Popular Science Monthly/Volume 36/February 1890/The Evolution of the Modern Railway Bridge
|THE EVOLUTION OF THE MODERN RAILWAY BRIDGE.|
OF THE STATE UNIVERSITY OF IOWA.
A BRIDGE is a structure over a river, ravine, or other opening, for the purpose of sustaining a moving load. This, in the case of a railroad bridge, consists of a heavy locomotive and train coming on at one end, rushing rapidly over the bridge, and off at the other end. This fact, that the load to which bridges are subjected is a moving load applied for only a short period of time and then removed, is a most important factor to be considered in calculating the necessary strength of the various members, as the strain produced in any piece of material by the application of a load is nearly doubled when the load is applied quickly as compared with that produced by the same load when applied gradually.
Bridges may be divided into the following classes: 1. The beam or girder. 2. The framed truss. 3. The arch. 4. The suspension bridge.
The most ordinary form which we see in this country, and the one most generally used for the purpose of railway bridges, is the framed truss, and that is the one the development of which it is our purpose to show.
The one point to be carefully studied in all bridge construction is economy—that is, to get as much strength with as little material as possible; in other words, the maximum amount of strength with the minimum amount of material.
The simplest method of crossing any opening where the dimensions of the opening are not so great, or the load so heavy, as to forbid its use, is by means of a plank placed from one side to the other, making the plank of such a length that the ends may have sufficient bearing upon each side of the opening (Fig. 1).
In crossing an opening by means of a simple plank or beam, supposing we make the beam large enough, it answers every purpose and will hold up the required load. But in this there is great waste of material. We will take, for example, a plank twelve inches wide, and three inches deep, over an eighteen-foot opening—that is, the plank would have to be about twenty-one or twenty-two feet long, in order to allow the ends sufficient bearing surface upon the masonry on each side. This plank would hold up a certain amount of weight, but, as the weight is increased, in a very short time the plank would begin to bend and buckle in the center. In order to increase the strength of this primitive bridge, we could place another plank beside it, making the bridge twenty-four inches wide, and, if the passing load were made to bear upon the entire width of this bridge, of course the bridge would bear just twice as much as one plank; but, in order to double the strength of the bridge, we have also doubled the amount of material necessary in its construction, and therefore have not in any way increased the economy.
This system might be carried on to infinity, and almost any amount of required strength be obtained by placing a sufficient number of planks one beside the other. But, returning again to the two planks, instead of placing them one beside the other, suppose we place one plank on top of the other, and nail them together firmly, so that they shall act as one plank (Fig. 2). We
then have a bridge eighteen feet long, twelve inches wide, and six inches deep. In this bridge we have exactly the same amount of material we had when the two planks were placed side by side, but we have four times as strong a bridge instead of only twice; that is, we have doubled the amount of material, but we have multiplied the strength by four.
If one plank would hold up one hundred pounds on the center, then the two planks placed side by side would hold up two hundred pounds; while, placing the planks one on top of the other, and nailing them firmly together, they would hold up four hundred pounds. In this way we see that, in order to increase the strength of the bridge or beam faster than we increase the amount of material, the increased amount of material should go into the depth of the beam and not into the width of it. This is one of the first principles in the resistance of material, that the strength of a beam varies directly as the width—that is, if we make the beam twice as wide, it will hold twice as much; and that the strength varies as the square of the depth that is, if we make it twice as deep, it will hold up four times as much. If we make it three times as deep, it will hold up nine times as much of a load. So that you can readily understand that, in order to increase the strength of the bridge or beam without increasing the material in the same proportion, the increased amount of material should be put into the depth and not into the width.
We now have a bridge twelve inches wide and six inches deep, which will hold up four times as much as our original bridge, twelve inches wide and three inches deep, and the amount of material is simply doubled. To advance one step beyond this, suppose we take one of the planks and stand it up edgewise, and then place the other plank upon its flat side upon the top of this, as shown in Fig. 3, and nail the planks firmly together.
