Graphical Determination of Forces in Engineering Structures

Front Cover
Macmillan and Company, 1881 - Engineering - 405 pages
 

Contents

Change of Sign of Shearing Force in a Beam under Travel
43
Application of preceding Force and Cord Polygon Theo
51
Method of Sections applied to the Construction of Partial
64
CORE
71
48
75
ClerkMaxwells Theorem Reciprocal Force Diagrams
77
Problem To carry a Cord Polygon to given Forces through
85
Compression and Tension in Bars
88
Partial Diagrams of Maximum Stress in Hinged Archwork
94
Method of Determining the Stresses in the Parts of
100
Geometrical Signification of dy2
118
Theorem Moment of Inertia and Radius of Gyration of
124
Apportioning the Area of a Beam to the Bending Moment
130
Employment of the Methods of last article to an Unsym
132
Recapitulation of Formulæ
137
Point of Action of Resultant of Stresses and Trace of Neutral
141
Transferring the Axes around which the Moments and Products
149
The Ellipse of Inertia and its Construction
155
Construction of Ellipse of Inertia around any Point of
167
Planes of Greatest and Least Stresses in a Beam
176
CHAPTER IV
197
Construction of Elastic Line Tangent Envelope of a Beam
204
Construction of Elastic Line Tangent Envelope for
210
Art Page 151 Remarks upon Choice of Constants
218
Moments over all the Supports of a Weightless Beam having only One Span Loaded and its Elastic Line
221
Extension of Problem to a Number of Concentrated Loads in any Spans
224
Example of Continuous Beam with Uniform Loading
225
Uniform Distribution of Pressure over Part of a Span
226
Scheme of Loadings for Determination of Maximum Positive and Negative Moments
229
Ratio of Ordinates of Constructed Elastic Line to those of the True Elastic Line
230
Shearing Force
231
Most Unfavourable Pressures
232
Recapitulation of most Unfavourable Conditions of Loading
235
Maximum Value of Reaction
236
Loaded Beam Inbuilt at A and B
237
Influence of Variable Cross Section upon the Stresses
238
Determination of the v and u Lines in a Continuous Beam of Variable Cross Section
239
Formation of Elastic Line Envelope of an Unloaded Span
241
Maxima of Shearing Force and Bending Moment in any Span of a Continuous Beam under Concentrated Loads
244
Formation of First Cord Polygon
273
Vertical through Centre of Gravity of As
274
Formation of other Force and Cord Polygons
275
Formation of other Force and Cord Polygons
276
Axes of the Central Ellipse
277
215
278
Relation between the u Intercepts
281
Reaction Intersection Curve Envelope of Force U and Envelopes of the Reactions Ū and Ữ
282
Arch Hinged at the Springings A and B
283
Practical Construction of Arches Hinged at Springing
284
Arch Centring 224 Forces resisted by an Arch Centring
285
CHAPTER VI
287
Anchoring the Chain
288
Suspension Bridge with Oblique Suspending Rods
291
Auxiliary Girders employed to Stiffen Suspension Bridge
292
CHAPTER VII
296
Turning Force Polygon round through an Angle
302
Conditions Simplifying Construction
310
Cohesion
313
Fluid Pressure behind a Retaining Wall
324
Counterforts
331
Centre of Gravity of a Trapezium
332
Section II Unsymmetrical Tunnel
336
Lamberts Problem Projection of an Irregular Quadri
350
Poles and Polars in Conic Sections
361
Ideal Circular Conic Section through the Summit of
367
Pascals Theorem
374
Projectivity of Points and Rays
384
LVIII
390
To construct an Involution of the Second Species
392
To find the Central Point O of the Involution of which we have two pairs of Conjugate Points
393
Forms Projective in the Circle LXIX General Theorem
394
Property of a Mobile Tangent cutting two Fixed Tangents
395
A Tangent moving between two Fixed Tangents the Rays generate two Projective Pencils
396
Case of Involution in a Circle
397
Preceding Section extended to Conics
398
Extension of lxxvii to the Parabola
402
Desargues Theorem in Conics
403
Application of Desargues Theorem in Conics when no Points are at Infinity
404

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Page 405 - AM)— EXPERIMENTAL MECHANICS. A Course of Lectures delivered at the Royal College of Science for Ireland. By RS BALL, AM, Professor of Applied Mathematics and Mechanics in the Royal College of Science for Ireland.
Page xviii - Ces procédés ont de plus le précieux avantage de porter toujours en eux-mêmes le principe de leur vérification, de telle sorte que s'ils peuvent, comme toutes les méthodes graphiques, laisser un doute sur une fraction décimale, chose très-indifférente en ce genre d'applications, ils sont en revanche exempts de ces chances d'erreurs grossières que comportent les longues opérations arithmétiques et les formules algébriques, où rien ne parle aux yeux.
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