The Strength of Materials

Name: The Strength of Materials | A Treatise on the Theory of Stress Calculations for Engineers
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A Treatise on the Theory of Stress Calculations for Engineers

John Case(Author)

Elsevier (Publisher)

2nd Edition

Published on 20. June 2014

574 pages

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978-1-4832-2155-7 (ISBN)

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Front Cover
The Strength of Materials: A Treatise on the Theory of Stress Calculations for Engineers
Copyright Page
Table of Contents
Dedication
PREFACE TO FIRST EDITION
PREFACE TO SECOND EDITION
CHAPTER I. DIRECT STRESSES
1. The Purpose of the Theory of Stresses
2. Definitions of Load and Stress
3. Measurement of Stress
4. Strain
5. Measurement of Strain in Tension and Compression
6. Hooke's Law
7. Young's Modulus
8. Stress-Strain Diagrams
9. Magnitudes of Stresses and Strains
10. Limitations and Scope of Mathematical Theory
11. Factor of Safety and Working Stress
12. Fluctuating Stresse
13. Principle of St. Venant
14. Initial Stresses
15. Rods of Varying Section, and Distributed Axial Loads
16. Composite Bars in Tension or Compression
17. Adhesion Stress in Reinforced Concrete
18. Temperature Stresses
19. Temperature Stresses in Composite Rods
20. Abrupt Changes of Section
21. Work Done During Tension and Compression
22. Resilience
23. Stress Due to Sudden Application of Load
24. Waves of Stress
25. Velocity of Propagation of Stress in a Straight Rod
26. Maximum Stress
27. Stress in a Rotating Ring
28. Poisson's Ratio
29. Strain Due to Two Stresses at Right Angles
30. Change of Area and Volume Due to Strain
31. Bulk Modulus
32. Relation between E and K
33. Modified Values of E when Lateral Strain is Prevented
CHAPTER II. DISPLACEMENT DIAGRAMS AND REDUNDANT FRAMES
34. Displacement Diagrams
35. Application of the Principle of Virtual Work
36. Simply-stiff and Redundant Frames
37. Conditions for Simple Stiffness
38. Self-strained Frameworks
39. Stresses in Redundant Frames
40. Strain Energy of a Framework
41. Theorem Relating to the Strain Energy of a Framework
42. Second Theorem Relating to the Strain Energy of a Frame
43. The Theorem of Least Work for a Framework which is not Self-strained
44. Method of Calculating Stresses in Redundant Frames which are not Self-strained
45. Frameworks which are Self-strained
46. Alternative Method: Use of Displacement Diagrams
CHAPTER III. SHEARING STRESSES
47. Shearing Stress
48. Complementary Shear Stresses
49. The Shearing Stresses on a Cross Section must always Actin Directions Tangential to the Boundary
50. Measurement of Shear Stress
51. Shear Strain
52. Modulus of Rigidity
53. Strain Energy due to Shear
CHAPTER IV. RIVETED JOINTS
54. Introductory
55. Possible Types of Failure of Simple Riveted Joints, Neglecting Friction
56. Group-Riveted Joints
57. Eccentric Loads
CHAPTER V. ANALYSIS OF STRESS AND STRAIN. COMPOUND STRESSES: ANALYSIS OF STRESS
58. Introductory
59. Stress-components on any Plane due to a Direct Stresson a Given Plane
60. Stress-components on any Plane due to a Shearing Stress on a Given Plane
61. General Two-dimensional Stress System
62. Stress-components on any Plane in a General Two-dimensional Stress-system
63. Principal Planes
64. To Find the Principal Stresses
65. The Principal Stresses Found from First Principles
66. Maxi-mum Shear Stresses
67. Strain in any Direction due to Strain in a Given Direction
68. To Find the Direct Strain in Any Direction due to a Given Shear Strain
