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when hung with the weight attached to the end of it, the piers must be so high as to give the chain a sinking or curve of the one full seventh of the span. The ends of the chains must descend from the tops of the piers with the same inclination that they take inwards, until each end reaches the bottom of a digging, large enough to contain stones and other materials sufficient to counterbalance the weight of the bridge and what may chance to be thereon. The chains, if only one to a side, must be made with four branches at each end, to be let down through as many stones, and to be bolted below. These stones are laid flat on the bottom of the digging: other fat stones may be placed thereon, to bind and connect the whole, that they may have the same effect as a platform of one piece; four or more joists will be necessary for the upper tier-to extend from end to end of the bridge—each will consist of more than one piece; the pieces had best pass each other side by side, so that the ends may rest on different joists on the lower tier. The splice will then extend from one joist to another of the lower tier, and must be bolted together by one bolt at each end of the splice. The plank flooring is laid on this tier. It will be probably found most convenient that the chains be made with links as long as the space between the joists: every other suspender must attach to a link of the chain edge upwards, perhaps this may best be done by a clevis to go through the upper link of the suspender, and embrace the link of the chain and receive a key above-the other suspenders will come up through the flat links of the chain and receive a key above the lower end of the lower link of the suspender may be made so wide as to receive the end of the lower tier of joists.
In the year 1801, I erected the first bridge on this construction over Jacob's creek, on a contract with Fayette and Westmoreland counties, to build a bridge of seventy feet span, twelve and a half feet wide, and warrant it for fifty years (all but the flooring) for the consideration of six hundred dollars. Nothing further of the kind was attempted for six years. The exclusive right was secured by patent in the
1808. There are eight of these bridges erected now; the largest of which is that at the Falls of Schuylkill, 306 feet span, aided by an intermediate pier; the passage eighteen feet wide, supported by two chains of inch and half square bar. There is also one at Cumberland (Maryland) supported by two chains of inch and quarter bar, span 130, width 15 feet. Another over the Potomack above the Federal city, of nearly the same dimensions as that at Cumberland. This season, one has been thrown over the Brandywine, at Wilmington, 145 feet span, supported by four chains of inch and zths square bar, breadth 30 feet, it has two carriage ways, and one or two foot passages. There are two erected near Brownsville, in Fayette county, the spans 120 and 112 feet-inch and quarter iron, breadth 18 and 15 feet. There was one built last season over the Neshamany, in Buck's county, near 200 feet span, one pier. An incorporated company at Frankfort, have begun to build one over the Kentucky river, span 334 feet, with one pier. Another incorporated company at Pauling's Ford, on Schuylkill, are taking measures to erect one this summer at that place near 200 feet span, without any pier.
The following particulars it is thought will enable any person to make a rough estimate for any particular case. A bridge of 300 feet span and 30 feet wide, with two or more passages, so arranged that one may undergo repairs while the others are in use.
support such a bridge with four chains of inch and half square bar, would require about twenty tons of iron, and would be equal in strength to eighteen bars of iron one inch square--a strength capable of bearing 540 tons weight. And supposing the timbers to be of pine or other light wood, the whole materials will not amount to 140 tons; consequently the bridge will have an excess of power of at least 400 tons beyond its own weight.
A bridge of the same span fifteen feet wide would be supported by two such chains.
One of 150 feet span and 15 feet wide, would require about five tons of iron—the chains being one half the length of those in the first case stated, and the materials only one fourth of the weight. But in order to possess that strength on which these calculations are made, the chains must be allowed a sinking or curvature of nearly one sixth of the span; and when this proportion is adhered to, the strength will be the same, whether extended to three feet, or to three hundred.
When there is but one space or span, and no middle piers, nearly half the chains are taken up in fastening; but the same fastening would serve for any number of spaces.
The smith's work will cost two or three cents per pound, and the carpenter's work is not worth naming.
The scantling will cost about as much as the plank for flooring. No scaffolding is necessary for raising the bridge.
With allowance for thickness at the ends of the links, and wasteage in making, &c. a chain of inch and half square bar will weigh sixteen pounds per foot one of inch bar will be about seven and a half pounds per foot. About one fifteenth of the span will give curve sufficient, and one fifth the weight of the chains will be iron sufficient for suspenders, bolts and keys.
An estimate on these principles for a bridge of 500 feet between the abutments, with only one pier, will not amount to seven thousand dollars, exclusive of abutments and pier. Compare this with the Philadelphia Schuylkill bridge of the same extent, which cost sixty-five thousand dollars after the abutments and the two piers were completed; total expense, three hundred thousand dollars.