We now have a bridge twelve inches wide, as we originally had, but fifteen inches deep, or what is known as the T-bar or girder, and the only difficulty about this bridge is the trouble in making it stand up; being so much higher than it is wide, it has a great tendency to tip over. But supposing the planks are made to stand in this shape, which is a simple matter, we then have a bridge fifteen inches deep, which will hold about seven times as much load as the original plank. Of course, if the bridge were made fifteen inches deep and the same width, that is, twelve inches wide, it would hold twenty-five times as much as the original bridge; but by turning one of the planks upon the edge we have increased the depth and decreased the breadth, so that the breadth of the bridge under the top plank is only one fourth of what it was before, and the total strength of the bridge is from seven to eight times that of the original plank. Now, in order to obviate some of the difficulty in making this bridge stand up, suppose we take the plank that is upon the edge and make two planks, each of them twelve inches wide but only an inch and a half thick, and then nail the floor plank upon the edges of this, making an inverted box, as shown in Fig. 4. We then have a bridge that there is no trouble in making stand, as it has twelve inches of bearing surface, and we have the same amount of strength as when it was in the shape of the T-bar, and we have what is technically known as the U-bar or channel-bar.
In this U-bar there is this trouble: that, having the sides only an inch and a half thick and twelve inches deep, there is a tendency to bend in the sides that is, a tendency to give sidewise; and in order to obviate this we take the top plank and split it in two, making two planks twelve inches wide and an inch and a half thick. Nail one on the top and the other on the bottom: we get what is called a box girder (Fig. 5), and which has about nineteen times the strength of the original three-inch plank and only double the amount of material.
So far we have considered our bridge as being only twelve inches wide. We now wish a bridge wider than this, but with no more material in it except what may be needed in order to make the floor. Suppose we take the top and bottom plank of this box girder, cut them in two lengthwise, making out of each two planks six inches wide instead of twelve, and we fasten these
upon each of the vertical planks, as shown in the drawing. We then have what is technically known as an I-bar, or flanged girder (Fig. 6). Provided these flanged girders are so braced as to prevent their bending sideways, the two flanged girders are of exactly the same strength as the box girder, and, as you see, can be placed at any distance apart, and the floor simply placed on top of them or on the lower flange, and we have a bridge as wide as we wish, with the strength of the box girder.
This I-bar, or flanged girder, is one of the most generally used forms of construction for bridges of short spans.
So far we have considered the material used to be simply wood, but I-bars are now made of iron or steel, and within the last few
years entirely of steel, owing to the fact that the improved method of making steel has rendered it even cheaper than wrought iron.
Let Fig. 6 represent a side-view of the flanged girder, or I-bar, of which Fig. 6 A is an end-view.
Suppose this beam to be supported at each end and a load placed upon the center. Then the tendency of that load would be to bend the beam down in the shape of the dotted line, and, in case the load is sufficient, it would break in that way.
Before the breaking-point is reached the top and bottom of this beam are subjected to totally opposite classes of strain, as you will see. If you bend the beam, the tendency in the bottom of it is to pull the beam apart, or, in technical language, the bottom flange of the beam is in tension—tension being the force which tends to pull apart the particles of the beam. Thus, if you take a string fastened at one end, and hang a weight on the other end, the string is in tension, the action of the weight being to pull the particles of the string apart.
The top flange of the beam is in compression—that is, the particles of which the beam is composed are forced together. It is the same strain obtained if you take a vertical post and put a weight on top of it; that weight tends to force together the particles of the post, and the post is said to be in compression.
It is well to get a thorough understanding of these two kinds of strains, as they are the principal strains that have to be considered in all bridge-building. There is a point between the top and bot-tom of the beam at which the character of the strain changes from compression into tension, where there is no strain at all, and the amount of strain in the beam decreases from the outside toward the center until this zero-point, or neutral plane, is reached; and, as the greater part of the strain comes upon that portion of the beam farthest from the center, you will at once see the economy and necessity of placing as much of the material as far from the center as possible—that is, placing the material where it is going to do the most work, and this is what has led to the adoption of the flanged girder, or I-beam, as a favorite method of construction. The principal part of the material is placed at the two outside edges of the beam where the strain is the greatest, and the amount of material between these two outside flanges is simply enough to keep the flanges apart.