69. General Two-Dimensional Strain
70. Maximum Shear Strain
71. Principal Strains
72. Single Direct Stress Required to Produce same Maximum Strain as a Given Stress System
73. Relations Between E, C, K and m
74. Strain Energy of Combined Stresses
75. Principal Stresses in Three-Dimensional System
76. Strains in Three-Dimensional Stress System
77. Strain Energy in Three Dimensions
CHAPTER VI. FAILURE OF MATERIALS UNDER COMPOUND STRESSES
78. Introductory
79. The Various Theories of Failure
80. The Significance of these Theories
81. Representation of the above Theories
82. Analysis of Experiments
CHAPTER VII. THIN CYLINDRICAL AND SPHERICAL SHELLS UNDER INTERNAL PRESSURE
83. Introductory
84. Thin Cylindrical Shell of Circular Section
85. Thin Spherical Shell under Internal Pressure
86. Thin Cylindrical Shell with Hemispherical Ends
87. Thin Tube under External Pressure
CHAPTER VIII. THE TORSION OF CIRCULAR SHAFTS
88. Introductory
89. Relations between Twisting Moment, Twist and Shear Stress
90. Principal Stresses in a Twisted Shaft
91. Torsion Combined with Thrust or Tension
92. Strain Energy of Torsion
93. Keyways and Serrations
CHAPTER IX. BENDING MOMENTS AND SHEARING FORCES DUE TOSTEADY LOADS
94. Bending Moments and Shearing Forces Deftned
95. Concentrated and Distributed Loads
96. Relation between Load, Shearing Force and Bending Moment
97. Cantilever with Concentrated Load
98. Cantilever with Uniformly Distributed Load
99. Cantilever with Non-uniformly Distributed Load
100. Cantilever with any Manner of Loads
101. Freely Supported Beam with Concentrated Load
102. Freely Supported Beam with Uniformly Distributed Load
103. FreelY' Supported Beam with Non-uniformly Distributed Load
104. Another Graphical Method of Drawing Bending-Moment Diagrams
105. Freely Supported Beam with Couples applied to Both Ends
106. Freely Supported Beam with Couple applied Between the Supports
107. Beam Freely Supported at each End, carrying a Uniformly Distributed Load, acted on by Couples at both Ends
108. Freely Supported Beam with Uniformly Distributed Loadover Part of the Length
108a. Useful General Method for Drawing Bending Moment Diagrams
CHAPTER X. BENDING MOMENTS AND SHEARING FORCES DUE TO TRAVELLING LOADS
109. Introductory
110. A Single Concentrated Load Crossing a Bearn
111. Uniformly Distributed Travelling Load of Sufficient Length to Cover the Whole Span
112. Two Concentrated Loads
113. Several Concentrated Loads
114. Influence Lines
115. Single Concentrated Load
116. Uniformly Distributed Load
CHAPTER XI. LONGITUDINAL STRESSES IN BEAMS
117. Physical Discussion
118. The Theory of Uniform Bending
119. Modulus of Section
120. Application to Practical Cases of Bending
121. Moment of Resistance of Section
122. Beams having Initial Curvature
123. Beams made of Materials having Different Strengths in Tension and Compression
124. Reinforced Concrete
125. reinforced Concrete Beam of Rectangular Section
126. Oblique, or Unsymmetrical Bendin
127. Geometrically Similar Beams
128. Strain Energy Due to Normal Stresses
129. Change of Cross Section in Uniform Bending
130. Secondary Stresses in Beams
131. General Properties of Moments of Inertia
132. Given the Moments of Inertia about the Principal Axes, to Find the Moments of Inertia about any other Line through the Centroid of the Area
133. To Find the Principal Moments of Inertia
134. Ellipse of Inertia, or Momental Ellipse
135. Given the Moment of Inertia about an Axis through the Centroid of an Area, to Find the Moment of Inertia about any other Parallel Axis
