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.

Also, tang E C G = log 2a – log b, or 2.255273 – 2.698970 = tang 9.556303 of which the angle is 19° 48′ and 90° – 19° 48′ is 70° 12′ = angle G C A or A C H.

The height of the tower being one hundred feet, and the angle at the tower 70° 12′, we have

which double, and we have 590.4; finally, add twice the breadth of the tops of the towers, and the whole length of cable is, from anchorage to anchorage,

The formula for the maximum tension, (that at the point of suspension,) is

which becomes

Number 10 iron wire (20 feet per lb.) will support 1,648 lbs. per strand; this is the ultimate strength; the maximum load for safety is 400 lbs. per strand; whence 2,966 tons, or 6,642,500 lbs. will require 16,606 strands; and if we use two cables, each must have 8,303 wires; or four cables of 4,151 each. The permanent load on suspension bridges should never be more than one sixth of the ultimate strength; one eighth is a good standard. The accidental load should never exceed one fifth of the whole strength of the cables. The permanent weight supported by the Niagara bridge is only one twelfth of the ultimate strength of the cables.

ANCHOR CHAINS.

The maximum tension being 6,642,500 lbs. the whole section of the four anchorings will need to be

or 111 square inches for each shaft; which is obtained by eleven links ten inches wide and one inch thick. If we so attach the anchor chains to the masonry as to reduce the tension one fourth at the first arch, (see Fribourg anchoring,) we may fasten three bars of the chain at that point, and descend from the first to the second arch with eight bars; and leaving two bars at that point, proceed to the bottom with the remaining six.

Where there is no natural rock to build the masonry into or against, enough artificial stone must be put down to balance the bridge and load.

ANCHORING MASONRY.

The entire weight of the bridge and load being 4,500,000 lbs. and the whole tension, as above found, 6,642,500 lbs., or upon each tower 3,321,250 lbs.; this is the tension tending to draw the masonry out of each shaft. This tension must be reduced on account of the inclination of the pulling force. The tower is one hundred feet high. The distance on the line of tension from the top of the tower to the anchoring, as already found, is 295.2 feet; whence the actual effort to move the anchor masonry, is thus,

295.2 to 100 as 1,660,625 to the effort or 562,542 lbs. If rock weighs 160 lbs. per cubic foot, which is resisted by a column of masonry of 3,321,250
160 = 20,758 cubic feet, or 20 × 20 × 52 feet, or by a mass 15 × 15 × 91 feet.

TOWERS.

The height of towers being one hundred feet, and the mean thickness being one fifth of the height, we have mean section 20 × 20; or top 12 × 12, and base 28 × 28.

SUSPENDING RODS.

Assuming the horizontal distances between the centres of the vertical suspenders as five feet, their lengths, then, will be found by formula

and placing for Y² the distances 5, 10, 15, 20, etc., we have, commencing at the centre,

and so on, until we arrive at the tower. Whatever distance above or below the vertex of the curve the road-way is placed, is of course constant, to be added to or taken from the above lengths.

The manner of putting in any camber is simple both in theory and practice. The strain upon the suspenders is merely the direct weight of the road-way and load. If this is 3,500 lbs. per foot, the five feet supported by two rods (one each side) will weigh 17,500 lbs.; each rod or wire rope must hold 8,750 lbs.; this can be done by a section of one half inch area. For extra strains, however, on so large a span as 1,000 feet, one inch of area is not too large.

OF THE STIFFENING TRUSSES, GIRDERS, AND STAYS.

The object of the girders supporting the rails is to diffuse the applied weight; these girders may be made of a Howe truss four or five feet deep, by trussed girders, only simply deep and stiffly framed track strings. They should be able to distribute the load applied at one point at least fifteen or twenty feet. The side trusses transfer to a still greater extent any applied load. Mr. Roebling estimates the combined effect of trusses and girders in the Niagara bridge as transferring the weight of a locomotive over a length of two hundred feet. This transferring counteracts the local depression. The Niagara truss is formed by a system of vertical posts, five feet apart, and diagonal rods passing from the top of the first post to the foot of the fifth; the inclination being 45°, spreads the weight placed upon any one pair of posts over twice the height of the truss, or about forty feet. As to the actual dimensions of the girders supporting the rails, if we intend them to spread an applied weight over forty feet, they must be as stiff as a bridge of forty feet span. And as regards the truss, if we would effectually distribute the applied weight and check vibration, the trussing should be as strong as the counterbracing in a large span upon the ordinary plans. The principle of trussing a suspension bridge may be thus explained. See fig. 106. Suppose that in place of supporting the three trusses D s w, s m m′, and m′ m d, upon piers at w and m′, we suspend these points from the cable A c B. The cable is flexible, and when we apply a load at m, the truss will assume the position D s c n d, but between D and s, s and n, n and d, the truss will be quite stiff. What we require, then, is to make the figure o p m m′, incapable of changing its form, which is done by diagonal bracing.

