OF THE TRUSS.

171. The most simple bridge that could be built, consists of a single piece of timber placed across the opening to be spanned. This form is applicable to spans under twenty feet. The proper dimensions are found by the formula:—

d = √(4wL
5000b) = the depth.

Example.—The depth of a beam of twenty feet span, and twelve inches wide, to support a load of twenty thousand two hundred and fifty lbs. is

d = √(4 × 20,250 × 20 × 12
5000 × 12) = 18 inches.

A beam 12 × 18, and of 20 feet span, will therefore bear safely a load of 20,250 lbs., applied at the centre.

In this manner is formed the following table, giving the scantling of sticks for railroad stringer bridges, of twenty feet span and under.

Span.Breadth.Depth.
51212
101213
121215
151218
181220
201221inches.

The first scantlings exceed the requirement of the rule, but are none too large to resist the shocks to which such sticks are exposed.

Cross-ties of plank, 2 or 3 by 6 or 8 inches, and plank braces underneath, (as shown in the fig. at the end of chapter VIII.,) should be bolted to the main timbers; the same bolt passing through the tie beam and plank. The longitudinal pieces should be firmly notched and bolted to the wall-plates, and these latter either built in or scribed on to the masonry.

Fig. 61.

172. For a span of from 20 to 50 feet, we may use the combination shown in fig. 61. The piece A B, must be so strong as not to yield between A and D, or D and B. The pieces C E must be stiff enough to resist the load coming upon them which is as follows. A locomotive engine of the heaviest class will not exceed fifty tons weight, each pair of driving wheels will support ten tons, and on each side five tons, 2240 × 5 = 11,200 lbs.; or to allow for shocks and extra strains, 15,000 lbs. Each brace, then, must support seven thousand five hundred pounds, which for compression simply would require only seven and one half square inches of sectional area; but the brace being inclined, the strain is increased as follows:—

A E to E C as 7,500 to X.

And A E being ten feet, and A D fifteen feet, E C becomes eighteen feet, whence

10 to 18 as 7,500 to 13,500 lbs.;

which would require only thirteen and one half inches for compression, or a piece 4 × 3½. But is this enough for flexure?

On page [124] the load which may be safely borne, by a rectangular post of wood, is shown by the formula

W = 2240bd3
L2.

Substituting for b and d, the dimensions 4 × 4, we have

W = 2240 × 4 × 43
182, or 573,440
324, = 1,770,

which is evidently too small.

Placing 6 × 7, for b × d, we have

W = 2240 × 6 × 73
182 = 14,227;

exceeding by a small amount the requirement.

Fig. 62.

173. It is evidently immaterial whether we support the point D upon C, or suspend it as in fig. 62, provided we prevent any motion in the feet of the inclines A c B c. Abutting them against A B, throws a tension against A B, found as follows:—

Representing by c D, the applied weight, draw D E parallel to c B; also E f parallel to A B; E f is the tension. The graphic construction gives results near enough for practice. Rigorously we have

A c D, similar to E c f;

also,

A c, to E c, as A D, to E f;

and

Ef = Ec × AD
Ac.

When a d and c d are differently inclined, proceed as follows. See fig. 102, p. [200] inverted.

Fig. 63.

Let d b represent the weight; e h shows the tension. The triangles a c d, and a b e, are similar; as also e b h and d b c; whence

b e = a b, c d
a c, and e h = c b, b e
d c = tension.

In practice place w for b d; i. e. the actual weight.

In this plan, if the chord is able to resist the cross strain between A and D, it will also resist the tension. This cross strain is found by the formula already given and illustrated.

174. From what precedes, we have the following dimensions for bridges such as are shown in figs. 61 and 62. The details of 62, at f and c, and at E, 61, are shown in figs. 62 A, 62 B, and 61 C.

Fig. 62 A.

Fig. 62 B.

Fig. 62 C.

Span.Rise.A B.C E.Rod b.
20812 × 12(5 ×8)—21¼ inches.
251012 × 15(5 ×9)—21⅜ inches.
301212 × 18(5 ×10)—21½ inches.
351312 × 20(5 ×10)—21⅝ inches.
401414 × 21(5 ×12)—21⅝ inches.
451514 × 22(6 ×12)—21¾ inches.
501614 × 24(6 ×12)—21¾ inches.

