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.

by George L. Vose

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.

Fig. 71.

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.

Name.	Span.	Rise.	Width.	Rad. of Arch.	Scantling of Arch.
Bamberg,	208	16.9	32	422	13½ × 15½
Scharding,	194	18.8	25	258	12½ × 15½
Vilshoven,	179	11.1	27	378	13½ × 15½
Freysingin,	153	11.6	25	246	12½ × 14½
Ettringin,	139	8.0	25	305	12½ × 15½
Ersingin,	126	7.0	25	285	11½ × 14½
Augsberg,	114	10.6	25½	158	12½ × 14½
Neucettringin,	103	6.8	25	200	13½ × 15½

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:—

W × (S/2)²
Rn.0011 = Scantling in sq. ft.

Where R is the rise of the arch;

n, the number of ribs;

W, width of bridge;

and S, span of bridge.

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

20 × 22500
30 × .0011 = 16½ sq. feet of

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

From 100 to 150 feet span, he makes the rise 1
20 span,

From 150 to 200 feet span, he makes the rise 1
18 span,

From 200 to 300 feet span, he makes the rise 1
15 span,

From 300 to 400 feet span, he makes the rise 1
14 span,

From 400 to 500 feet span, he makes the rise 1
13 span.

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:—

0.806R
S

Where R, shows the rise,

and S, shows the span.

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.

Fig. 72.

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.