136. Graphical Determination of Moment of Inertia of an Irregular Section
137. Table of Moments of Inertia
138. Note on J Sections
CHAPTER XII. BENDING STRESSES AND DIRECT STRESSES COMBINED
139. Introductory
1404. Stress Due to Combined Bending and Thrust
141. Eccentric End Load
142. Circular Section
143. Rectangular Section
144. Unsymmetrical Bending with Eccentric End Load
145. Core of Rectangular Section
146. Bending and Axial Thrust: No Tensile Stresses
147. Bending and Axial Thrust: When there are Tensile Stresses
148. Bending and Axial Tension Combined
CHAPTER XIII. SHEARING STRESSES IN BEAMS
149. Introductory
150. Elementary Treatment of the Distribution of Shearing Stress
151. Special Cases
Beams of Constant Section
152. Shear in Built-up Plate Girders
153. General Remarks on Shearing Stresses in Beam
154. Principal Stresses in Beams
155. Superimposed Beams
156. Shear in Reinforced Concrete Beams
157. Shear in Oblique Bending
CHAPTER XIV. THE DEFLECTION OF BEAMS
158. Introductory
159. General Equations
160. Reinforced Concrete Beams
161. Cantilever with Concentrated Load
162. Cantilever with Uniformly Distributed Load
163. Supported Cantilever with Distributed Load
164. Beam with Uniform Bending Moment
165. Beam Simply Supported at the Ends and carrying a Uniformly Distributed Load
166. Freely Supported Beam with Concentrated Load
167. Rules for applying Macaulay's Method
168. Freely Supported Beam with Distributed Load over a Portion of the Span
169. Beam Supported at Each End, with a Couple Applied at an Intermediate Point
170. Beam with Terminal Couples and Distributed Load
171. Relative Movement of Supports
172. Beams with Non-Uniformly Distributed Load: Graphical Treatment
173. Simply Supported Beam
174. Cantilever with Irregular Load
175. Beams of Varying Section
176. Non-Uniformly Distributed Load and Terminal Couples: Expressions for the Slopes
177. Non-Uniformly Distributed Load and Terminal Couples, with Varying Cross Section
178. Beam Acted on by Terminal Couples and Carrying a Concentrated Load
179. Introductory
180. Freely Supported Beam with Sinusoidal Distribution of Load
181. Freely Supported Beam with Uniformly Distributed Load
182. Freely Supported Beam with Concentrated Load
183. Introductory
184. Cantilever of Uniform Rectangular Section with Concentrated Load at the End
185. Cantilever with Uniformly Distributed Load
CHAPTER XV. BUILT IN, OR ENCASTRÉ, BEAMS
186. Introductory
187. Encastré Beam with Uniformly Distributed Load
188. Encastré Beam with Single Concentrated Load
189. Encastré Beam with Irregular Loading
190. Varying Section
191. Disadvantages of Built-in Beams
192. Effect of Sinking of Supports
CHAPTER XVI. CONTINUOUS BEAMS
193. Fixing Moments at the Supports
194. Theorem of Three Moments for Uniformly Distributed Load
195. Theorem of Three Moments for Concentrated Loads
196. Theorem of Three Moments for Irregular Loading
197. Irregular Loading and Varying Section
198. Disadvantages of Continuous Beam
199. Hinged Joints in the Spans
200. General Equations
201. Single Load at the Centre of a Long Beam
CHAPTER XVII. RIGID ARCHES
202. General Discussion
203. Arch Hinged only at the Abutments
204. Arch Built-in at Both Ends
205. Deflection of Arched Ribs
206. Temperature Stresses
207. Two-hinged Parabolic Arch with Uniformly Distributed Load
208. Two-hinged Parabolic Arch with Concentrated Load
209. Built-in Parabolic Arch with Uniformly Distributed Load
210. Built-in Parabolic Arch with Concentrated Load
211. Piston Rings
CHAPTER XVIII. STRUTS OF UNIFORM SECTION
212. Statement of the Problem