The braces, (column 4,) being in pairs and blocked together. In spans exceeding twenty-five feet, the braces d f, and the rods f g, should never be omitted. The size of the rod g f, is found by considering A, d, f, as a small bridge.

175. In all light bridges, like the one under consideration, all parts should be fastened by bolts, to prevent springing by reaction. A bridge with but little inertia, or dead weight, tends to jump up when the engine has passed over it. Fastening takes the place of weight in a large span.

As soon as the rise admits, the points C, on each side of the bridge, should be connected to resist lateral motion. When the height is not enough for this, the same points may be joined to a floor beam extended out beyond the truss.

Though the dimensions are given for this plan up to fifty feet span, it is very seldom advisable to go beyond twenty-five or thirty feet; as frames consisting of a few long timbers are not so rigid, and free from vibration, as those made of a greater number of short pieces.

176. In extending this system one hundred or two hundred feet, we see at once that the pieces A c, B c, would become very long and would need to be made large and heavy. We should always so proportion any beam in a bridge that it is at once able to resist all of the several strains to which it may be exposed, without being unnecessarily large.

As to compression, the above system might be extended to almost any amount; but the braces would yield by flexure.

Instead of producing the braces A c, A′ c′, fig. 64, to their intersection, we stop at c and c′, insert c c′; to prevent the approach of these points, suspend the points B and B′ from c and c′, and commence again with the braces B D, B′ D; and so on as far as necessary.

To prevent the backward motion of the points B, and B′, either the chord A A′, or the counter-braces m, m, are necessary.

Fig. 64.

The pieces A c, A′c′ must support all of the load, including the weight of the bridge, lying within the rectangle B c, B′ c′. The next set of braces must sustain that part of the load only which comes over the centre of the bridge. Thus the braces should decrease in size as the centre is approached. The rods c B, c′ B′, must resist a tension equal in amount to the pressure on the braces, only being vertical they do not need the increase given to the braces on account of their inclination.

177. There is another method of stiffening a beam, as shown in figs. 65 and 66, by trussing rods, and a post. The dimensions being the same, the forces in both cases will be equal. The second, fig. 66, leaves the passage beneath the bridge clear.

Fig. 65.

The tension on the rods A c, B c, fig. 66, tends to draw the points A and B together, an effort which is resisted by the top chord A B.

In extending this system, as in art. 176, the rods become either very long, or very large, from the small angle of inclination; evils which remedied as before, by supporting the post c B, fig. 64, from the foot of the first rod, fig. 64, and commencing again from c.

Fig. 66.

To prevent the motion of the triangle c B G, fig. 64, about the angle B, we must introduce either the upper chord c c′, or the counter rod c A. If the lower chord is omitted the rod D B must be of the same size as E B. In this truss, either the top or the lower chord simply may theoretically be omitted, due allowance being made in the size of the rods. In practice it is never advisable to omit either, as both are required for lateral bracing, and for support of the road-way.

Having said thus much of the general ideas that apply to all bridges, let us now look at some of the plans most in use; and to become familiar with the subject, work out the dimensions of an example of each kind.

178. As rods, nuts, and washers are used in all bridges, the following table may not be out of place:—

Column 1 gives the diameter of rod.

Column 2 strength at 15,000 lbs. per square inch.

Column 3 the weight per lineal foot.

Column 4 side of the square nut.

Column 5 the thickness of the same.

Column 6 the dimensions of washers.

Column 7 the thickness of washers.

Column 8 breadth (side to side) six-sided nut.

Column 9 breadth (across angles) six-sided nut.

Column 10 thickness of six-sided nut.

Column 11 number of screw threads per inch.

Column 12 gives the diameter of rod.

