## Engineering Methods for Analysing Strength and Rigidity – Glushkov

In this post, we will see the book Engineering Methods for Analysing Strength and Rigidity by G. Glushkov. The book is a theoretical treatise on the subject of higher order moments. The theory of moments developed into a specific branch of mathematics which became a useful tool for solving com­plicated problems in structural mechanics. A number of Soviet scientists developed the so-called moment-operational method, which has proved to be extremely efficient for solving various pro­blems of modern engineering. These problems arise when non-linear elasticity must be taken into account, when precise designing of non-uniform structural elements is required, when the loading of a structure is essentially non-uniform, etc.

The moment-operational method has been widely employed for compiling manuals containing numerous tables and formulas for designing beams, arches and frames. A number of scientific research works and textbooks present the theory of moments of higher order methods examples of problems solved by the moment-operational method.

The knowledge of the theory of higher moments as well as of the moment-operational method will serve to extend the field of their application to new problems.

The book was translated from the Russian by N. Lebedinsky and was published by Mir in 1974.

Many thanks to Akbar Azimi for providing the raw scans. We did the cleaning from 2-in-1 scans. There might be warping in some pages but the text overall is very readable.

Contents

Part 1 Moments of Higher Order: Theory and Application 9

Chapter 1. Theory of Moments 9

1. General Concept of Moments of Area 9
2. Moments as Geometric Characteristics of Beam Cross Sections 18
3. Uniaxial Moments of Point Forces and Couples 36
4. Uniaxial Moments of Balanced and Unbalanced Systems 40
5. Uniaxial Moments of Areas of Simple Figures 45
6. Uniaxial Moments of Areas of More Complicated Figures 52
7. Uniaxial Moments of Compound Loads 56
8. Moments of Higher Order and Generalized Forces 64

Chapter II. Application of Theory of Moments 73

9. Rigidity or Uniform Beams 73
10. Geometrical Interpretation of Moments 74
11. Calculation of Displacement Integrals in Rod Systems 83
12. Application of Higher Moments to Loading of Parabolic Influence Lines 92
13. Formulas for Statically Indeterminate Structures 94
14. Rigidity of Beams Composed of Prismatic Parts 140
15. Moments of Area of Flexibility Diagram for Non-Uniform Beams 145

Part II Moment-Operational Method: Theory and Application 160

Chapter III. Moment-Operational Method 160

16. Principles of Moment-Operational Method 160
17. Bimoments 162
18. Differential and Integral Bimoments 163
19. Application of Moment-Operational Method for Solving
Linear Differential Equations 170

Chapter IV. Rigidity of Non-Uniform Beams 173

20. Determination of Displacements by Coefficients of Flexibility Polynomial Expression 173
21. Determination of Displacements by Derivatives of Flexibility Analytical Expression 178
22. Determination of Displacements by Flexibility Integrals 182
23. Dermination of Displacements when Rigidity Follows Power 194
24. Determination of Displacement Integrals by Coefficients of Flexibility Polynomial 196
25. Determination of Displacement Integrals by Derivatives of Flexibility Analytical Expression 199

Chapter V. Multispan Non-Uniform Beams 202

28. Equation of Three Moments in Flexibility Polynomial Coeffi­cients 202
27. Equation of Three Moments in Derivatives of Analytically Expressed Flexibility 207
28. Equation of Three Moments in Flexibility Integrals 210
29. Mohrs Integrals for Non-Uniform Beams 219

Chapter VI. Beams on Elastic Foundation 223

30. General 223
31. Prismatic Beams on Foundation of Constant Rigidity 224
32. Prismatic Beams on Foundation of Linear Rigidity 227
33. Beams on Foundation of Hyperbolic Rigidity 229
34. Beams on Elastic Foundation with Moment Reaction 236

Chapter VII. Beams Under Combined Flexure and Compression 238

35. General 238
36. Prismatic Beams Under Arbitrary Transverse Loads and Constant Axial Forces 239
37. Rotating Rod of Constant Rigidity Under Compression and Flexure 255
38. Prismatic Beam Under Arbitrary Transverse Load and Uni­formly Distributed Axial Forces 260
39. Prismatic Beam Under Arbitrary Transverse Load and Linear Axial Forces 270
40. Prismatic Beam Under Arbitrary Transverse Load and Axial Law Distributed Along the Beam According to Polynomial 283

Chapter VIII. Application of Moment-Operational Method to Certain Complex Problems 285

41. Stability of Bars Under Axial Compression 285
42. Beams on Elastic Foundation Under Combined Compression and Bending 290
43. Non-Uniform Beam Under Axial Force 294
44. Higher Moments of Vector Quantities in Space 306
45. Rigidity of Beams: General Case of Non-Linear Stress-Strain Relationship 320

Chapter IX. Application of Moment-Operational Method to Structural Mechanics of Ships 331

46. Flexure of Irregular Decks 331
47. Non-Uniform Beams on Elastic Foundation 341
48. Stability and Vibration of Irregular Decks 346 1. shubham29912708 says: