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Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 34 (Paperback) Loot Price: R258
Discovery Miles 2 580

# Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 34 (Paperback)

## Books Group

Loot Price R258 Discovery Miles 2 580

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1881 Excerpt: ...We may therefore regard a point on the traversing bar as describing the locus, and since the extremities of the links which rotate describe exceptional loci, we will suppose the describing point different from these. The locus described is evidently symmetrical about the line of centres. Moreover, since the circular points are triple points, and there are three double points on the line of centres, we must, in order to have a unicursal curve, have on this line a contact of two branches whose common tangent isperpendicular to the line of centres. For we cannot have four double points on the line of centres identically, nor one double point finitely distant from that line; since, then, there would be another double point on the other side of it. Now, taking A as origin, and the line of centres as the axis of x (see figure), we have x--a cos p + (b + K) cos 6, y = a sin J + (4 + K) sin 6, x = ccosif + Kcos9-(-d, y = c sin ij + K sin 9; Solution by Professor Minchin, M.A. This is the famous "Equation of Three Moments," restricted to the case of a uniformly loaded continuous beam. Demonstrations of the equation will be found in various works on Applied Mechanics; among others, see those of Bresse and Collignon. Briefly the proof is this, --Let A, B, C be any three consecutive points of support; let M1; M:, M3 be the bending moments at these points; A0 and A1 the shearing forces just behind and just in front of A; B0 and B, C0 and C the shearing forces just behind and just in front of B and 0 respectively; I = AB, V = BC; u and w' the loads per unit length in the spans AB and BC. FT Now the bending moment at any section is equal to--, in the well P known notation of the subject. First take B as origin, BA as axis of x, and the downward vertical as axis ...

### General

 Imprint: Rarebooksclub.com Country of origin: United States Release date: March 2012 First published: March 2012 Authors: Books Group Dimensions: 246 x 189 x 2mm (L x W x T) Format: Paperback - Trade Pages: 32 ISBN-13: 978-1-130-36760-7 Barcode: 9781130367607 Categories: Books Promotions LSN: 1-130-36760-6

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