123456789101112
Diameter.Strength of Rod.Weight per Foot.Square Nut.Thickness.Square of Washer.Thickness of Washer.Six-Sided Nut.Six-Sided Nut.Six-Sided Nut.Screw.Diameter.
½2,9400.661¼¾2½¼1⅜1½9
16		12½
¾6,6301.491½⅞3¼1¾2⅞10¾
111,7752.65214⅜1⅞2¼1⅛81
1⅛14,9103.3621⅛4½⅜2⅛27
16		1¼71⅛
1¼18,4054.172¼1¼5½2¼211
16		17
12		71¼
1⅜22,2605.022½1⅜5½½2½2⅞17
16		61⅜
1½26,5055.972¾1½6½2⅝3⅛111
16		61½
1⅝31,0957.012⅞1⅝6½⅝2⅞35
16		113
16		51⅝
1¾36,0758.1331¾7⅝33½251¾
1⅞41,4159.333¼1⅞7½⅝3¼3¾2⅛4½1⅞
247,13010.623½1⅞8⅝3½42¼4½2
2⅛53,19012.003¾28½¾3⅝43
16		2⅜42⅛
2¼59,64013.4042⅛9¾3¾46
16		2½42¼
2⅜66,45015.004⅛2¼9½¾44⅝2⅝42⅜
2½73,62016.704¼2½10¾4¼4⅞2¾3½2½
123456789101112

179. Let us now assume the following data:—

Span200feet,
Rise (centre to centre of chords)25feet,
Width20feet,
Length of panel15feet,
Weight (bridge and load) per lineal ft.4,000lbs.

HOWE’S BRIDGE.

Fig. 67.

Fig. 67.

Lower Chords.—The tension, at the centre of the lower chord, is found by dividing the product of the weight of the whole bridge and load by the span, by eight times the height, or

T = W × S
8h,

which becomes, with the above data,

T = 800000 × 200
200 = 800,000 lbs.

Here the tension and the total weight are equal, a result which can occur only when the rise is one eighth of the span. This is the best ration between these dimensions, as then the horizontal and vertical forces are equal.

As to the proportion of the panel, (or the rectangle inclosed by the chords and any two adjacent posts,) the ratio of base to height should be such as to make the inclination of diagonal about 50° from the horizontal; if much less, the timbers become large and heavy; and if more, the number of pieces is unnecessarily increased.

The braces at the end of a long span, may be nearer to the vertical than those near the centre, as they have more work to do. If the end panel be made twice as high as long, and the centre panel square, the intermediates varying as their distance from the end, a good architectural effect is produced.

To determine the size of the lower chords, to resist the above 800,000 pounds of tension, proceed as follows: Each side truss will support one half of the whole load, or 400,000 pounds; which, at 2,000 pounds per inch, will require 200 square inches of section. Four sticks of 8 × 12 inches, give an area of 384 square inches, which must be reduced as follows: Deduct 72 square inches for the area cut out by the splicing blocks, 40 inches for the bolts connecting the pieces, 28 inches for inserting the foot blocks, and 10 inches for inserting the washer, and we have remaining 234 square inches; which exceeds by a little the exact demand. This excess (about one seventh) is a necessary allowance for accidental strain, to which all bridges are subjected.

Fig. 67 A.

The splices used in bridge framing are shown in fig. 67 A and fig. 67 B. For the first, the depth of insertion and length of the block depend upon the tension upon the chord. The following dimensions have been much used and are perfectly reliable:—

Span of Bridge.A CB CC D
Feet.Feet.Inches.Feet.
501.001½1.50
1001.2522.00
1501.752½2.25
2002.0032.75

There is no need of cutting more than one notch, as in the figure; the resistance of the triangles is thereby lessened, and the work increased.

Fig. 67 B.

In fig. 67 B, the rods must of course be able to resist the tension upon the one piece which is cut.

Upper Chord.—The upper chords of a bridge suffer compression, to the same amount numerically, as the tension on the lower chord; as whatever tension is thrown by any brace upon the lower chord, reacts as just so much compression upon the upper. In the case at hand, 800,000 lbs. in all, or 400,000 on each chord.

The resistance to compression being one thousand pounds per inch, renders necessary four hundred inches of section to each chord; four pieces 8 × 12 give in all three hundred and eighty-four inches of section, which requires no reduction, as the whole chord pressing together and being properly framed is not weakened by splicing. The splicing blocks in the upper are merely plain pieces, inserted one half inch, the only duty being to keep the sticks at the proper horizontal distance.

The spaces between the pieces should be large enough to allow the rods to pass without cutting the chords; (two inches answers every purpose). The bolts for splicing, have no very great strain to bear. In small spans from ½ to ⅝, and in large bridges from ⅝ to an inch is enough.

