478

HISTORY OF ENGINEERING.

Hook I.

5:2 = whole weight : vertical weight at the crown, 13 : 30 = weight at the crown : horizontal thrust.

G5 : GO = whole weight : horizontal thrust.

Therefore the proportion of 13 to 30 is that of twice the height {65 feet) to the half of thespan (300 feet). As the same load at the crown is produced by the other half of the bridge,this must be doubled, or say as 65 : GO :: 10100 tons : 9323 ; 10,000 tons being the wholeweight, and 9323 the horizontal thrust. Some mathematicians consider the horizontalthrust as only the half of this quantity, but this is a mistake.

Now this thrust is the same in every part of the arch, as is well-known; therefore thewhole of this thrust is borne by the middle joint of the seven ribs, and amounts to above1300 tons on each joint. Did the whole joint bear alike, there would be little danger, butwhen the arch is set up on its mold, and the middle frame or key-stone nicely fitted in, andthe seafFolding removed, every thing comes into a new situation, all settles. The joints aresqueezed close, and even the solid metal of the whole bridge suffers a compression : this isequivalent, as far as relates to the figure of the arch, to a yielding of the abutments. Oneinch of compression in the half arch will cause the crown to sink nearly 5 inches. A totalcompression of 3 inches in above 300 feet is no unreasonable supposition; this will producea sinking of 15 inches at the crown : should this take place without a change of shape inthe half arch, it is evident that the enormous pressure of 9000 tons will be borne by theupper end of the joints of the key-frame, and the lower end of the same joints will be muchless pressed. The frames will be hanging by their upper angles, and the upper rail of theframe will be strained with the greatest part of the thrust. I should fear exceedingly thatso brittle a substance as cast-iron would be very apt to chip off at the upper angles of theframes at the crown of the arch ; if any cement be admitted into the joints, I apprehendthat the sinking and the inequality of pressure will be vastly greater. If, indeed, the inter-mediate half arch between the crown and the abutments shall bend a little, this will tend toequalise the pressure on the joints at the crown. It may even bend so much, if ill-joined,as to make the middle joints bear most on the lower angles; but this is highly improbable,because the general shape of the half arch makes it almost incapable of bending, even thoughthe radial joints are not very accurate.

The method that occurs to me as the most effectual to prevent this risk is to form amiddle piece of the arch, so as to keep the mutual pressure diffused over the whole joints,even though the whole arch should settle considerably. Thus, instead of making the jointsstraight lines, I would make them arches of circles of about 25 or 30 feet radius, or still lessradius and more curvature, so as to lengthen as much as possible those joints which are tobear so great a strain. I would not, however, make more than two of these joints, becauseif these be allowed to slide a little on each other, having no joggles, the joints will keepclose, like the joints of a sector. It will not hurt the style of ornament if this middlepiece should differ greatly from the rest. I would also make this middle piece (or key)entirely of wrought-iron, as much better suited for preventing chipping at the angles, andfor affording fixtures for diagonal ties, which may be found necessary for stiffening thisweakest part of the arch. For if such ties or struts be attached to parts of cast-iron, andmuch greater strain be exerted there than in other parts, they are in great danger of snap-ping. It should be carefully kept in mind in this structure, that when a bar is sustaininga very great compression endways, or in the direction of its length, it is more easily brokenacross by any transverse strain. I have made many experiments on this kind of strain ; apiece of white marble \ inch square and 3 inches between the props bore 38 pounds.When compressed endways with 300 pounds, it broke with Impounds. The effect ismuch more remarkable in timber and softer bodies, but is considerable in all. and thiscircumstance will make it hazardous to employ ties in the bridge. We extend theiraction to considerable distances, so as to create great strains on particular points. YetI think that ties may be usefully and safely employed, diverging from the lower side of thismiddle piece, and connecting it with several frames on each side, in order to .stiffen, bysupporting the middle points.

The part of the arch which requires the greatest accuracy in the construction is about80 or 100 feet on each side of the middle and the lowest ring of frames all over, if those beclose-jointed; the rest is free from all risk. The portion mentioned of the middle must becarefully jointed up to the roadway, so as to make one mass; this being set on the arch-ringwill tend to force it up a little at the haunches; hut the work above it will effectually pre-vent this, although not executed with such accuracy.

In the forming of this profile, by which the haunches are filled up, it is asked whether itis more advisable to cast the frames in long masses or in smaller frames. In carrying theprinciple of masonry through the whole, one is prompted to cast the pieces, so as to inter-rupt the lines of joint, or to break joint, as masons call it. I should think this hazardous.If one half of a radial joint be closer than the other half, there is a great risk of the sides ofthe frames snapping in the middle. Plates of copper should be employed for making upall such deficiencies or even tin-foil, such as is used for the silvering of mirrors; perhapssome way might be fallen upon to apply heat to the pieces when set in their places so as to