213. Strut Pin-jointed at Both Ends
214. Limitations of Euler's Formula
215. Strut with Eccentric End-Load
216. The Effect of Initial Crookedness
217. Strut with One End Encastre, the other End being Freeto Rotate
218. Strut with One End Encastré, the Other End being Freeto take up any Position
219. Strut with Both Ends Encastré
220. The Imperfections of Real Struts
221. Eccentricity of Loading
222. Initial Curvature
223. Equivalent Eccentricity
224. Reduction in Strength
225. End Conditions
226. Range of the Euler Formula
227. Empirical Formulmæ
228. The Rankine-Gordon Formula
229. Straight Line Formulræ
230. Johnson's Parabolic Formula
231. Fidler's Formula
232. Perry's Formula
233. Robertson's Formula
234. Author's Formula
235. Stress Determining Strut Failure
236. Factors of Safety for Struts
237. Shearing Forces in Struts
238. Braced Struts
239. Equivalent Eccentricity
240. Crinkling
241. Short Struts where Bending is Negligible
242. Long Struts
CHAPTER XIX. TAPERED STRUTS
243. Introductory
244. General Equations
245. Solid Strut of Uniform Stress
246. Tapered Hollow Struts of Uniform Thickness
247. Elliptically Tapered Struts
248. Rules for Design of Straight-Taper Struts
249. To Find the Failing Load of a Solid Strut of Given Shape
250. To Find the Euler Crippling Load of a Strut Symmetrical about the Central Section
CHAPTER XX. BEAMB UNDER LATERAL AND LONGITUDINAL LOADS COMBINED
251. Deflection Due to Lateral Loads Influenced by End Loads
252. Deem Supported at Each End, Carrying a Uniformly Distributed Transverse Load, and End Thrus
253. Beam Supported at Each End, Loaded with a Uniformly Distributed Lateral Load, Terminal Couples and End Thrust
254. Approximate Formulmæ
255. Continuous Beams with Longitudinal Forces and Lateral Loads
CHAPTER XXI. FRAMEWORKS WITH STIFF JOINTS
256. Nature of the Problem
257. Rectangular Portal
258. Secondary Stresses in Trianaulated Frameworks
259. Secondary Stresses Due to Rigid Joints
260. Effects of Lateral Loads
261. Effects of End Loads
CHAPTER XXII. BENDING COMBINED WITH TORSION AND THRUST
262. Introductory
263. Torsion Combined with Pure Bending
XXIII. Stability of Bent and Twisted Rods
268. Non-Circular Rods
269. Stability of Thin Deep Cantilever with Concentrated Load
270. Thin Deep Cantilever with Distributed Load
271. Thin Deep Beam under Constant Bending Moment
272. The Case of I-Beams
273. Uniform Bending Moment
274. Other Cases
CHAPTER XXIV. SPRINGS
275. General Properties of Springs
276. Coiled Springs
277. Geometry of Hellcal Springs
278. Close-Coiled Helical Spring: Axial Pull
279. Close-Coiled Helical Spring: Axial Couple
280. Open-Coiled Helical Spring: Axial Force
281. Open-Coiled Helical Spring: Axial Couple
282. Plane Spiral Springs
283. Close-Coiled Conical Spiral Spring
284. Approximate Theory of Leaf Springs
CHAPTER XXV. STRESSES IN CURVED BEAMS OF LARGE CURVATURE
285. Introductory
286. Winkler's Theory of the Flexure of Curved Bars
287. Pure Bending
288. Formula! for h2
289. Deformation of the Central Axis
290. Application to Hooks
291. Chain Ring
292. Ring with Stud
CHAPTER XXVI. GENERAL ANALYSIS OF STRESS AND STRAIN
293. Need for General Analytical Methods
294. Stress Components
295. Stress Equations of Equilibrium
296. Plane Stress with No Body Forces: Cartesian Co-ordinates
297. Plane Stress with No Body Forces: Polar Co-ordinates
298. Displacements in Cartesian Co-ordinates
299. Relations between the Strain Components
300. Relations Between the Stresses and Displacements in a Two-Dimensional Stress System