The object in framing a built beam for a bridge chord, is to make a stick which shall be uniformly strong. This is done by cutting the pieces in the centre of the panel, and by having no two joints in either chord in one panel; though in long spans this cannot always be done. Figs. 67 D and 67 E (page [153])

BRACES.

The whole load being800,000 pounds,
Each truss supports400,000 pounds,
Each set of braces200,000 pounds,
Each brace (there being 4)50,000 pounds,

which must be increased for inclination as follows: The length of diagonal is twenty-nine feet, (the height being twenty-five and length 15,) whence

25 to 29 as 50,000 to 58,000 lbs.;

which would need fifty-eight square inches, or 7 × 8 for compression; which, however, is quite too small for flexure. 12 × 12 placed in the formula gives

W = 2240 × bd3
L2,

or

W = 2240 × 12 × 1728
841 = 55,296 lbs.

In practice, smaller braces than 12 × 12 would answer, because the four braces in a set may be fastened together, making a post of four pieces 8 × 12, or in all a built post of 44 × 12 inches; twelve being the depth, whence

W = 2240 × 44 × 1728
841 = 202,511 lbs.;

the forty-four inches being made by blocking the braces four inches apart. The second set of braces are to be treated in the same manner, the weight to be supported being only the rectangle included by those braces; i. e. the whole bridge and load less the two end panels.

As the centre of the span is approached, the pressure on the braces becomes very small; and the scantling of the braces will be reduced to about 6 × 7 inches.

RODS.

The weight upon the first set of rods is the same as that upon the end sets of braces; in the present case 800000 ÷ 2 = 400000 on each side truss, and 400000 ÷ 2 = 200000 on each end; and if there are five rods in each set, each rod bears 40,000 lbs. Referring to the table on p. [146], opposite to 41,415 lbs., is the diameter 1⅞ inches; whence the first set must contain five rods, of 1⅞ inches diameter. The second set decrease in size as the weight is lessened by the two end panels. The nut and washer for the rod are also found in the same table.

COUNTERBRACING.

180. When a load is placed on the point C′, fig. 64, the truss tends to sink at that point, and a corresponding rise takes place at C. This motion changes the figure A B C E, from a rectangle to an oblique angled figure; the diagonal E B being shortened, and A C lengthened. This motion is easily checked by the introduction of the counter brace E B.

Fig. 64.

The action which this timber is called upon to resist, being caused by the moving or variable load on one panel, the brace must resist the load coming thereon, (say fifteen feet,) and is thus the same size as the brace at the centre of the span.

The counter braces may be so confined between the braces, at the intersection, as not to move laterally or vertically, but must not be fastened to the braces; because the action of the separate timbers is thus trammelled.

Fig. 67 C.

The manner of adjusting the braces and counter braces to the chord is shown in fig. 67 C. It was formerly the custom to abut the braces against a block on one side of the chord, and to screw the rod against a block on the opposite side; the whole strain acting to crush the chord crosswise. This has been remedied by the arrangement shown in the figure, the two blocks being cast in one piece and connected by a small hollow cylinder passing between the chord sticks.

Fig. 67 D.       Fig. 67 E.

This system is known as Howe’s bridge, and may be seen in almost any section of the country; and though in many cases badly proportioned, and of bad material, if properly made answers a very good end.

The following table has been formed for the use of engineers and builders, giving, together with the table of nuts and washers, all dimensions required.

Span.Rise.Panel.Chords.End braces.Centre braces.End rod.Centre rod.
501072—8 × 10725 × 52—1⅛2—1
751292—8 × 10825 × 52—1½2—1
10015113—8 × 10926 × 62—1¾2—1
15020134—8 × 121026 × 73—23—1
20025154—8 × 161227 × 75—25—1

PRATT’S BRIDGE.

Fig. 68.

181. Assume the following data for an example:—

Span100feet.
Rise12feet.
Panel10feet.
Weight per lineal ft.2,500lbs.

The tension on the lower, or the compression on the upper chord, will be

250000 × 100
96 = 260,417 lbs.

The manner of dimensioning the chord, and of splicing, is the same as already described for Howe’s.

