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 ...
|Country of origin:
||246 x 189 x 2mm (L x W x T)
||Paperback - Trade
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