It is believed that saving the expense of one pier, the duration of materials, facility of erection, as well as repairing, is worthy of public attention.
There is no reasonable doubt, that in some extraordinary case this kind of bridge will be extended to one thousand feet, when the subjcct shall be fully understood; and should it ever be necessary, I would undertake to satisfy any person concerned, that it is capable of a still greater extension.
As the bridge has no support but the chains, two things ought to be accurately understood; i. e. how much iron can bear at a direct pull endwise, and what it can bear in the other positions in which it is to be employed. As to the first, my experiments agree with the opinions of those who have investigated the subject; but I have made my calculations at 60,000 lbs, to the inch square bar, which is something less than the strength of iron of the lowest quality.
But what a chain will bear when the two ends are fastened, and the weight affixed to the middle, or rather equally distributed along it, is a question that I presume may be determined by fastening one end of a line, and extending the other horizontally over a pully
whirl with a given weight attached to it, (say 10 lbs.) then let as many pounds be placed along the middle part at distances horizontally equal. The middle part of the line will then represent the chains loaded as when supporting the bridge. The end that hangs in the manner of a plummet, determines the tension, and the pullywhirl equalizes it between the two parts. The conclusion is unavoidable, that a line or chain will bear just as much with the curve of the middle part, as it would bear attached like a plummet; and this will be found equally true in a long distance as in a short one; so unequivocally true is it that the balance at the end determines the tension—that the line was as tense before any weight was put on the middle part, as when the ten pounds were affixed to it. The same ten pounds will balance fifteeen or eighteen pounds, provided the line is permitted to sink until the balances find their proper level or equipoise. It is also clear, that when there is little or no curve, one pound creates more tension than ten, when the curve is greatly larger. I have stated the strength of the chain at 60,000 lbs. per inch bar, when the sinking or curve is nearly one sixth of the span. By some hasty experiments that I have made, it appears that with a sinking of one ninth, it will bear 45,000 lbs. and at a sinking of one fourteenth, it will bear 30,000 lbs. and at a sinking of one thirtieth, it will bear only 15,000. Thus we see the effects of greater or less curve. Another purpose to be answered by the line and balances, is to find what position the chain would naturally take when supporting a bridge. We know it forms no part of a true circle, nor what is called the catenarian curve; the latter is formed by the weights being equal along the curve line, but in the case of a bridge, the weights are equal along the horizontal line.
To find the proportions of the several parts of a bridge of one hundred and fifty feet span, set off on a board fence or partition one hundred and fifty inches for the length of the bridge, draw a horizontal line between these two points representing the underside of the lowest tier of joists on this line mark off the spaces for the number of joists intended in the lower tier, and raise perpendiculars from each, and from the two extreme points, then fasten the ends of a strong thread at these two perpendiculars, twenty-three inches and one quarter above the horizontal line-the thread must be so slack that when loaded, the middle of it will sink to the horizontal line; then attach equal weights to the thread at each of the perpendiculars and mark carefully where the line intersects each of them. The distances between those marks on the curve line, is the length of each link for its respective place; and the distances from each of these marks to the horizontal line is the length of each suspender for its proper place.
It will sometimes be convenient to have a pier so nigh the abutment, that a part of the bridge can be attached to the chain as it descends to the ground to fasten. In one case, where the elevation of the chain at the pier is but twenty feet, there is forty feet attached to the chain, and ten more to reach the abutment. In all these cases, the line and balances determine every thing.
In a bridge of but one arch or space, it must be considered a grievance, that the chains, including the branches, must be nearly twice as long as the bridge. I have just been trying on a space of 400 feet between two piers how much of the bridge can be attached to the chain as it descends to the bank to fasten; and it appears that about 170 feet may be attached to each end in this way. The two ends will and must be exactly in the position of a half bridge as far as they go, the end of the chain taking nearly a horizontal direotion, may be let into the bank as far as may be thought proper. Here then is a bridge of say 740 feet, with scarcely any mason work but two piers, and the chains very little longer than the bridge. Suppose a shorter space to be divided in this way, say 300 feet, the middie space would be about 175: the chains would then need to be but a little more than half as strong, and not much more than half as long.
The spaces or spans may be different in the same bridge, and the suspenders must be longer in the short spaces, for although with equal weight on all the spaces the curve would be in proportion to the span. But the large spaces having more weight of bridge to support, must have more than its proportion of curve and the short spaces less, in order that the tension may be equal on all
In a bridge of two or more spaces or spans a load on one will tend to sink it and raise the rest; to resist this tendency the framing