As the size of the opening to be crossed increases, the size of the flanged girder necessary to hold up a given load increases, so that in a very short time the piece of iron or steel necessary becomes so large as to make it almost impossible to handle if it is all in one piece, and also a great deal of the material in the flanged girder is absolutely of no use—that is, a great deal of it can be cut away and used to more advantage in other places.
This leads us at once to the framed truss or framed girder. There is one thing in connection with framed trusses to which I wish to call your attention, and that is, the whole foundation of the framed truss is based upon a triangle. You will readily see the object of this. Suppose four pieces of timber are framed together,
as shown in the drawing (Fig. 7), in the form of a square or rectangle. Then any strain coming upon one side of this rectangle tends to change the form of the figure, and, unless the joints are made perfectly stiff, the rectangle is changed to the shape shown in Fig. 8, where every piece is of its original length, and simply the angles have been changed. Now, suppose we divide this rectangle, by means of a brace or tie, into two triangles. Then not one of these timbers can be moved, or the form of the rectangle changed in any way, without lengthening or shortening the diagonal which divides it into triangles, and, therefore, the rectangle with the brace and tie forms a perfectly rigid figure (Fig. 9).
In other words, the triangle is the only figure the form of which can not be changed without changing the length of one of the sides; and thus any truss, to be perfectly braced and able to withstand any strains that come upon it, must be framed so as to be divided into a series of triangles.
Returning to our original beam thrown across an opening, we will suppose that we have a beam long enough and strong enough with the required load to cross an opening eighteen feet wide, and that we have an opening thirty-six feet wide which we wish to cross. That could be done by building a pier in the center of the opening and dividing it into two openings, each eighteen feet, as shown in Fig. 10; but, in the case of a bridge over a road or over a small river, it would not be advisable to block up the way by this pier, and some other method must be found to support the two inner ends of the beams. The simplest plan of doing it is shown in Fig. 11. Taking two beams that are each slightly
longer than eighteen feet, we throw them across the opening, as shown in Fig. 11. These two beams meet at the angle, the apex, A, of which is up, and, if the two lower ends are kept from sliding apart, will stand in that position. Now, if from the angle where these two beams meet we let down a rope or iron rod, run out the floor beams eighteen feet long, and connect the inner end of each to this rope or rod, we have a bridge covering an opening thirty-six feet long—that is, one end of each floor beam rests upon the ground, the other end is sustained by the rope or iron rod, and all the weight upon these ends of the beams passes up the rod, and then comes down the two diagonal beams to the abutments. The one thing necessary in this is that the lower ends of the two diagonal beams shall be so fixed as to make it impossible for them to slip out in the direction of the arrows, and this object is usually attained by making the floor stringers serve as a tie to hold them together. In the drawings, the full black lines are in compression and the dotted lines are in tension. Thus, you see the vertical rod or rope in the center is in tension—that is, a weight being at W, all of that weight comes directly upon the rod and is carried to the apex, A; then half of it passes to each side down the inclined braces, and they are in compression. The tendency at the foot of these braces is for them to slip out in the direction of the arrows. They are held together by the tie-rod or floor stringers, which are in tension. In regard to tension and compression, you may get a better comprehension of them if you understand that a cord or rope can be used for any member of a bridge that is in tension, while a post or some stiff piece of timber or iron is necessary for anything in compression—that is, in all these diagrams the dotted lines could be replaced by ropes or cords, while the full black lines are obliged to be iron or wooden posts or braces.
You thus see that we have the simplest form of a framed truss. This form of truss is called the king-post truss. Now, as the width of the opening increases, the height of the posts would also have to increase, and in a very short time would get so high, and make the inclined braces so long, as to become unwieldy. In order to overcome this, after a certain height has been reached, instead of continuing the king-post higher, we simply cut it off and substitute two posts or rods in its place (Fig. 12). In this the
length of span that can be covered with the same sized material is one half larger, and the bridge is divided into three panels, as they are called. A panel is one of any number of equal parts into which the truss of a bridge is divided by means of the posts or rods. This second truss is called the queen-post truss; here also the full black lines are in compression and the dotted lines are in tension. As you will notice in this truss, which is also the case in the flanged girder, the top part of the truss and the top flange are always in compression; so the lower chord is always in tension, as the lower flange in the flanged girders. This principle is the same in all framed girders.