SUSPENSION RODS.

The first sets of rods, A B, A′ B′, must sustain the whole weight of the bridge and load; which is 250,000 lbs. Each side 125,000 lbs.; and each end set of rods 62,500 lbs.; and if each set has four rods, each rod must support 15,625 lbs.

The rod being inclined, this amount is increased by the following proportion:—

12 (height) to 15.8 (diagonal) as 15,625 to 20,573 lbs.

This is half-way between the tabular numbers for rods of 1¼ and 1⅜ inches in diameter; 1⅜ will therefore answer. The next set of rods must be considered as supporting the whole load, less the two end panels, and so on as already explained for Howe’s bridge. The manner of applying the rods to the chords is shown in fig. 68 A. The bevel block should be connected with the block at the foot of the post, so as to prevent crushing the chord.

Fig. 68 A.

COUNTER RODS.

As both top and bottom chords are always used in this bridge, the counter rods have only the variable load on one panel to resist. The action is, in amount, the same as that on the counter braces in Howe’s bridge; but acts in a different direction, and in the other diagonal.

The weight of a passing load cannot be more than two thousand pounds per lineal foot. The panel being ten feet long, the whole weight coming on two sets of counter rods, (one set in each side truss,) is twenty thousand pounds; or ten thousand pounds on each set; and if there are put three rods in each set, we have 3,333 pounds per rod, which increase for inclination as follows:—

12 : 15.8 :: 3333 : 4389 lbs.,

requiring a rod of three fourths inch diameter.

The posts in this structure, correspond to the braces in the Howe bridge; only being vertical, they need not be so large.

182. The following table gives all the dimensions necessary for proportioning this truss.

Span.Rise.Chords.End post.C post.End rod.C rod.Counter rod.
50102—8 × 105 × 5422—1⅜2—11—1½
75122—8 × 106 × 6522—1⅝2—11—1½
100153—8 × 107 × 7622—1¾2—12—1⅛
125183—8 × 108 × 8623—1⅞3—12—1⅜
150214—8 × 129 × 9623—2⅛3—13—1⅛
200244—8 × 1610 × 10625—1⅞5—13—1⅛

And the following, the sizes of counter rods, for different panels.

Length of panel.Height of panel.Approximate diagonal of panel.Diameter of the rod.
One in a set.Two per set.Three per set.
1012161⅝1⅛⅞
1113171⅝1¼1⅛
1214181¾1¼1⅛
1315201¾1¼1⅛
1416211⅞1⅜1⅛
1518231⅞1⅜1⅛
16212621⅜1⅛
18252721⅜1⅛

The advantage possessed by this bridge, over Howe’s plan, is that the panel diagonals may be adjusted by the screws; by which control is had over the form of the truss, and of the duty done by the several parts. Change of form cannot be had by working upon verticals. Howe’s bridge must be adjusted by wedging the braces and the counter braces.

183. The manner of drawing the bevel block in this bridge, is shown in fig. 68 b. The proportions of the block depend upon the proportions of the panel; and the dimensions, upon the size of washer used.

Let C C be the centre line of the post, and A B the chord. Let o m, and o n, be the panel diagonals, and H and y, the length of the washers.

Fig. 68 B.

The depth of insertion of the block into the chord, depends upon the horizontal strain upon it. In a span of one hundred and fifty feet, with the rods at an angle of 50°, two inches have been found ample at the end of the truss, and one half inch at centre.

From D, perpendicular to m m, lay off D E; equal to H, also from E, at right angles to n n, make E E′ = y. From E′ draw the vertical E′ L.

The strain upon the rod o m, being represented by o m; and that upon o n, by o n, the resultant is shown, both in direction and amount, by o V. It is not necessary that this should pass through the centre of the post, as the excess of tension on o m, over that on o n, is absorbed by the lower chord.

Note.—Screwing up truss bridges, is a more scientific operation than is generally supposed. Many builders commence at each end, and lift the bridge from the scaffolding. By this method the greater part of the load is often borne by a few of the end sets of rods. The better method is to begin at the centre and work both ways towards the ends, being sure that each set of rods does its duty before the next is touched. The lift to be made by each set of rods, should first be calculated, and tested while screwing up, with the level.

