with axle loads of 12 tons.

The maximum bending moment

occurs at the centre of the span, and is—

18 x 512 × 4.5 = 36 foot-tons = 432 inch-tons

The dynamic effect of the live load will increase this bending moment by about 30 per cent., so that it may be taken as 562 inch-tons, or 46.8 foot-tons.

The equivalent uniformly distributed load which will produce the same moment in the centre of the beam is found thus

The dead load, consisting of main beams, sleepers, rails, guard-rails, and guard-timbers, is about 0.25 ton per foot run, so that the totally equivalent uniformly distributed load may be taken as 4 tons per lineal foot, and the maximum bending moment is

4 x 10 x 10
8

= 50 foot-tons, or 600 inch-tons

The moment of resistance of two beams of ironbark timber, each 12 by 12 inches, is

If ƒ is taken as 5.5 tons per square inch, which may reasonably be expected from good ironbark timber, the moment of resistance is 3,168.0 inch-tons, and the factor of safety

The factor of safety is quite sufficient for such a structure of ironbark timber.

Figs. 118, 119, and 120 illustrate the standard pile-trestle on the Toledo, St. Louis, and Kansas City Railroad.' The sleepers are 9 feet long x 8 inches wide x 6 inches deep, and the guard-rails 6 inches x 6 inches, notched 1 inch over sleepers.

1 "Treatise on Wooden Trestle Bridges," by Wolcott C. Foster. Published by J. Wiley and Sons, New York.

The main beams or stringers are arranged in groups of three under each of the rails, and are 7 inches wide x 16 inches deep on a span of 15 feet.

Cast-iron separators 4 inches thick are arranged between

7x 16"x 15'

FIG. 118.

the stringers over the caps, and the stringers are protected with sheet iron 30 inches wide, as shown in Fig. 119. The caps are 14 feet long x 12 inches x 12 inches, notched 1 inch

over the four piles, and the sway braces are 10 inches x 3 inches. On the Pennsylvania Railroad the sizes of the stringers used are given in the following table :

The stringers are generally long enough to extend over two trestles, and should break joint, and should be securely fastened to the caps by means of drift-bolts.

FIG. 121.

Fig. 121 shows the method of connecting the stringers over the caps adopted in the Pennsylvania Railroad, in which the tendency of the joint, when it settles under a weight through the support becoming weakened, is to close at the top and to open at the bottom. This arrangement provides most material where there is the greatest liability to split. The packing strips are notched over the caps as shown. On the Chicago, Milwaukee, and St. Paul Railroad, the standard pile-trestle in 1890 had six stringers in two groups of three, each 16 inches deep x 8 inches wide, on a span of 15 feet 9 inches, and two outside stringers each 16 inches deep x 6 inches wide. The dimensions of the stringers will depend upon the character of the timber available, and the train loads.

With an equivalent uniform load of 3.5 tons per foot run,

H

allowing for the dynamic effect of the live load, and stringers 16 inches x 8 inches on a span of 15 feet, we have—

1

=

For white pine or spruce Professor Lanza recommends f: 3000, and the experiments of Mr. Onward Bates on white pine stringers show that this value is about correct; henceMoment of resistance = 2048 x 3000 6,144,000 inch-pounds = 2743 inch-tons

Therefore the factor of safety would be

For yellow pine ƒ = 5000, and the factor of safety is 3.83. For Oregon fir ƒ = 6500, and the factor of safety is 54. The latter value of the factor of safety may be considered sufficient, but it is clear that American engineers do not use large factors of safety in their timber structures.

There are two distinct classes of timber trestle piers-(a) framed trestles, (b) pile trestles.

Framed trestles consist of square timber framed together; they are usually built upon a foundation of some kind, which may be a pile foundation, masonry, concrete, grillage, crib, solid or loose rock.

Framed trestles are provided with a sill which rests upon the foundations, and, in order that decay may be delayed as long as possible, the sill should be above the ground, and not covered with earth.

Framed trestles are used for almost any height, but they are exclusively used for lofty timber viaducts.

Pile trestles consist of two or more piles surmounted by a cap. When the height is less than 10 feet sway bracing is not used; above this height sway braces are used, bolted to the cap

1 Trans. Amer. Soc. C.E., November, 1890

and to the piles at their intersection. Pile trestles rarely exceed 30 feet in height; from 10 to 20 feet the outside piles are driven with a batter of from 1 to 3 inches per foot.

The timber used for piles should be straight and sound, free from wind-shakes, wanes, large loose black or decayed knots, cracks, worm-holes, and all descriptions of decay, and should be stripped of bark; they must be cut off square at the butt, and be properly sharpened.

Piles of Australian hardwood, which is liable to decay at the heart, should be free from large pipes.

The heads and feet of piles should be protected before driving, if they are liable to be injured by the hammer or ram. A wrought-iron ring is generally used at the head, and some form of iron shoe at the foot according to the nature of the material into which the pile is driven. Timber piles for viaducts are usually driven by a drop-hammer or ram, other methods will therefore not be considered. An upright frame is used with a pulley at the top, over which a rope passes which supports the hammer or ram. The frame consists of two uprights called leaders, from 10 to 60 feet long, placed about 2 feet apart, which guide the falling ram. The weight of the ram varies from 500 to 7000 lbs., but is usually about one ton, and it is provided with grooves or guides to fit the guides. The rope is usually wound up and the weight raised by a steamengine, but horses may be used hitched directly to the end of the rope, or men may be employed working a windlass or pulley directly at the rope. There are two methods of detaching the weight, i.e. letting the ram fall (a) by means of a nipper, (b) by means of a friction clutch.

A pile is considered to be sufficiently driven if the penetration from the last five blows with a ram weighing 2000 lbs. falling 25 feet does not exceed 5 inches. Heavier rams with smaller falls give better results, such as at Brooklyn, where a ram weighing 6720 lbs. was used falling 3 feet.

The bearing power of piles may be considered in the following manner-When a pile rests upon a hard stratum it should be treated as a long column, and its bearing capacity may be inferred by means of the tables, pp. 37, 38, and 39, Chapter II., or it may be calculated by means of formulæ such as those given in Chapter XII. The safe bearing pressure on a pile driven into a yielding stratum may be found in the following manner :