Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

The bridges built upon this plan upon the Alleghany Valley, and upon the Williamsport and Elmira roads, illustrate plainly the design.

185. Applying arch braces to lattice bridges, has suggested The Arch-brace truss bridge, in which the whole strength lies in a series of differently inclined braces, extending from the abutment to the head of each post; a very light lattice being used to prevent reaction, or as a counter-brace or stiffener. See fig. 69.

In trusses consisting of a series of triangles, when the span is large, (150 to 200 feet,) the immense weight coming at the feet of the second and third sets of braces, causes settling or depressing at twenty or thirty feet off from the abutment, which can hardly be removed. The remedy for such settling, is to transfer the load at once to the abutment; which is completely done in the above-named bridge. Each brace does its duty directly and well. Before the lattice-work is fastened, the bridge should be loaded with a maximum load. Then by fastening the diagonals, the recoil is prevented; and the effect of a passing load is to ease the counterbracing lattice, without otherwise affecting the truss.

Note.—A model of this bridge, made by the writer, of the following dimensions:—

Supported 2,500 lbs. at centre, besides a variable load of 150 lbs. applied as a rolling weight in the most disadvantageous manner. It represented a span of one hundred and fifty feet, and according to Weisbach’s formula for testing a model, proved the actual structure, (as far as can be proved by a model,) both strong and rigid to any desired amount. The longest bridge ever built upon this principle, was that of Schaffhausen, over the Rhine, which had a single span of three hundred and ninety feet. This bridge was not stiff, having no lattice, but was very strong. B. H. Latrobe, Esq. has adopted this form upon the Baltimore and Ohio Railroad.

The calculations for the parts of this bridge are as follows:—

The half number of panels is five; the diagonals of which, neglecting fractions, are

The weight upon each of these sets of braces, is the weight of the length of one panel; which, in the present case, is 3,000 × 15 = 45,000 lbs. As there is a brace under each chord stick, and assuming four sticks in each chord, we divide by eight, and have, in round numbers, 6,000 lbs. per brace; and correcting for inclination, as follows, we have the numbers below.

The last column has the several weights coming upon the different braces at their several inclinations; to resist which, the scantling might be very small, for compression, but flexure requires larger dimensions.

These braces should be confined laterally and vertically, as they pass each post, but not connected therewith; as this would not permit a free action of the brace, without straining transversely the post.

The length of beam, therefore, in which flexure is to be checked, is the distance between posts in any panel.

and applying the formula

we get, in round numbers, the following dimensions, the braces being bolted and blocked together:—

For the lattice-work, a double course on each side of each truss, in long spans, (150 to 200 feet); and a single course in shorter spans, of 3 × 6 plank, treenailed at intersections, is ample.

Fig. 69 A, shows the method of bringing the arch braces to the chord. To find the dimensions of the cast-iron block, make a complete drawing of all of the braces, at their proper angles, and then draw in the block around the feet, as shown in fig. 69 A.

Note.—The centre of pressure of the braces in fig. 69 A, is not, as might seem, at C; because the vertical components of the forces, coming down the brace, are much less in the braces at small angles than in those at the end of the span. The load applied to each brace being the same, and the inclines being found, we find the centre of pressure, or the centre of bridge seat as follows:—

The length of the brace is to the vertical height, as the applied load to the vertical pressure. In fig. 69 A, we have the following lengths of braces: a, 25; b, 37; c, 49; d, 64; e, 78; f, 92; and g, 106; and the weights corresponding thus,

In fig. 69 A, assume the foot of the fifth brace (B) as the centre of pressure, and adding the moments, (or products of vertical components on the braces by their distance from B,) and we have the sum on the land side 18,928, and on the water side 16,930; showing that the centre is taken too far from the land side. In the same manner A will be found too far from the land side. A third trial will give the place.

Fig. 69 B, shows the manner of splicing the arch braces: being subjected to compression, they are spliced in the same manner as the upper chords. Fig. C, shows the lower chord spliced. Figs. D and E, the connection of the posts, chord, and lattice. Figs. F, G, and H, the casting for applying the upper end of the arch brace to the chord. Fig. 69 K, the method of supporting the tracks at the end of the span, where the arch braces will not allow the floor beams to bear upon the lower chord.

McCallum’s patent railroad bridge.

186. This bridge represents a class of structures in which the upper chord is curved upwards (7½ feet in 200 in the Susquehanna bridge, New York and Erie Railroad), which curved chord has the effect of distributing an applied load at once to all of the braces directly, by means of the chord, as well as indirectly, by means of the braces, as in the common trusses. To this bridge is applied the arch braces A B, A B, fig. 70, which serves to aid the 2d, 3d, and 4th pair of diagonal braces in bearing their load.