LATTICE BRIDGES.

184. Town’s lattice, consists of a simple lattice-work of plank, 3 × 12 inches, treenailed together at an angle of forty, forty-five, or fifty degrees. It possesses great stiffness, without by any means having the material disposed in the best manner. Such bridges might well be made by the mile, and cut off to order according to the span.

The improved lattice, by Hermann Haupt, Esq., C. E., avoids all of the evils attendant upon the common lattice, and gives a very cheap, strong, and rigid bridge. In this plan the braces are placed in pairs, with vertical tie planks between them; by which the twisting seen in the common lattice, is removed. The braces are also brought to the vertical, as the point of support is reached, by which a good bearing is given to the end sets of timbers.

To vary the size of the braces, as the strain upon them decreases, would be both inconvenient and expensive; but the same effect may be produced by varying the distance between them, making it greater as the centre is approached.

S. W. HALL’S WOODEN TRUSS AND ARCH BRIDGE.

Inverting Mr. Haupt’s design for a lattice of improved construction, (which consists of vertical ties and inclined braces,) we have the base of the above-named bridge; where the inclined timbers are used to resist tension, as below.

This being a very good plan, and the arrangement for building being such as to secure the thorough execution of the work in its most minute detail; it is thought best to extract at some length from a letter from the inventor, dated July 31st, 1856, not however being confined to the matter therein.

The first claim, is for a new form of truss, formed of posts vertical, or nearly so, and tension pieces, inclining downwards toward the centre; thus differing from nearly all other plans. Timber resists double as much extension as compression; and when large enough to resist the simple tension, does not have to be increased as in resisting compression for flexure; but requires a larger allowance for joints, as tension tends to pull the joints apart, while compression forces them together.

The following result was obtained, showing the superior strength of timber work in resisting by tension. Two models, containing the same amount of timber, were tested. The one built with vertical ties and braces, broke by crippling the brace, under 2,400 lbs.; while that constructed with verticals and suspenders, inclining towards the centre, sustained 4,200 lbs. with no visible change of form.

The second claim is for more efficient bearings and connections than common, and this with less cutting away of timber. The arch and arch braces have a full, fair bearing at top and bottom. The first sets of tension braces, (those extending from the top of the arch braces towards the centre,) are sustained by two pins at each joint; which gives six pin bearings, or twelve for one set of braces, of six inches each, (the pin being two inches in diameter, and plank three inches thick,) equal in all, to seventy-two inches of bearing surface at least, for each five feet lineal of bridge, or one hundred and forty-four inches for ten feet.

The third claim, is that the bearings, at joints, are central, and that the shrinkage of the timber is towards and not from them as in many plans.

The pin holes are bored by machinery smooth and true; the treenails when of wood are of seasoned oak or locust, turned to a perfect fit, and when of iron are made hollow.

These bridges, after three years, stand within an inch of their shape as framed without exception. One indeed supporting an aqueduct, which throws upon the truss a constant load of 2¾ tons per foot, not including the weight of the bridge, without any apparent settling.

The connections being fast, prevent reaction and vibration from variable loads, the strains in this case are reversed, the bridge tending to spring up instead of settling.

The fourth claim, is for the small brace connecting the lower with the intermediate chord; by which additional connections are obtained, and smaller timbers rendered available.

The fifth claim, is the formation of a stronger chord than by the plan of using a few large sticks. The chord being made of a great number of small pieces, the strength is of course less affected at any one point, by a joint, than when only a few pieces are used.

In the bridges built by the above engineer, are to be seen some of the most perfect built beams in the country. The following conditions being observed, the most uniform, and highest average strength possible is obtained.

First. To cut but one stick in any one panel.

Second. To cut no stick at the centre of the bridge.

Third. To place every joint in the middle of the collateral piece.

The chords are cut by two rows of pins, two inches each; and if the chord be fifteen inches, the cutting at centre, where there is no joint, is but four fifteenths of the whole section. To resist the parting of any two sticks, there is the resistance to shearing of ninety-six pins; and the section of each being three square inches, the whole resistance is two hundred and eighty-eight inches of area. If the intermediate chord has the same number, the whole area to resist shearing, in the lower chord, is five hundred and seventy-six square inches. The bearing surface of each pin in the chord stick is 2 × 3 inches, or six inches; and 96 × 6 = 576: and in both chords 1152 inches.