301. Equations for Finding the Displacements in a Two Dimensional Stress System
302. Two-Dimensional Strain System
303. Transformation to Polar Co-ordinates
CHAPTER XXVII. SOME PROBLEMS IN TWO DIMENSIONS
304. Some Particular Solutions of the General Equation
305. Narrow Cantilever of Rectangular Section with Concentrated Load
306. Narrow Cantilever of Rectangular Section with Uniformly Distributed Load
307. Solution of V4V = 0 in Polar Co-ordinates
308. Thick Hollow Cylinder under Radial Pressures
309. Incomplete Circular Plate with Terminal Couples
310. Semi-Circular Plate Subjected to Terminal Shearing Forces
CHAPTER XXVIII. THICK CYLINDRICAL AND SPHERICAL SHELLS
311. Thick Cylindrical Shell under Radial Pressures
312. External Pressure Negligible
313. Longitudinal Stress
314. Compound Tubes
315. Driving Fits on Solid Shafts
316. Purpose of Wire Winding
317. General Equations
318. Shear Stress, or Stress-Difference (p + t), Limited Throughout
319. Shear Stress Limited in Tube: Tensile Stress Limited in Windings
320. Wire Winding at Constant Tension
321. Temperature Stresses in Thick Tubes
322. Thick Spherical Shells
CHAPTER XXIX. STRESSES DUE TO ROTATION
323. General Equations
324. Rotating Disc of Uniform Thickness
325. Case· 1. Thin Solid Disc
326. Case 2. Thin Hollow Disc
327. Rotating Circular Cylinder
328. Case 1. Solid Cylinder
329. Case 2. Hollow Cylinder
330. Disc of Varying Thickness
CHAPTER XXX. THE TORSION OF NON-CIRCULAR SHAFTS
331. Physical Discussion
332. Mathematical Analysis
333. Torsion of Thin Tubes of any Section
334. Solid Sections of Irregular Shape
335. The Torsion of Hollow Shafts of any Section
CHAPTER XXXI. STRESSES IN FLAT PLATES DUE TO BENDING
336. Statement of the Problem and Assumptions
337. General Equations
338. General Solution when the Load is Uniform
339. Solid Circular Plate, Uniformly Loaded over the Whole Area: Edge Freely Supported
340. Solid Circular Plate, Uniformly Loaded over the Whole Area: Edge Clamped
341. Annular Ring Freely Supported at the Outer Edge and Loaded Uniformly Round the Inner Edge
342. Solid Plate Uniformly Loaded Round a Circle: Edge Freely Supported
343. Solid Plate with Load Concentrated at the Centre
344. Rectangular Plate, Supported at the Edges
CHAPTER XXXII. THE WHIRLING OF SHAFTS
345. Definition of Whirling Speed
346. Unloaded Shaft
347. Single Concentrated Load on a Light Shaft
348. Single Concentrated Load on a Heavy Shaft
349. Shaft Subjected to End Thrust
350. Shaft Subjected to End Thrust and Torque
CHAPTER XXXIII. TRANSVERSE OSCILLATIONS OF BEAMS DUE TOPULSATING AND TRAVELLING LOADS
351. Introductory
352. Free Oscillations of a Beam Simply Supported at Both Ends
353. Pulsating Sinusoidal Load on Freely Supported Beam
354. Alternating Load Uniformly Distributed on Freely Supported Beam
355. Single Pulsating Load on Freely Supported Beam
356. Freely Supported Beam Subjected to a Load which Varies Uniformly with the Time
357. Concentrated Load Advancing over Freely Supported Girder
358. Uniformly Distributed Load Advancing over Freely Supported Girder
359. Single Pulsating Load Advancing over Freely Supported Girder
CHAPTER XXXIV. ALTERNATING STRESSES AND FATIGUE
360. Introductory
361. Raising the Yield Point by Stress
362. Effects of Time on Recovery of Elasticity
363. Recovery of Elasticity with Moderate Heat
364. Primitive and Natural Elastic Limits
365. Hysteresis
366. Fatigue Range
367. Theory of Fatigue, Hysteresis, etc
APPENDIX: TABLE OF ELASTIC CONSTANTS
ANSWERS TO EXAMPLES
INDEX

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