233. Undoubtedly the finest specimen of a bridge of large span upon the suspension principle, or indeed upon any principle, is that built by John A. Roebling, across the Niagara River, a short distance below the falls. The dimensions below of this admirable structure are from the final report of the above-named engineer.

231. The following items are extracted from the report above referred to:—

“The trains of the New York Central, and Canada Great Western Railroads have crossed regularly at the rate of thirty trips per day for five months. (At present over two years.)

“A load of forty-seven tons caused a depression at the centre of five and a half inches.

“An engine of twenty-three tons weight, with four driving wheels, depressed the bridge at the centre 0.3 feet. The depression immediately under the engine was one inch; the effect of which extended one hundred feet.

“The depression caused by an engine and train of cars is so much diffused as scarcely to be noticed.

“A load of three hundred and twenty-six tons produced a deflection of 0.82 feet only. The Conway tubular bridge deflects 0.25 feet under three hundred tons; the span being only one half that of the Niagara bridge.

“The specified test for the wire was, that a strand stretched over two posts four hundred feet apart should not break at a greater deflection than nine inches; also, that it should withstand bending square and rebending over a pair of pliers without rupture. This test corresponds to a tensile strain of 90,000 lbs. per square inch, or I,300 lbs. per wire of twenty feet per pound.”

The wire is preserved from oxidation by coating with linseed oil and paint. Upon the durability of wire cables employed for suspension bridges the following fact came to light: Upon taking down the cables of the footbridge, put up in 1848, by Mr. Ellet, the wire was found so little impaired that Mr. Roebling did not hesitate to work it into the new cables; also, the original oil was found to be still soft and in good condition, having been up six years.

That iron-work lying under ground has been completely covered with cement grout, as this is found by the above-named engineer to be an effectual guard against oxidation.

Engineers wishing to study the details of the Niagara bridge, will find the final report of Mr. Roebling full of valuable matter, both as regards the making of cables, anchoring, stiffening, and the effect of passing trains.

Note.—This engineer is at present engaged upon a still greater work, namely, a railroad suspension bridge across Kentucky River, of 1,224 feet span, 300 feet above the water. There is no lower road-way in this bridge, the cross section being a triangle base upwards.

235. Note.—The Britannia tubular bridge, across the Menai Straits, is doubtless a great work, and also an enormously extravagant one. If no other structure were possible it would be admissible; but it is equalled in strength and by far surpassed in economy by Mr. Roebling’s system of trussed suspension bridges. The cost of material alone in one span of the Britannia bridge, of 460 feet, exceeds the entire cost of the Niagara bridge of 800 feet span; add to this that we are sure of the strength of wire cables, but not of tubes, and that the 800 feet span of the Niagara bridge weighs only 1,000 tons in itself against 1,400 in a 460 feet span of tube, and it will not be difficult to prove the superiority of the suspension over the tubular system; thus,

When we double the linear dimensions we increase the weight by the cube; and the cost of a tube is very nearly as the weight; whence a tubular bridge of 800 feet span will cost 2 × 2 × 2, or eight times 500,000, or $4,000,000 against $400,000. Thus,

Fig. 105, shows the anchoring of the Fribourg bridge.

Fig. 107, the manner of fastening the ground stays of the Niagara bridge.

Fig. 108, connection between cable and suspender.

Figs. 109, 109 A, another method of effecting the same.

Fig. 110, floor beam attachment to suspender.

Figs. 111, 112, floor beam attachment in Niagara bridge.

Fig. 113, connection of land and water cables in Fribourg bridge.

Figs. 114, 114 A, fastening of cables at G, (fig. 105).

Fig. 115, Mr. Roebling’s pendulum connection for the cables of two adjacent spans.

BOILER PLATE BRIDGES.

236. These structures fulfil every requirement of safe, durable, and rigid bridges; being open however to the contingency attendant upon all similar structures of wrought iron, namely, the becoming crystalline when exposed to vibration. Time only will show whether this is a sufficient cause for their non-adoption.

