 20. General Rule for Bending Moment Applied to Various Types of Beams. ART. 21. Internal Resisting Moments, Section Modulus. ART. 22. Center of Gravity, General Rule, Method of Filing Calculations. ART. 23. Moment of Inertia, Reduction Formula, Application to More Common Geometrical Figures, Computations. ART. 24. Practical Review Problems.
CHAPTER V DESIGN OF BEAMS
ART. 25. Safe Loads for Wooden Beams, Allowable Fiber Stresses for Timber. ART. 26. Vertical Shear, Shear Diagrams, Method of Plotting. ART. 27. Safe Loads for Steel Beams, Properties of I Beams. ART. 28. Cast-iron Beams, Gear Teeth. ART. 29. Beams of Uniform Strength. ART. 30. Modulus of Rupture. ART. 31. Practical Problems. 4
CHAPTER VI DEFORMATIONS
ART. 32. Modulus of Elasticity. ART. 33. Deflection of Beams, General Equations. ART. 34. Practical Problems.
CHAPTER VII SHAFTING
ART. 35. Twisting Moments, Torque. ART. 36. Internal Resisting Moment in Torsion. ART. 37. Polar Moment of Inertia. ART. 38. Shafts in Pure Torsion, Work and Horse power. ART. 39. Shafts for Combined Torsion and Bending, Equivalent Bending and Twisting Moments. ART. 40. Practical Problems, Table of Horse-power Transmitted by Shafting.
CHAPTER VIII COLUMNS
ART. 41. Analysis of Stresses Acting in Columns. ART. 42. Radius of Gyration. ART. 43. Derivation of the Rankine Formula for Columns. ART. 44. Cast-iron Columns. ART. 45. Structural Columns. ART. 46. Comparison of Column Formulae. ART. 47. Practical Problems Relating to Columns.
CHAPTER IX RIVETED JOINTS
ART. 48. Thickness of Pipes, Cast-iron Water Pipe. ART. 49. Lap Joints, A.S.M.E., Standard Rules for Efficiency. ART. 50. Butt Joints, Double, Triple and Quadruple Riveted. Efficiencies. ART. 51. Application of Riveted Joints to Boilers. ART. 52. Practical Problems on Applications of Riveted Joints, Structural and Mechanical.
CHAPTER X COMBINED STRESSES RESILIENCE
ART. 53. Tension and Compression, Crane Hooks. ART. 54. Stresses in Various Machine Frames. ART. 55. Modulus of Resilience. ART. 56. Formulae for Elastic Resilience. ART. 57. Stresses Due to Temperature. ART. 58. Practical Problems.
CHAPTER XI REINFORCED CONCRETE 169
ART. 59. Cement and Concrete. ART. 60. Reinforced Concrete, Types of Bars. ART. 61. Slabs and Beams. ART. 62. Columns. ART. 63. Design of Concrete Beams and Floors. ART. 64. Design of Columns and Footings. ART. 65. Practical Review Problems.
CHAPTER VIII - COLUMNS
ART. 41. STRESSES IN COLUMNS
When a short specimen is placed under a compressive load, the specimen tends to fail in shear. For example, a cast-iron specimen of the form shown in Fig. 8 will fail by shearing along the plane A B. This plane makes an angle of 45 degrees plus the angle of repose of the material, with the vertical. As the length of the specimen relative to the diameter is increased, this angle of shear becomes, less marked, and eventually the specimen will fail by buckling of the fibers. A specimen which has a length of at least ten times the least cross-sectional dimension of the specimen is referred to as a column or strut.
The action of the internal stresses in a column is somewhat similar to a beam, with this difference that in addition to the bending stress there is also present a direct compressive stress. As stated before, if the specimen is very short, the unit stress under a load of P pounds equals S=P/A. This unit compressive stress continues to exist as the length is increased, but there is an additional stress set up due to bending, so that the safe load that can be carried by a column gradually decreases for a given cross section as the length increases. A column will bend in a plane parallel to the shorter side of the column. Hence to make a column equally strong in either direction it is essential that the cross-section be symmetrical with respect to both axes. This is not always possible, owing to the difficulties of construction.
Columns are usually made of wood, cast iron, steel, or concrete. The load carried by a column will depend upon how the ends of the column are arranged. Three classes of columns are recognized.
I. Columns having ends fixed, as shown in Fig. 75.
II. Columns having one end fixed and the other end free as in Fig. 76.
III. Columns having both ends free or pin ended as shown in Fig. 77.
Columns in Class I are used in building and bridge construction. The column in such cases is rigidly secured to beams or concrete pedestals or similar fixed fastenings.
Columns in Class II are met with in the construction of machines, as, for example, the piston rod of an engine.
Columns in Class III are met with in bridge and machine construction. The connecting rod of a steam engine is a good illustration of a pin-ended column.
Experiment has shown that columns of Class I are the strongest, Class II is second, and Class III the weakest.
If the column is loaded eccentrically the safe load is materially effected, as a greater bending action is thereby induced.
PROB. 132. Calculate the theoretical angle of shear for cast-iron and wood specimens when subjected to a direct compressive stress. The angle of repose of these materials can be found in any reference book on Mechanics.
The action of the internal stresses in a column is somewhat similar to a beam, with this difference that in addition to the bending stress there is also present a direct compressive stress. As stated before, if the specimen is very short, the unit stress under a load of P pounds equals S=P/A. This unit compressive stress continues to exist as the length is increased, but there is an additional stress set up due to bending, so that the safe load that can be carried by a column gradually decreases for a given cross section as the length increases. A column will bend in a plane parallel to the shorter side of the column. Hence to make a column equally strong in either direction it is essential that the cross-section be symmetrical with respect to both axes. This is not always possible, owing to the difficulties of construction.
Columns are usually made of wood, cast iron, steel, or concrete. The load carried by a column will depend upon how the ends of the column are arranged. Three classes of columns are recognized.
I. Columns having ends fixed, as shown in Fig. 75.
II. Columns having one end fixed and the other end free as in Fig. 76.
III. Columns having both ends free or pin ended as shown in Fig. 77.
Columns in Class I are used in building and bridge construction. The column in such cases is rigidly secured to beams or concrete pedestals or similar fixed fastenings.
Columns in Class II are met with in the construction of machines, as, for example, the piston rod of an engine.
Columns in Class III are met with in bridge and machine construction. The connecting rod of a steam engine is a good illustration of a pin-ended column.
Experiment has shown that columns of Class I are the strongest, Class II is second, and Class III the weakest.
If the column is loaded eccentrically the safe load is materially effected, as a greater bending action is thereby induced.
PROB. 132. Calculate the theoretical angle of shear for cast-iron and wood specimens when subjected to a direct compressive stress. The angle of repose of these materials can be found in any reference book on Mechanics.
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