The Elements of Graphical Statics and Their Application to Framed Structures: With Numerous Practical Examples of Cranes--bridge, Roof and Suspension Trusses--braced and Stone Arches--pivot and Draw Spans--continuous Girders, &c., Together with the Best Methods of Calculation, and Containing Also New and Practical Formulae for the Pivot Or Draw Span--braced Arch--continuous Girder, Etc, Band 1

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J. Wiley and son, 1875 - 404 Seiten
 

Inhalt

The modern geometry
xxxix
The modern geometry in engineering practice
xlii
Practical significance of the graphical statics
xliii
Literature upon the graphical statics
xlvi
Graphical dynamics
l
GENERAL PRINCIPLES CHAPTER I
1
NotationRepresentation of forces by lines 122
2
Resultant of any number of forces 4 Conditions of equilibrium
3
Order of forces in force polygon a matter of indifference
4
Forces acting in same straight line
5
Braced semiarch
6
Roof truss
8
Application of method to bridges
11
Braced arch
12
Ritters Method of Sections
14
CHAPTER II
16
Case of forces parallel
18
Influence of a couple
24
General method for determination of centre of gravity
30
CHAPTER IV
33
Culmanns principle
36
Loading continuousLoad area
45
Load systems
53
MOMENT OF INERTIA OF PARALLEL FORCES
54
Centre of action of the statical moments considered as forces
60
Practical applications
76
APPLICATION TO BRIDGES
84
Maximum moments
90
SUPPLEMENT TO CHAPTER VII
98
ART PAGE 2 Ritters method
99
Method by resolution of forces
100
CHAPTER II
101
PRINCIPLES OF THE CALCULUS 4 Differentiation and integration
102
Powers of a single variable
105
Other principles
106
Illustrations
107
First differential coefficient
109
CHAPTER III
110
Change of shape of axis
112
Beam fixed at one end load at other
113
Beam as aboveUniform load
117
Beam supported at both endsConcentrated load
118
Beam as aboveUniform load
119
Beam fixed at one end supported at otherConcentrated load
120
Beam as aboveUniform load
121
Beam fixed at both endsConcentrated load
122
Inflection points etc
124
B THE CONTINUOUS GIRDER OF CONSTANT CROSSSECTION CHAPTER VIII
125
Determination of tangents to the elastic curve
128
Division of the moment area
129
Properties of the equilibrium polygon
130
Polygon for the positive moment areas
131
Construction of the fixed points and of the equilibrium polygon
132
Construction of the moments at the supports
135
The second equilibrium polygon
136
Determination of moments at the supports
138
Comparison with girder fixed horizontally at both ends
139
CHAPTER IX
141
CHAPTER X
147
Concentrated load
153
Determination of the maximum shearing forces
159
Method by resolution of forcesDraw spans
166
CHAPTER XII
168
Example
172
ᎪᏒᎢ PAGE 116 Beam fixed at one end supported at the other
175
Practical construction
178
Practical construction
180
The pivot draw with secondary central span
181
Supports not on a levelReactions
183
Beam over four level supports
184
Practical construction
186
Pivot spanExample
187
Method of passing in construction from one span to another
190
Method of procedure for any number of spans
192
ExampleCentral span of seven spans
193
Uniform live load over any single spanMoments at supports
207
Triangle for momentsLoaded span
208
Unloaded spansMoments
209
Practical rule and table for finding the above
210
Reactions at supportsLoaded span
212
Triangle for reactions
213
Reactions for unloaded spansTables for
214
Concentrated load in any spanMoments
216
Triangle and table for moments
218
Reactions at supportsConcentrated load
219
Recapitulation of above formulæ
221
Continuous girder with variable end spans
225
Continuous girder with fastened ends
226
Tables for momentsEnd spans variable
229
ART PAGE
239
APPLICATION TO THE ARCH
251
Arch fixed at abutmentsContinuous at crown
257
Analytical formulæ for horizontal thrust and vertical reactions
264
SUPPLEMENT TO CHAPTER XIV
271
NotationThe outer forces in general
277
ARCH HINGED AT ABUTMENTS ONLY A Parabolic arc ART PAGE 8 Horizontal thrust
283
Intersection curve
285
CHAPTER IV
287
A Parabolic arc 14 Determination of H V and M
289
Intersection curve
291
Determination of H V and M
293
Intersection curve
297
CHAPTER V
299
Fundamental equationsGeneral
300
Arch with three hinges
301
CHAPTER VI
304
Horizontal thrust
305
Horizontal thrustCircular arch
307
Parabolic arch Formulæ for V H and M
307
Circular arch Formulæ for V H and M
308