Either of these trusses can be inverted whenever it is desired, so that the truss comes below the floor, as shown in Figs. 13 and 14; the only difference that it makes is in the character of the strain that comes upon the different members of the truss. The
vertical member in the upright truss is in tension, and when the truss is inverted it is in compression, as shown in the drawing. The braces become ties, and the floor stringers are in compression. Whenever it is desired to make the floor come upon the top of the truss, then the bottom chord or tie-rods can be omitted entirely, and the horizontal thrust taken by means of the masonry abutments (Figs. 15 and 16). There the weight comes directly down from the top of the bracing, and the lower end of the braces are held in place by the masonry abutments.
From some combination of these trusses can be constructed any form of bridge, with the exception of the suspension bridge and the arch. By increasing the number of panels or by combining a number of king-post trusses (Figs. 17 and 18), we have what is known as the pony truss, and for short spans one that is used to a great extent on all railroads.
Every bridge is composed of two or more trusses. The ordinary railroad bridge is composed of simply two trusses, one upon each side. These trusses are connected at the top and bottom, and the train can either run over the top of the bridge, or through the bridge on the bottom chord.
In the pony truss, the only distinctive feature is that the trusses are not deep enough to allow of their being fastened together across the top, when the train runs through upon the bottom chord, and therefore they can only be used for very short spans, and. it is considerable trouble to so brace them as to keep them in a true vertical plane. These pony trusses, however, when used as a deck bridge, that is, when the train runs on the top, can be braced so as to form a very firm bridge, and practically it is simply a box girder (Fig. 5).
The members of a bridge at the top and bottom of each truss, either horizontal, inclined, or curved, are called chords; that at the top is called the top chord (A B, Fig. 22), the bottom one, the bottom chord (CD, Fig. 22). In the bridges we are considering, they are usually parallel.
The brace or strut is a compression member, and may be either vertical or inclined (E F, Figs. 21 and 22), the object of which is to keep the two chords apart. The tie is a tension member, and also may be either vertical or inclined (G H, Figs. 21 and 22). The lower chord being always in tension is sometimes called the straining piece.
In some types of bridges which we will take up at once there is no bottom chord (Fig. 19). We have what is called the Fink truss. As will be readily seen, it is merely a combination of the inverted king-post trusses, combined in such a way as to suit any required span. In this bridge the bottom chord is not in any way necessary to the proper construction of the truss, but in case of a long span it is usually put in as shown by the dotted line, not in any way to increase the strength of the truss, but simply to add to its stiffness and stability. The Fink truss was invented by Albert Fink, and manufactured for many years by the Louisville Bridge and Iron Company. For short spans, or what are usually called shore spans in many-span bridges, it is a most convenient and economical method of construction, and has been very much used. The top chord is in compression, as shown in the drawing, and is usually made of wood, although this is not by any means necessary. The posts, or vertical compression members, are usually of iron, and the tension members consist of round iron rods, fastened by means of an eye and pin at the ends. The next form of truss is that known as the Bolman truss (Fig. 20). In this also, as in the Fink truss, there is no bottom chord necessary. The distinctive characteristic of the Bolman truss is that from the lower end of each vertical compression member the tension members run directly to each abutment, differing in this respect from the Fink truss, where most of the tension members run across simply one or two panels of the bridge. In this way any load coming upon the top of one of the panels in the Bolman truss passes down the vertical compression member and is at once carried to the abutments by means of the tie-rods. Theoretically, this bridge is one of the most simple that can be constructed; but when the span becomes of any great length, the length of these tie-rods becomes so great as to render them unmanageable, and within very small limits they become impracticable for that reason. Hence, the Bolman truss has not been used to any considerable extent. By the addition of the bottom chord to support the floor timbers of the bridge, either the Bolman or the Fink bridge can be used as a through bridge as well as a deck bridge, although to achieve the utmost economy in their use they are both eminently deck bridges.
We will now take up the different kinds of trusses that are used in ordinary railroad work, all of which are simply some combination of the king-post trusses, either upright or inverted. The first and most common form in this country is what is known as the Howe truss (Fig. 21). In this the braces are diagonal and the tension members are vertical.
