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The elements of graphic statics - Karl von Ott
THE ELEMENTS OF GRAPHIC STATICS
By KARL VON OTT,
TRANSLATED FROM THE GERMAN BY GEORGE SYDENHAM CLARKE,
LONDON; E. & F. SPON; 1905
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The elements of graphic statics
TRANSLATOR'S PREFACE.
The solution of problems of all kinds by purely graphic methods forms an important branch of study in the training of a Continental Engineer, and the publication of such considerable works as those of Reuleaux, Culmann, Bauschinger, and Levy, affords the best proof of the value attached to the subject.
In England, not with standing the valuable contributions to Graphic Statics made by Professor Clerk-Maxwell and the late Professor Rankine, the subject can hardly be said to have received the recognition it merits. It is true indeed that the power and facility conferred by certain isolated processes, such for instance as that of stress diagrams, are universally acknowledged; but these processes have for the most part been viewed as mere artifices for effecting special purposes, and not as applications of the principles of an important general method.
The present work, which has in Germany already gone through three editions, is for its size one of the most complete elementary treatises on the subject, while its essentially practical character and the extreme simplicity of the mathematics involved will, it is hoped, render it widely useful in an English form. In carrying out the translation the Author's text has, as far as possible, been adhered to; but the peculiarities of German idiom cannot always be literally rendered, and in such cases a certain amount of freedom must necessarily be claimed.
It was thought advisable to omit entirely the first portion of the work treating of Graphic Arithmetic, which, though it certainly forms a useful and appropriate introduction to the study of Graphic procedure, has not been much used in practice.
Some few notes have been added where further explanation seemed desirable, or where, as in the case of the treatment of wind pressure on roofs, a divergence from English practice seemed to call for some remark. All such additional matter incorporated with the Author's text has been enclosed in brackets.
In England, not with standing the valuable contributions to Graphic Statics made by Professor Clerk-Maxwell and the late Professor Rankine, the subject can hardly be said to have received the recognition it merits. It is true indeed that the power and facility conferred by certain isolated processes, such for instance as that of stress diagrams, are universally acknowledged; but these processes have for the most part been viewed as mere artifices for effecting special purposes, and not as applications of the principles of an important general method.
The present work, which has in Germany already gone through three editions, is for its size one of the most complete elementary treatises on the subject, while its essentially practical character and the extreme simplicity of the mathematics involved will, it is hoped, render it widely useful in an English form. In carrying out the translation the Author's text has, as far as possible, been adhered to; but the peculiarities of German idiom cannot always be literally rendered, and in such cases a certain amount of freedom must necessarily be claimed.
It was thought advisable to omit entirely the first portion of the work treating of Graphic Arithmetic, which, though it certainly forms a useful and appropriate introduction to the study of Graphic procedure, has not been much used in practice.
Some few notes have been added where further explanation seemed desirable, or where, as in the case of the treatment of wind pressure on roofs, a divergence from English practice seemed to call for some remark. All such additional matter incorporated with the Author's text has been enclosed in brackets.
CONTENTS.
PART I.
COMPOSITION OF FORCES.
1. Forces acting in the same Straight Line
2. Forces acting in any Directions at a Point
3. Forces acting on a Rigid Body
4. Equilibrium of the Forces acting on a Jointed Frame
5. Parallel Exterior Forces
THE SIMPLE BEAM
6. Determination of Transverse Forces
7. Determination of Bending Moments
8. Effect of a Travelling Load
9. Treatment of Travelling Load. Example
10. Approximate determination of Maxima Moments
11. Stationary Load with fixed distribution
12. Uniformly distributed dead Load
13. Seduction of concentrated Loads to a uniform Loading
14. Example
15. Combined effect of permanent and accidental Loading
RESOLUTION OF FOBCES,
16. Resolution of a Force in two directions
17. Resolution of a Force in three directions
INTERIOR FORCES OB STRESSES.
18. Calculation of the interior Forces due to the exterior Forces
PART II.
BRACED STRUCTURES.
19. General considerations
20. Equilibrium of Forces in a braced Structure
21. Roof Trusses
22. Dead Weight of Roofs
23. Snow Pressure
24. Wind Pressure
25. Note on treatment of Wind Pressure
STRESS DIAGRAMS.
26. German Truss
27. English Truss
28. Belgian, or French Truss
29. Bowstring Roof
30. Simple Truss
31. Simple inverted Truss
32. Queen-post Truss
33. Inverted Queen-post truss
34. Simple Cantilever
35. Braced Cantilever
36. “Perron” Roof
37. Lattice Cantilever
38. Braced Beam of General form
39. Combined braced Beam
40. Braced Beam with parallel Booms
41. Combined braced Beam with parallel Booms
42. Braced Beam with parallel Booms and without Verticals
BRACED BEAMS WITH TRAVELLING LOADS.
43. Effect of travelling Load on braced Structures
44. Maximum Stress of Booms
45. Maximum Stress of bracing Bars
46. Girders with parallel Booms
47. Braced Girders for Railway Bridges. General Case
48. Crossed, or redundant Diagonals
49. Special Cases
50. Fixed Load in place of travelling Load
51. Concentrated Loads on small Spans
THE ARCH
52. Construction of the Line of Resistance of an Arch
PAET III.
ELEMENTS OF THE THEORY OF STRENGTH OF MATERIALS.
53. Strength of a Prismatic Bar
54. Resistance to Bending. General considerations
55. Determination of Stresses at any Gross Section
56. Practical Application
57. Determination of the Moment of Resistance
58. Centre of Gravity and Moment of Inertia of a Plane Area
59. Moments of Inertia of simple Sections
60. Examples, Resistance to Flexure
61. Resistance to Crippling, Example
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