The great distributing power of the curved chord, is shown by the fact that a bridge of 125 feet span, actually supported a railroad train before the diagonal bracing was introduced. The whole strain was thrown through the curved chord and arch braces to the abutments. The bridge is counterbraced by the pieces d d and d d, adjustable by screws at the ends.

The following test was applied to a span of 190 feet of this plan of bridge. Placing the load as near as possible to the centre, the following deflections were produced.

Upon removing the load, the bridge entirely recovered its form.

187. As the span increases, the benefit derived from the curved chord also augments; and though in the latter part of the present chapter its application to small spans is shown, it may not be worth while to adopt it.

Bridges transferring the load directly, from each panel to the abutment, would not be aided, to an amount worth the increased expense, by adopting the curved top chord.

In case of any settling at the centre of the span, the reverse effect is seen from that produced in a truss with horizontal chords; i. e., when the ends of the upper chords in the latter draw in, those of the former push out; and when in such bridges, arch braces are not used, the top chords of adjoining spans must be wedged apart, in place of tying together as in common plans, over the centre of the piers.

THE ARCH.

188. The arch has been applied to long spans for a great while, and when care has been taken to prevent flexure, answers very well. The repair of such bridges, if any of the arch timbers decay, is difficult; but is effected, in the largest arches.

The most correct ideas on wooden arch bridge building, are to be found in Weibeking’s Traite d’une parte essential de construire les grandes pents en charpente. This engineer, (General Director of Roads and Bridges in Bavaria,) has built a great number of wooden arches of the best description, which show him to be master of both the science and the art.

The general plan of his bridges is shown in fig. 71. They consist of curved ribs formed of long pieces scarfed and bolted together, from which the road-way is supported by posts.

The bridges of Neucettringin, Freysingin, Bamberg, Scharding, Wertach, Vilshoven, and Altenmarkt, all testify to the good judgment of this man. The spans vary from one hundred to two hundred feet; and the width from twenty-five to thirty-two feet. The proportions which he gives for the ratio of rise to span, are valuable; as they are the result of his own experience. He states, generally, that one tenth of the span is the best rise; but that for convenience, it is better to keep it lower. The following table shows the dimensions he has adopted in practice.

189.

The last column shows the scantling of the arch timbers; these being placed three deep, in spans of less than 150 feet; and in larger spans, 3 deep at centre, and 5 deep at ends. Mr. Weibeking’s formula for determining the scantling of ribs, is as follows:—

Example.—Required the scantling of the ribs of a bridge of 300 feet span, 20 feet wide, and 30 feet high. The formula becomes,—

section, of all of the arches; or two parallel arches, 2½ feet wide, by 3¼ feet deep each.

190. The bridge built by Mr. Burr across the Delaware at Trenton, New Jersey, is a good specimen of an arch. It is composed of white pine planks, from thirty-five to fifty feet long, and of a scantling 4 × 12. These planks are laid close together, breaking joint, having an entire depth of three feet. The arches are stiffened by horizontal tie beams, supporting the road-way, and by diagonal bracing. The spans are 160, 180, and 200 feet, and the rise twenty-seven feet.

191. The bridge over the Susquehanna, at Columbia, built in the same manner, consists of twenty-nine arches, each two hundred feet clear span, supported on two abutments and twenty-eight stone piers. The clear water-way of this bridge is 5,800 feet; and the entire length, including piers and abutments, one and one fourth miles. There are three sets of arches, which allow of two carriage roads and one railroad, the whole width being thirty feet.

192. An arch to support a passing railroad train must be very rigid. It is customary to connect them with a light truss, which effectually counter braces the arch, and prevents that change of form which would otherwise take place; depending entirely upon the arch for strength.

Wherever the load is applied, the arch tends to sink, and a corresponding rise takes place at the opposite point. A load placed at E, fig. 71, settles the arch at that point and causes it to rise at C. A load placed at the curve of the arch depresses the centre, and elevates the haunches. To counteract these movements a light, stiffening frame may be used, its strength being able to resist the variable load passing over the bridge. The strain thrown by the arch upon the truss, advances from the opposite end to meet the train, passes it at the centre, and finally goes off from the bridge behind the load.

When the arch is the truss, or when a truss is made with curved chords, the counteracting effect of the truss is not completely obtained. We should not depend upon the curved chord as an arch, but only as a member of the truss.