This form of truss has probably been built a hundred times more than any other form that is in use. It is not in every respect an economical truss; but the reason of such general use is the fact that it is one of the most simple to construct. The full lines are those in compression, and are usually built of wood. In the Howe truss, the lower chord, which is in tension, is also built of wood, while the only iron-work about it is the vertical rods and cast-iron blocks for the ends of the post. You will thus see the advantages of this truss in a country where wood is very plenty and iron is scarce. The construction of the iron-work is very simple, and the parts are in pieces, so that they can be easily handled by one gang of men with the ordinary block and tackle. The angle blocks are all duplicates, so that, after a pattern has once been made, a great many similar pieces can be made from it; and this, in the absence of skilled labor or proper shops for doing bridge work, is a great saving of time.
In all Howe trusses a very large "factor of safety" has to be used in order to take into account the uncertain character of the wood. By a factor of safety we mean this: you have a given load which is to be supported by a bridge; if all the material used in that bridge were absolutely perfect, the size of each piece would have to be exactly large enough to bear its part of the strain, and no larger; but as neither in iron or steel, and particularly in wood, can you calculate just exactly how many pounds of strain any particular piece will stand, in order to make it perfectly safe you use, in calculating the size of the bridge members, the load it is to bear multiplied by five, and sometimes even by ten, and then make the bridge theoretically strong enough to hold up this load that is, five or ten times the amount of load that ever can come on it—and this five, or ten, or six, as the case may be, is called the factor of safety; that is, if all material used in the bridge were absolutely perfect, the bridge would hold up five or ten times as much as ever would come upon it; and wherever a great deal of wood is used the factor of safety has to be very large, as the amount of strain that wood will bear is very uncertain, and varies under different circumstances.
You will readily see that the Howe truss can be used either as a deck bridge or a through bridge, and remember that the Howe truss is the type of bridge that was generally used upon railroads so situated that wood was plenty and iron expensive, and without money enough to send a long distance for iron bridges; and there have been some remarkable examples in this country of the durability of Howe-truss bridges designed by ordinary carpenters without any technical education.
As the price of iron decreased, in a very short time the lower chord of the Howe-truss bridge was made of iron instead of wood, as it was found to be much more economical, and it was then what is called a "combination bridge"; that is, of wood and iron.
The next form of bridge is what is called the "Pratt truss" (Fig. 22). The distinctive feature of this is that the compression members are vertical, while the tension members or ties are inclined or diagonal. In this, the amount of iron, supposing the tension members to be of iron and the compression members of wood, is increased and the amount of wood is decreased. This was a very natural result as the price of iron decreased. In a short time the wooden posts were removed and iron posts substituted for them, and we then have an entire bridge of iron, in which the compression members are vertical and the tension members inclined, and it is the most generally used form of iron bridge in this country; it may be called the typical American railway bridge.
The next form of truss that we will examine is what is known as the Warren triangular girder (Fig. 23). You will see that each of the pieces connecting the upper and lower chords acts both as a tie and a brace—that is, is subject to both compression and tension. The only advantage that can be claimed for this bridge is simplicity and a fewer number of parts than any other form of bridge truss; but by thus reducing the number of parts we have increased the size of the parts that are used, and thus, to some extent, done away with the advantage. Each of the tie-braces, as they are called, crosses one panel, and the bridge is thus divided into bays two panels long. The vertical rods, as shown in the drawing,
are not in any way necessary to the theoretically proper construction of the truss, but are simply put in to support the chord between the panel-points and make it able to bear the cross-strain that comes upon it from the floor system, provided the bridge is a through bridge. When the bridge is used as a deck bridge and the floor system laid upon the top chord, there is the same necessity for vertical posts.
In countries where it is possible to procure good timber of large size, the Warren triangular bridge is as economical and convenient a form of truss as can be built. To use it in its most economical manner the lower chord is usually made of iron, as that simply has to withstand tension; but the tie-braces are made of wood, and also the top chord. One point which is to be studied carefully in the Warren triangular truss is the fastening of these braces, as they must be fastened in such a manner that they not only will resist compression, but also that they will act as ties and resist tension. This necessitates a rather more complicated method of fastening.