Each side truss consists as it were of a top and bottom chord connected by a vertical web. The whole being of wrought iron, requires that the section of the upper chord should be to that of the lower, as ninety to sixty-six.

The general plan of such bridges is shown in fig. 116. This is the patent wrought iron girder bridge of Mr. Fairbairn. The upper chord is formed by connecting the four plates a a a a, by angle irons. The web is formed either by a single or a double plate, stiffened laterally by T iron placed at the vertical plate joints, as shown generally at B, and detailed at C and D; or by a pair of plates separated by a space as at B′, thus forming a rectangular tube. The lower chord is made by bending horizontally the lower part of the web, and to the flanges thus formed riveting the plate m m. The suspending rod f is applied to the upper chord by a washer as at E.

The central connecting web, acting as do the braces and ties in a wooden truss, should be more stiff at the ends of the span than at the centre. This is easily effected by joining the web plates towards the end by stronger T irons than at the centre. The joints for the rib, or the vertical plates, either single or double, are shown in figs. C and D.

An example of the need of such increased stiffness towards the ends, was given to the experimenters upon the Britannia model tube, which (tube) was found to yield by buckling near the ends of the span sooner than elsewhere. Thus advised, the vertical plates were made thicker as the end of the span was approached. Examination of the principles of proportioning a common wooden truss would have shown this without experiment.

The tensile and compressive strength of rolled boiler plates (by the table on page 193,) is, extension 12,740 lbs. per square inch, compression 7,500 lbs. The strength of such work depends in a very great measure upon the size and disposition of rivets. In plates exposed to compression, the strength is not so much affected by riveting as in those subjected to tensile strains; as to whatever amount the plate is cut away, by the same amount is the resistance to tension reduced.

237. Mr. Fairbairn found that to obtain the maximum strength of riveted plates, the section of the rivets should equal that of the plates, that is, in a plate four inches wide, if there are two rivets, the area of each must be one inch; or the diameter 1⅛ inches; thus leaving a section of

which divided by four gives seven sixteenths of an inch as the distance from the edge of the plate to the side of the first rivet; and seven eighths of an inch between rivets. If the bolt yields by shearing, the rim is destroyed by detrusion, or crushing across the fibres. That the rivets and plates may be equally strong, their products of area of section by the actual strength per unit of area must be equal. The detrusive strength of wrought iron (see page 193) is 12,500 lbs. per inch, whence the proportion

where 1 is the resisting length of the plate at right angles to tension, and d, the sum of rivet diameters. Thus suppose we have a plate 13.2 inches wide, to be fastened with nine rivets of 0.8 inch diameter; we have

and the above proportion becomes

which is the length of plate section at right angles to tension. As there are nine rivets, there will be eight spaces between them, and one space at each edge of the plate, half as large as those between; or reducing all to the same size,

and as the whole plate section after punching is six inches,

for the edge space, and two thirds inch between rivets. Proceeding thus, the result compares with the practice of Mr. Fairbairn as follows:—

The difference between the results, or 0.041 inch, less than one sixteenth inch, will be partially absorbed by the remark of Mr. Fairbairn that the area of the rivet should be nearly as much as that of the plate, and partly by the difference in results showing the detrusional force of iron.

238. In experimenting to determine the resistance of rivets, Mr. Fairbairn found that by the common plan of riveting, fig. 117, the strength of plates when whole, single, and double riveted, was as follows, the section of the punched plate being in each case equal to that of the whole one.

This loss of strength made him fearful of the ability of the tension plates of the Britannia bridge to do their duty; and he was led to adopt what he terms “chain riveting,” which consists in placing the rivets as in fig. 118, or in the same line of tension. The strength of plates thus made he considers as great at the joints as elsewhere.

239. As to the diameter of rivets, we have the following results of the practice of the best English engineers.

240. As to the distance in the direction of the force from rivet to rivet, also from the first rivet to the plate end, we gather the following from the best executed works in boiler plate. See fig. 118.

Plates exposed to compression,

Plates exposed to extension,

the diameter being that of the rivet.

The distance at right angles to the force has already been given.

241. If we knew the lateral adhesion of rolled plates, that is, the resistance of the fibres to sliding horizontally past each other; we should determine the distance of rivets in the direction of tension as follows:—

Let R, equal the resistance per unit of area for detrusion or shearing, R′ the lateral adhesion of rolled plates, and we should have

also

and

whence

and finally

supposing the piece 1, 2, 3, 4, fig. 118, to split out.