193. Many combinations of arch and truss have been built in America for railroad bridges. The principle of connecting the two systems is by some thought bad, as they can hardly be made to bear equal parts of the load; whence each must have more than half the necessary strength of the whole. Others maintain that by a proper arrangement of parts a perfect adjustment may be made, by which the load may be placed more or less on either. There seems to be no very good reason why the two systems should be combined, as either may be made strong enough to bear the largest loads.

Both arches and arch braces, however, are very usefully applied to bridges which have been made too light.

194. The manner of applying arches is well shown in the bridges of the Pennsylvania Central Railroad, built by Hermann Haupt, Esq.

These bridges are on Howe’s plan, to which have been added strong wooden arches. The systems are connected by adjusting the counter braces against the arch by set screws. The arrangement is simple and effectual. The name of the builder is sufficient to warrant the stability of the bridge.

195. However nicely we may form an arch, it will settle more or less when the scaffolding is removed, according to its flatness; which depression increases with time. Mr. Weibeking expresses it in inches as follows:—

To allow for this settling, the curve when laid down on the platform for building the arch, should be made a little more convex than the completed arch is required to be; the amount of excess being that shown by the formula.

As a bridge composed of a curved rib when the span is large yields at D, C, and E, fig. 71, when the load is applied in the middle, the strength must of course be increased by increasing the depth of the rib; and not to make this too heavy, a framed or built beam should be used as in fig. 72. Here it must be remembered that the two ribs must be so framed as to resist both tension and compression; for when a load is placed at D, the lower rib will be extended at d, and compressed at c′, and e; while the upper one will be compressed at D, and extended at C and E.

OF THE ROAD-WAY.

196. The flooring of any system is about the same; consisting of transverse floor beams, placed either on the top or bottom chords, (according as the road-way is more or less elevated above the water-way,) which support longitudinal timbers, upon which are placed cross-ties. In some cases, two curves of diagonal plank have been placed across the floor beams, spiked at right angles to each other, by which the bridge is considerably stiffened laterally.

General dimensions for the floor may be thus:—

LATERAL BRACING.

197. To prevent vibration in a horizontal direction, a system of diagonal bracing is necessary. The chief pressure upon these braces is caused by wind; and may be found by considering the bridge as turned over upon the side, and loaded with a weight equal to the maximum pressure of the wind, which may be taken as forty pounds per square foot.

It is unnecessary to vary the size of these braces, except in very long spans, when they should increase from the centre to the ends. For short spans, (less than one hundred feet,) a brace 5 × 5 is large enough. For larger spans 7 × 7 is sufficient.

198. Diagonal bracing, when it can be introduced, is a very desirable part of a bridge. When the road is on the lower chord this cannot have place in full, but may be applied as in fig. 74.

By increasing the height of truss in any bridge, the tension and compression on the chords is lessened; but the length of posts and rods is increased. As a general thing, one eighth of the span gives the best results.

199. In framing a large bridge, it is customary to cut the top chord sticks a little longer than to dimension; to allow for compression in settling.

200. Bridges in exposed situations have been sometimes blown off from the masonry. If a bridge slides off from the masonry, the whole force of the wind must be fifteen twenty-fourths of the whole weight of the bridge; but if, as is generally the case, the masonry is rough, (and not hammered,) no amount of wind will cause the bridge to slide.

The bridge will upset, turning about its lower edge, when the whole pressure of the wind, multiplied by half the height of truss, overbalances the whole weight, multiplied by the half width. In very exposed places the rod A D, fig. 74, answers a very good end; when the road is upon the upper chord, and a rod from B to the masonry, when upon the lower.

201. The effect of running a train over a skew bridge, is to depress one side before the other; as the load comes upon the centre of one truss before it does upon the opposite one. This produces a side rocking in the engine, dangerous alike to the bridge and to itself.

The floor timbers transferring the load to the chords should not be at right angles to the axis of the road, but parallel to the abutment. Thus in fig. 75, a wheel at B, throws one third of its weight upon the abutment at E; and two thirds upon the chord at C; while in fig. 75 A, the wheel at B, throws two thirds of the load upon C, but one third also upon D.

202. In a very long, oblique span, the floor timbers may be arranged as in fig. 76, that is, inclined at the entrance and exit of the bridge, but at right angles at the middle of the span.

203. The preservation of timber in wooden bridges may be accomplished by covering with boards, whitewashing, painting, and by Kyanizing. Covering and whitewashing are the best, if care is taken to prevent dry rot by giving a good circulation of air about the timbers. The oil in paints prevents the escape of moisture from within as well as the entrance of that from without; and should not be used unless the wood is well seasoned. The best plan is to thoroughly whitewash and cover the frame of the bridge, and to paint the outside of the covering.

204. In framing two or more continuous spans, the chords should always be connected over the piers; as there is thus given something for the upper chords to pull against, and a counter thrust for the lower.