Another great advantage connected with the use of the triangular truss is the ease with which, when necessary, any piece can be removed and replaced by a new piece without in any way impeding the passage of trains over the bridge during the operation. In the case of wooden or combination bridges this becomes a matter of great importance, as the timber in these bridges is exposed to alternate dryness and moisture, and thus, in a comparatively short time, decays, and there soon is the necessity of replacing the bridge piece by piece; therefore any bridge that is constructed in such a manner as to make this possible, without impeding the traffic on the road, possesses a great advantage over other forms of bridges. The triangular truss is a favorite method of construction on all railroads in the southern part of this country running through that belt where it is possible to obtain, at comparatively slight cost, yellow pine for the requisite timber.
We come next to the last type of bridge that has been used, to any great extent, upon the railways of this country. This bridge is called the Post bridge (Fig. 24), taking its name from its inventor. The characteristic features are that the compression members are inclined at what is claimed to be the most economical angle—that is, the most economical in regard to the amount of strength obtained for the amount of material used. They are
so inclined as to cross one panel of the bridge, while the tie-rods, running at an angle with the braces, cross two panels. This is the only advantage that can be claimed for this form of truss, and much of this so-called advantage is more than counterbalanced by some of the difficulties encountered in the actual construction; and whether the bridge really in itself is a more economical bridge than the Pratt, yet remains to be practically proved.
We stated in the beginning that bridges consist of arches and suspension bridges as well as framed trusses. The relation between
the framed truss and the arch will be readily seen by an examination of Fig. 25. Take a truss of the Pratt pattern; then, in place of having the top chord parallel with the lower chord, let the compression members be increased in length, as shown in the drawing, and the top chord take the form of an arch, and we have the bow-string girder. The ends of the arch on each side are simply held together by means of the lower chord, which acts as a tie-rod upon them.
Now, in the case of a masonry arch (Fig. 26), which has the weight all on top, there is no necessity for the tie-rod to hold the ends of the arch together, for the reason that the ends of the arch are always built so as to abut against heavy masonry which will withstand the horizontal thrust, and thus without the intervention of any tie members we have a perfect bridge by means of the
arch, all the weight coming upon the top being passed from one stone to the other in the arch until it reaches the two abutments the same as in a framed truss.
The suspension bridge (Fig. 28) is nothing more or less than the arch turned upside down. In the arch, as we have seen, the
only strain that comes upon it is compression; in the suspension bridge, on the other hand, the only strain that comes upon the sustaining member or cable which is stretched between the points of support is tension. In the arch bridge all the weight comes above the arch and presses down upon it; in the suspension bridge all the weight comes below the suspension chains and simply hangs from them. In the suspension bridge the cables, chains, or any other flexible devices are stretched between the two points of support, the ends carried over the tops of the towers, and firmly anchored in the ground beyond. Then the roadway of the bridge is simply hung by tie-rods from this suspension cable.
The suspension bridge is undoubtedly one of the oldest forms in existence. At the time when our ancestors were either swimming across creeks, or cutting trees, making them fall across in order that they might walk over on them—that is, one thousand years ago—the Japanese were building suspension bridges which are in use to-day, using iron chains for suspension cables, and in every way building them in as scientific a manner as the East River Bridge in New York is built to-day. Of course, there was a certain crudeness as to the methods which were used, but this in no way affected the scientific principles on which the bridges were built. It is not our purpose, however, in this paper to take up the question of suspension bridges.
We pass now to the last form, and in this country at least the latest form, of the framed truss—that is, the cantilever bridge. The object of the cantilever bridge is to make possible the economical construction of long, clear spans of a rigid truss, and thus do away to a great extent with the necessity of suspension bridges, as there are many disadvantages besides the mere one of expense that are connected with the use of suspension bridges. The other advantages of the cantilever will be taken up later.