Sq. in.
The whole chord timber, (both chords,) is (6 × 3 × 14),252
In the intermediate chord, (6 × 3 × 12),216
Whole timber section,468
Deduct 4 pins for both chords, 468 – (4 × 2 × 3 × 6) or 468 – 144 =324
Deduct for joints 3 × 10 + 3 × 8 or 324 – 54, Square inches of available area.270

Comparing the amount thus cut away with that cut away in other plans, we have the following figures;—

A. Hall’s Bridge, (actual bridge,)30
100
B. Howe’s bridge, (actual bridge,)35
100
C. Page 163, (Handbook R. R. Construction,)39½
100
D. McCallum’s, (Susquehanna bridge,)58
100

The sixth claim, is the peculiarly convenient form for applying an arch,—the superiority consisting in convenience for attachment; in the connections being less affected by shrinkage than when posts are locked into arches; in the timbers not being weakened by cutting. The arch is loaded with the tension timbers, inwardly, and acts as a general arch brace, transferring at once all of the several tensions to the abutment, thus really combining the arch with the truss.

The liability of this plan to decay, certainly appears to be less than that of most plans of wooden bridges now in use; as will be plainly seen by observing the position of the joints; falling rain finds a much easier access to almost any other joint than the pin hole. The timber work being made of plank, all the timbers are small, and are thus much more likely to be sound.

Fig. 69.

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:—

Length,7 feet.
Height,1 foot.
Width,1 inch.
Chords,¼ × ½ inch.
Braces,¼ × ⅓ inch.
Lattice,¼ × 1
16 inch.

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 Span being150feet,
The Rise20feet,
The Panel15feet,
Weight per foot of bridge and load3,000lbs.

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

√202 + 152 = 25 feet,

√202 + 302 = 37 feet,

√202 + 452 = 49 feet,

√202 + 602 = 64 feet,

√202 + 752 = 78 feet.

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.

20 : 25 :: 6000 : 10000

20 : 37 :: 6000 : 15000

20 : 49 :: 6000 : 20000

20 : 64 :: 6000 : 25000

20 : 78 :: 6000 : 30000.

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.

In panel No. 1, it will be 25 feet.

In panel No. 2, it will be 18 feet.

In panel No. 3, it will be 17 feet.

In panel No. 4, it will be 16 feet.

In panel No. 5, it will be 16 feet.

and applying the formula

2240bd3
L2 = W

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

For the 1st panel, 25 feet long, 8 × 10

For the 2d panel, 37 feet long, 8 × 10

For the 3d panel, 49 feet long, 8 × 10

For the 4th panel, 64 feet long, 8 × 10

For the 5th panel, 78 feet long, 8 × 10.

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.

GENERAL TABLE OF DIMENSIONS FOR ARCH BRACE TRUSS.
Span.Rise.Chords.Ties.Braces.Lattice.
50102–8 × 101–8 × 102–6 × 62 × 9 or 3 × 6
75122–8 × 101–8 × 102–6 × 62 × 9 or 3 × 6
100153–8 × 102–8 × 103–6 × 62 × 9 or 3 × 6
150204–8 × 123–8 × 104–6 × 82 × 9 or 3 × 6
200254–8 × 163–8 × 104–6 × 92 × 9 or 3 × 6

Fig. 69 K.

Fig. 69 A.

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,

a, 25 : 20 :: 6000 : 4800.

b, 37 : 20 :: 6000 : 3243.

c, 49 : 20 :: 6000 : 2450.

d, 64 : 20 :: 6000 : 1870.

e, 78 : 20 :: 6000 : 1540.

f, 92 : 20 :: 6000 : 1304.

g, 106 : 20 :: 6000 : 1132.

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.

Fig. 69 C.

Fig. 69 D.       Fig. 69 E.       Fig. 69 F.

Fig. 69 G.       Fig. 69 H.

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.

Fig. 70.

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.

Load.Deflection.
41.40 tons,0.013 feet,
95.35 tons,0.038 feet,
140.70 tons,0.061 feet,
187.20 tons,0.061 feet.

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.