205. Bridges should never, when it can be avoided, be placed either upon a curve or upon a grade; particularly upon the former, as the effect of a load is thereby very much increased, in the first case causing a lateral, and in the second a vertical shock.

PILE BRIDGING.

206. In shallow water, in marshes, and in similar situations, where an embankment would be expensive, pile bridging is very useful. Indeed, whenever we are at liberty to obstruct the passage beneath the road, it is well to adopt this system, unless over twenty feet high. It is cheaper than any other, easier to repair, the parts are quite independent of each other, and such bridges last full as long as other wooden structures.

Different plans for pile bridging are given in figs. 77 to 82. Figs. 77 to 81 show plans for temporary pile work, to be used during construction. Nothing lighter than fig. 82, ought to be permanently used. A pile bridge upon a curve may need stronger lateral bracing upon the convex, than upon the concave side of the curve; and also in running water; in which cases, such a form as fig. 81 may do good service.

(For pile-driving, and for proper dimensions, see chap. XII.)

TRESTLING.

207. Trestling is a system of vertical posts, and of caps and braces, used both for temporary and for permanent works; temporarily to pass a road over low ground where embankments are to be made, and permanently over deep, dry gorges, where the amount of earthwork or masonry would be too great.

American railroads show all sizes and arrangements of trestling, from twenty to two hundred feet high. Figs. 83 and 84 show temporary works, and fig. 85 permanent.

The main part of the design in trestles is to connect the several posts and caps by well-formed triangles; the equilateral being the best.

The finest example of this system of building is the Genesee high bridge, over Genesee River near Portageville, on the Buffalo and New York Railroad; built by H. C. Seymour, Esq. It is eight hundred feet long, and two hundred and thirty feet above the river. It has eight stone piers, thirty feet high, upon which are placed trestles one hundred and ninety feet high, seventy-five feet wide at base, and twenty-five at top. Upon the top of all is placed a bridge fourteen feet high. To build this viaduct was used 1,500,000 feet, board measure of timber, which covered, when standing, two hundred and fifty acres; also, sixty tons of bolts. The whole time occupied in building was but eighteen months, the whole cost being $140,000.

DRAWBRIDGES.

208. In crossing rivers or bays open to navigation, it is required from any companies building a bridge, to leave a free passage for shipping. This is done by making that part of the bridge over the channel movable; (a draw).

Draws may lift up, (being counterbalanced,) may slide back upon the fixed part of the bridge, or may turn on a pivot. Fig. 86 shows a draw much used at present, and answering every purpose. Each half of the movable part must be calculated as a small bridge. The rods c c c support the overhanging part of the draw while open. The whole revolves upon a centre pin and a set of rollers.

CENTRES.

209. Centres are temporary wooden frames, used in the construction of stone arches. Their duty is to hold the masonry, while it is unable to support itself.

For arches from five to fifteen feet span, a centre made of boards or planks, fig. 87, is all that is necessary. For longer spans, when the ground beneath the arch can be used, the form, fig. 88, answers well. When there is no support but the abutments or piers, something similar to fig. 89 must be adopted. This is the plan adopted by George Rennie, chief engineer at the Waterloo bridge over the Thames at London.

Centres are strained in a different manner as the arch progresses; first at the haunches, and last at the crown. Excess of weight at any point causes a settling at such, and a rise takes place at some other place. By loading the arch temporarily, such motions are checked.

These frames are placed vertically upon the pieces F F, which being connected with the braces D D by the folding wedges c c, admit of adjustment of the height of the centre. The distance between the ribbed frames depends upon the form of the arch, and the span, or upon the weight to be supported; varying from one to four feet. The centres are covered with a course of narrow plank, placed parallel with the axis of the arch, upon which the voussoirs rest.

210. The method of putting a bridge upon the masonry is shown in figs. 90, and 91; the former when the road-way is upon the upper, and the latter when upon the lower chord.

211. In figs. 92 to 100, are given several plans for spans from five to seventy-five feet. Fig. 92, shows the simple beam braced beneath with diagonal plank; the bolts passing through the ties, stringers, and braces. The stringers are bolted to the wall plates, and when the bridge is upon a curve notched also, by cutting the bolster. Fig. 92 A shows the plan. This form answers for openings from five to twenty feet. From fifteen to thirty feet, we may use figs. 94, 95, 96, and 97. From twenty-five, to fifty and sixty feet, figs. 93, 97, and 98. And from fifty to seventy-five feet, figs. 99 and 100.

The following tables give reliable dimensions for bridges upon the above plans.

The ties being notched three inches on to the stringers, without cutting the latter.