To show the development of the cantilever bridge, we will take two king-post trusses (Fig. 29); putting them together, we
form a bridge of two spans, which has an abutment at each end and a pier in the center. In case this was for the passage of a river, the center pier would come directly in the center, obstructing navigation to a great extent, and otherwise prove an inconvenience. We use the king-post truss merely as the most simple form of truss that is built. In any other form that could be built the result would be the same; that is, for a bridge of two spans there would be a pier in the center of the river, and for any span that could be built of any of the types of bridges which we have noticed thus far the amount of open space that would be left in the center of the river may be less than that required by navigation, so that, from what we now have, our only remedy would be the use of the suspension bridge.
In order to do away with this, and make a wider opening in the center of the river, suppose we take away the center pier and replace it by two piers directly under the king-posts of the truss (Fig. 30). In this way we see we have left a large, clear span in
the center of the river, and we have in no way increased the amount of material necessary for the building of the bridge, and the two spans that we are using are now balanced, each upon the top of its respective pier. These two spans are fastened together in the center, and the shore ends of both are anchored firmly, in order to keep them from tipping up whenever a load comes upon the river end. We thus see that we have doubled the clear span in the center of the river, and we have what is called a cantilever bridge; that is, a truss supported at one end, and extending out over an opening, there being no support under the other end. Now, suppose it was desired to make this center opening still larger, we have simply to move the piers apart (Fig. 31). We
have our two cantilever spans. The shore end of each is firmly anchored down, and the two other ends, A B, project simply into space. If we build thus, the two ends, A B, are firmly fixed and can not in any way yield to the load that may come upon them. If we now construct an ordinary framed truss, of either the Howe, Pratt, or any other type, and instead of putting this truss upon two piers or abutments we simply hang it between the two ends of the cantilever spans, A B, which are projecting over the river, the weight of this truss will be sustained by the tie-rods from the king-posts, or in the case of the cantilever that run over the tower and are anchored down upon the other side. We thus see that by increasing very slightly the amount of material used in the construction of the "bridge we have an open, clear span in the center three times the width that would be possible with the ordinary framed truss, and we have what is known and has lately become famous as the cantilever bridge. The spans C A and B D are called the cantilever spans, and A B the suspended span.
The variations in the cantilever bridge are almost infinite, although the principles in all of them are the same. In the place of using the upright truss, for example, this truss can be turned over, and the ties then become braces, the floor comes upon the
top, the shore ends being firmly anchored in place, and, the suspended span held in place, we have a cantilever of the type that has just been erected across the Hudson at Poughkeepsie (Fig. 32), while the first example given you is the type of cantilever that crosses the St. John River at St. John, New Brunswick (Fig. 31).
Then, when a greater length is desired and increased strength, as in the case of the bridge across theof Forth, in Scotland, we simply combine the two, putting the two king-post trusses base to base, and hanging the suspended truss between (Fig. 33).
In that way we have the strongest form for the cantilever bridge, and there is hardly any limit to the length of span that can be made by this method.
The advantages gained by the use of the cantilever for long-span bridges are as follow:
As a substitute for the suspension bridge it is, up to a certain length of span, less expensive, and it can be given great rigidity and stability which are impossible in the suspension.
As a substitute for the ordinary framed truss it has the advantages of not requiring any false works for its erection. In the erection of the ordinary bridge there must be built first a timber frame or staging between the piers to sustain the weight of the different parts of the bridge while it is being put together. This is a great expense; and in some cases, where the bridge is far above the water, the current very rapid, or an existing necessity of not obstructing the water-way, becomes impossible. In the erection of a cantilever, each cantilever span is balanced on its own pier and built out each side from the tower in such a manner as to preserve this balance until the shore ends are anchored firmly, after which the river ends can be extended as far as desired. The suspended span, which is never of extraordinary length, can usually be built directly from the ends of the cantilever spans, and the necessity of false work entirely done away with.
