BOILER PLATE BRIDGES.

Spans from 25 to 100 feet.

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.

Fig. 116.

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

4 – 2¼ = 1¾ inches,

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

12,500 : 15,000 :: 1 : d

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

9 × 0.8 = 7.2 = d,

and the above proportion becomes

15,000 : 12,000 :: 7.2 to 6 inches,

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,

8 × 2 = 16, 16 + 2 = 18;

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

6
18 = .33 or ⅓ inch

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

Diameter of rivet.Distance between rivets.
Mr. Fairbairn⅝ inch, or 0.625 inch,0.8
Handbook⅔ inch, or 0.666 inch,0.8

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.

Fig. 117.

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.

Whole plate,100.
Single riveted,56.
Double riveted,70.

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.

Thickness of plate,¼,5
16,		⅜,7
16,		½,9
16,		⅝,11
16,		¾.
Diameter of rivet,⅝,6
8,		⅞,1,1,1⅛,1¼,1⅜,1½.

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,

cb = 2 diam., df = 1½ diam.

Plates exposed to extension,

cb = 2½ diam., df = 2 diam.

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

R × a = R′ × (2 d × t);

whence d = R × a
2R′ × t;

where a = area of rivet,

d = distance,

t = plate thickness.

also

2d′ + d = R × d
R′;

and

2d′ = R × d
R′ – d;

whence

d′ = [R × d
R′ – d]/2

and finally

d′ = ½[R × d
R′ – d]

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

T = WS
8h (see Chap. VIII.)

becomes

33000000
96 = 343,750 lbs.

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

171875
7500 = 22.9 square inches.

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

171875
12740 = 13.5 square inches

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

One top plate10 × ¼ =2½square inches.
One bottom plate10 × ¼ =2½square inches.
Two side plates8 × ¼ =4square inches.
Four angle irons¼ × 8 =8square inches.
In all,17square inches.

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

In the flanges,18 × ⅜ =6¾
Bottom plate,18 × ¼ =4½
In all, 11¼

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

Whole weight of bridge and load is, in round numbers,344,000 lbs.
One half,172,000 lbs.
And upon each end of the truss,86,000 lbs.

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.

Span,60 feet,
Length,66 feet,
End bearings, each,3 feet,
Rise,5 feet,
Width,28 feet,

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.

CHAPTER X.
STONE BRIDGES.

A complete treatise on stone bridging would be of little practical value to the American engineer, and would occupy too much of the necessarily small space allowed here. The object in the present chapter is to give the manner of dimensioning stone arches of from ten to sixty feet span, and of proportioning retaining walls, piers, and abutments.