The diameter of the semi-spherical head of the rivet should be three times the thickness of the plate to be riveted; that of the conical head four times; and the height of both of the heads, one and one half the plate thickness.

242. Examples of the application of the preceding remarks.

Suppose we wish to build a boiler plate bridge of one hundred feet span, twelve feet rise, weight of bridge and load 3300 lbs. per lineal foot. The tension by formula

becomes

Each side truss will bear one half of this or 171,875 lbs., and as wrought iron resists eleven thousand pounds of compression per square inch, the required section of the top chord will be

Also the lower chord resisting fifteen thousand pounds per square inch, must have

of area nearly.

If we make the tube at top of one fourth inch iron, and 8 × 10 inches; fastening the plates by one fourth inch angle iron, four inches on the side, the section becomes

In the lower chord, if we bend the web plates (of ⅜ inch) so as to form a flange of eighteen inches in width, and to that rivet a bottom plate 18 × ¼, we shall have

The web acting as both ties and braces, must be able to support the following load.

to resist which, at eleven thousand pounds per square inch, requires eight inches nearly, regarding the plate as a brace.

Now the side of the bridge being one hundred feet long, and twelve feet wide, will contain any system of bracing that we choose to draw thereon. Suppose, for example, that we chalk a line upon the erected bridge representing an arch-brace, extending from the end to the centre. Such a brace has actual existence in the bridge; and the same idea holds good for any system of braces that may be assumed. We ought, therefore, to take the most disadvantageous system that can have place, and giving such a good bearing upon the abutment, estimate its width and thickness. Suppose that we draw a natural size representation of Howe’s bridge, the end braces must support a load of eighty-six thousand pounds, which at eleven thousand lbs. per inch, requires a section of nearly eight inches; and if the plate is one half inch thick, the brace must be sixteen inches deep. The manner, however, in which the plate would yield is by bulging laterally; which is to be checked by the before-mentioned T connecting irons at the sides. It may be thought that the above method of considering the plates as braces, would give very little thickness by assuming very wide plates. The answer to this is, that the side plates must not be so thin as to need more stiffening angle irons by weight, than a thicker plate with less stiffening. Of course the weight should be minimum.

243. As an actual example of this plan we have the following, built by Mr. Fairbairn for the Blackburn and Bolton Railroad, across the Leeds and Liverpool Canal.

for a double track. Top chord of three eighths iron, web of five sixteenths, lower flange of three eighths, and vertical web plates stiffened by T irons.

This bridge was tested as follows:—

Three engines, weighing twenty tons each, running from five to twenty-five miles per hour, deflected the bridge .025 feet. Two wedges, one inch high, being placed upon the rails, and the engines being dropped from that height, the bridge was deflected at the centre .035 ft.; with wedges of one and one half inches the deflection was .045 ft. The cost of this bridge (in England) was estimated by Mr. Fairbairn at $4,500, while that of a cast-iron bridge of the same span was $7,150.

244. Example 2.—Manchester, Sheffield, and Lincolnshire Railroad (England) Bridge, at Gainsborough, on the river Trent. Two spans, each one hundred and fifty-four feet. Rise twelve feet. Top chord, double rectangular tube, 36¾ × 16 inches, vertical web as before, and horizontal plate for the lower chord. The floor beams are wrought iron girders, cruciform in section, ten inches wide, and one foot three inches (15″) deep, placed four feet apart.

245. Example 3.—Fifty-five feet boiler plate bridge, built by James Millholland, in 1847, for the Baltimore and Susquehanna Railroad Company. Each truss consists of two vertical plates 55 × 6 feet, formed of plates thirty-eight inches wide by six feet deep, the plates being fastened together by bolts passing through cast-iron sockets. The lower chord is formed by riveting two bars 5 × ¾ inches to each side of each truss plate; making in all eight. Top chord—one bar of the same size on each side of each plate, compression being made up by a wooden chord between the plates. Height of bridge, six feet; length, fifty-five feet; width, six feet; weight, fourteen tons; cost, $2,200, or forty dollars per foot. The inventor thinks thirty dollars per foot enough when a considerable amount of such bridging is wanted.

Note.—White, buff, or some light color should be used in painting iron bridges, as such throw off, and do not absorb heat from the sun.