CHAPTER XV
311
Forces acting upon a crosssectionNeutral axis
312
Kernel of a crosssection
313
Position of kernel for different crosssections
314
Proper position of resultant pressure
316
Pressure lineTrue pressure line
317
Support line
318
Continuous girderAll spans differentGeneral formulæExam ples 233
319
Dimensions of the arch
320
Construction of the pressure line
322
Practical example
324
Increase of depth due to change of form
326
CHAPTER XVI
327
Cable with auxiliary stiffening truss
329
Method of loading causing maximum strains
330
Example
332
Analytical investigation of the forces acting upon the stiffening truss
333
Concluding remarks
335
General method of calculation 237
337
NOTE TO CHAP VIII OF THE INTRODUCTIONUPON THE MODERN GEOMETRY
341
NOTE TO CHAPTER I
346
Character of strains in the pieces as indicated by the strain diagram
347
Roof trussMethod of checking the accuracy of the diagram
348
Application to bridgesBowstring girderMethod of tabulation illustrated
350
Strains in the flangesTable
353
Method of calculation by moments
354
Girder with straight flangesHowe or Murphy Whipple system of bracing
355
spans
359
NOTE TO CHAPTER II
362
NOTE TO CHAPTER V ART 51
364
NOTE TO CHAPTER XII
365
Relative economy of the continuous girder
374
Continuous girdersupports out of level
377
NOTE TO CHAPTER XIV THE BRACED ARCH 19 Practical example of the braced arch
382
Arch hinged at both abutments and crown
383
Arch hinged at abutments only
386
Temperature strains for above
394
Advantage of arch with fixed ends for long spansComparison with the St Louis arch
404
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Seite vi - Und nun fahre hin, gern hätte ich dich zum Fundament einer auf wissenschaftlicherer Basis gegründeten Ingenieurkunde gemacht, allein kaum darf ich die Hoffnung hegen , so viel Kraft in mir zu finden , um das Ganze dieses umfangreichen Faches umzuarbeiten: das ist ein Werk, das mir vor Augen schwebt, wie einer jener alten mittelalterlichen Dome sich vor dem Kunstler erhob, der ihn entwarf und der der Hoffnung sich nicht hingeben konnte, ihn je in seiner Vollendung zu schauen.
Seite 124 - They can be easily found by finding the values of x which make the expression for the moments zero. Thus for a beam fixed at one end and supported at the other, uniform load, the inflection point is at a distance from the fixed end of x = £ the length.
Seite 199 - ... that a partial solution of the problem by mathematical calculation is attended with considerable difficulty, and that a complete solution for the bending moment and shearing force at every section, under moving, partial and irregular loads, taxes the powers of the best mathematicians and is well nigh impossible, on account of the complexity of the formula;, so far as any practical application of them by the engineer is concerned.
Seite 15 - Hence, if a number of forces lying in the same plane and » having a common point of application...
Seite 100 - Hence, if any pressures act in a plane, the sum of their moments, with respect to any point in that plane, will equal the moment of their resultant with respect to that point. A little consideration will show that if the pressures reduce to a couple, the moment of the couple will equal the sum of the moments of the several pressures. Of course, if the point is taken in the direction of the resultant...
Seite 9 - The other verticals, as well as the diagonals and the segments of the main tie, are in tension. stresses have been calculated for a wind striking the roof horizontally. The load at each joint may be taken to be equal to the pressure due to the wind striking a surface whose area is equal to that portion of the roof supported by one bay of the rafter, inclined at the same angle as the tangent to the rib at the joint. The area corresponding to each bay of the rafter may be taken in this case at 10 x...
Seite 241 - P, and the r + ith support is given by (4), and the tangent of the angle which the curve makes with the horizontal is given by (3 a). If in...
Seite xlvi - Most, Ueber eine allgemeine Methode, geometrisch den Schwerpunkt beliebiger Polygone und Polyeder zu bestimmen.
Seite 365 - The bending moment at any Imaginary transverse section of a beam Is equal to the algebraic sum of the moments of all the forces to either side of the section. bending of strata (Geol.).

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