In all bridges of long span that the weight of the bridge itself is by far the greatest load that the bridge has to bear. In bridges of short spans, the weight of the locomotive and train coming upon them suddenly constitutes the greatest load, as the weight of the train is greater than the weight of the bridge itself; but as the size of the bridge increases, its weight increases very rapidly, and the weight of the locomotive and train becomes almost nothing as compared with the weight of the bridge itself; that is, if any of these long bridges are built strong enough to hold themselves up, with a very slight margin of safety above that, there is scarcely any danger of their ever falling from any weight that could come upon them from an outside load. For this reason, in building short-span bridges, the amount of economy that can be exercised in the use of material is very small, as the bridge must be built stiff and rigid, even if this necessitates the using of much more material than the absolute weight of the tender and locomotive that come upon it would demand. For this reason plate girders or flanged girders have many advantages connected with their use for short-span bridges, because the whole amount of material used is comparatively of little value, and extreme stiffness and rigidity are the result; while in the case of long-span bridges, such as cantilever, or any remarkably long bridge, every calculation must be made with the greatest care in order to reduce the amount of necessary material as much as possible, because by reducing the amount of material used the weight is reduced, and that again reduces the amount of material. The factor of safety to be used can be only two or three in long-span bridges, while in short spans it should run up even to ten.
Although cantilever bridges are of rather recent use in this country and in Europe, and much has been written claiming them as an invention of modern times, still, the same can be said of them that was said of suspension bridges—that there at present exists in Japan, built by the order of the Mikado two hundred and fifty years ago, as perfect and scientific a cantilever bridge as any that are built in this country or in Europe; and in this way, as in many others, the Japanese show that two or three hundred years ago they had advanced to a wonderful degree in the study of applied mechanics and the "strength and resistance of material." The only trouble is, that they stopped advancing for two or three hundred years, and up to ten or twenty years ago were not as far ahead as two hundred years earlier.
In closing, I wish to call your attention for a few moments to some of the differences that exist between the American and English practice of bridge-building, and the causes that have led to these differences. The characteristic difference is in the methods used in joining together the different parts of the bridge. American bridges, as a class, are pin-connected—that is, the different members, when possible, are joined by means of a steel pin passing through holes in the ends of the pieces. These joints are perfectly flexible, and each member is designed to do its own particular work. English bridges, as a class, have "riveted connections"—that is, the members are fastened rigidly together, and each member is designed to act simply as a part of a rigid, inflexible whole.
The causes that have led to this difference are as follow: In the construction of bridges the English engineer started with the flanged girder of cast or rolled iron, or some other form of a stiff beam, and as the bridges increased in size so as to necessitate the framing of a truss, his whole effort was directed toward making that truss as nearly similar to the original flanged or box girder as possible. This led to perfect rigidity at the joints.
The American engineer, on the other hand, had very little or no iron and steel to work with, and of necessity used wood. As the necessary bridges were of considerable span, the only possible solution of the problem was the pinning together of small pieces of wood so as to form a connected series of triangles. The joints in wood could not easily have been made rigid, and it was not desirable that they should be, as the strength of wood is very slight when the strain is applied in any direction other than in the direction of the fibers of the piece, and the use of the pin joint, theoretically at least, insures this line of action. There has been much ingenuity displayed by our engineers, in the years gone by, in the combinations of triangles used in bridge-designing, and in many cases this has led to absurdities. The whole tendency, however, at present in American practice is to extend the use of riveted joints, and in English practice to extend the use of the "pin connections." Both are working in opposite directions, but from opposite sides, and therefore toward the same point.
One great drawback to the more general use of pin connections by English engineers is the immense first cost of the plant necessary to do the work. Our bridges are usually designed and built by the same company, so that the design within certain limits corresponds to the available plant of the manufacturer, and the expensive tools can be used over and over again. In English practice, however, the bridges are designed according to the ideas of the individual engineer, and then some firm has to build them in all their details to correspond with the design. If the construction necessitates expensive machinery and tools, no company would undertake them at any reasonable cost, as there would be very little chance of any other similar design being offered upon which they could use the same tools.
In riveted work, however, the tools required are within certain limits the same, regardless of the details of design. Pin-connected bridges are much more economical for large work than riveted ones; and this fact, taken in connection with the unrivaled facilities we have for doing the work, accounts for the fact that in the building of large bridges American firms can underbid any others, and not in any way lower the character of the work done.
- Lattice riveted bridges and double intersection trusses have not been discussed, as their introduction would only have obscured the object of the paper.
In regard to the advantages of the American pin-connected bridges for long spans, we may say that from the most recent data the time required for the erection of the bridge, after everything is ready, is only about one twentieth of that required for the erection of the English riveted bridges.