CHAPTER XIV.

DECKS OF IRON AND STEEL BRIDGES.

THE deck of a bridge usually consists of cross-girders, sometimes called floor beams, and longitudinals, sometimes termed stringers. The cross-girders are spaced at the same distance apart, centre to centre, as the apices of the triangles in lattice girders, or at the panel-points of trusses. In a railway bridge, the sleepers, rails, guard rails or timbers rest directly upon the stringers, and these discharge their load upon the cross-girders, which in like manner discharge their load upon the apices or panel-points of the main girder or truss.

The weight of rails, guard rails, spikes, sleepers, etc., in railway bridges for heavy traffic may be taken as 400 lbs. per lineal foot of bridge for each line of way.

The stringers in truss bridges are usually constructed as plate web girders, having an effective depth of from to of the span; but in lattice girders, where the distance between the apices is much smaller than in truss bridges, rolled iron or steel girders are frequently used. Stringers of iron or steel are spaced from 6 to 8 feet centres transversely to the bridge. Where timber is cheap, timber stringers consisting of two or more groups of beams are spaced 5-feet centres, so that the middle of each group is immediately under the rails.

Timber stringers usually rest on the top flanges of the cross-girders, but iron or steel stringers may rest in a similar manner upon the top flanges of the cross-girders, or be built into them (see Plate II.).

The cross-girders are usually constructed of plate web girders, and are riveted to the vertical compression members in truss bridges, or suspended by means of hangers. In girders

with trough-shaped bottom booms, the cross-girders are attached immediately above or below the apices of the triangulation, or panel-points.

The open deck illustrated in Fig. 113 is commonly used in America, but occasionally in England, and more frequently in the colonies. The deck is formed (if of timber) by means of planks from 3 to 4 inches thick, laid diagonally or transversely. Upon this floor is laid the ballast and sleepers as a loose road, which is maintained in the same manner as the permanent way on the rest of the railway. In many English railway bridges, Mallet's buckle plates or cambered plates of iron or steel are riveted to the cross or longitudinal girders, forming a continuous metal floor, upon which the ballast, sleepers, and rails are laid as a loose road as before. There are various systems of flooring suitable for bridges, such as Hobson's

patent flooring, shown in Figs. 317 and 318. Fig. 319 is a trough section manufactured by Messrs. Braithwaite and Kirk. Lindsay's patent flooring may be used in a similar manner; also Westwood and Baillie's corrugated flooring.

All the forms of bridge floors illustrated in Figs. 317, 318, and 319 may be used without either cross-girders or longitudinals, provided the height and pitch of corrugations or troughs, and the thickness of metal, are proportioned with regard

FIG. 319.

to the maximum concentrated wheel loads. The strength of the troughing when connected together in a bridge floor is very great, as each trough acts as a girder; again, a load concentrated on one trough would be partly borne by adjacent troughs.

Figs. 317 to 319 are very suitable for bridge floors where the headway is limited, as the sleepers lie in the troughs, well supported by ballast. All these forms may be obtained of various sizes and thicknesses of metal in iron and steel, and they are largely used for bridge decks. Fig. 319 is shown on Plate V., as applied to a highway bridge.

The decks of bridges are very varied, and must be determined with reference to the locality and nature of the traffic. In towns the standard form of street-paving will influence the design of the decks of the bridges. For country bridges the decks may be formed as illustrated in Fig. 108 and Plates III. and V.

The deck of a bridge forms an invariable portion of the dead load, and is independent of the span of the main girders of trusses.

To design the floor of a bridge consisting of an American deck resting upon stringers 20 feet long, measured from centre to centre of the cross-girders. The cross-girders are attached to the panel-points of the main trusses, and have an effective span of 15 feet. Let the four driving-wheels of the consolidation locomotive, Fig. 326, be arranged symmetrically on the longitudinal stringers, so as to produce the maximum bending moment (Fig. 320).

The dead load, consisting of rails, sleepers, spikes, guard rails, etc., as shown in Fig. 113, may be taken as 400 lbs. per lineal foot of bridge, or 200 lbs. on each stringer. The

weight of the stringer itself may be assumed to be 110 lbs. per lineal foot; so that the total dead load is

(110+200)20 = 6200 lbs. = (say) 3 tons

The maximum bending moment due to the dead load is

The maximum bending moment due to the live load is

12(2·625)+6(575) 66 foot-tons.

The total bending moment is—

66+7.5=73.5 foot-tons

If the material is steel, the working stress by the new French formula is

This working stress is high for longitudinals, and the formula appears to give greater values than would be allowed in the

best American practice where the impact is considerable. We will therefore adopt 4.5 tons as the working stress.

Let the effective depth be taken as of the span, or 2 feet, then the moment of resistance is

fad 45 × 2 × a = 9a foot-tons

=

Two angles 5 × 3 × may be used both for the top and bottom flanges; thus in the bottom flange the effective area is 2(77 -7)=8.75 square inches, which gives the necessary

area.

Rivets. Assume that the rivets are inch diameter and 4 inches pitch; there will be, therefore, 3 per foot, each 0.6 square

inches area, or a total of 1.8 square inch. The maximum shearing stress will occur at the points of attachment of the longitudinals to the cross-girders when the live load is so distributed that the first driving-wheel is close to the cross-girder; the shearing stress will then be about 14 tons, or 7 tons per foot horizontally and vertically. Let f denote the intensity of stress upon the rivets; then

1·8f=7, and ƒ= 3.9 tons per square inch

The rivets in question are in double shear, hence this stress is very safe for shearing.

The pressure on the bearing area may be denoted by p; then, if we have a 3-inch web plate

p× 3 × 3 × 3 = 7, and p = 7 tons

which is safe for steel, hence 3-inch rivets 4 inches pitch are sufficient.

Thickness of the Web Plate.-The method of determining the thickness of the web plate must take into consideration the maximum intensity of shearing stress and the tendency to buckle. It has been shown that the intensities of shearing stress on two planes at right angles to each other are equal, and it is usually assumed that the web resists the whole of the shearing stress in a plate web girder, and that this shearing stress is equally distributed over the depth of the web.

If a series of planes inclined at 45° be drawn so as to divide the web plate into a series of strips of one inch wide, then each of these strips may be treated as a column, the length of which is equal to the effective depth of the girder multiplied by the secant of 45°. The load upon these elementary columns is the mean shearing stress acting over an area of 1 inch by the thickness of the web.

Let the length of the column = d sec 45°.

=

t = the thickness of the web.

=

f a constant for the material 16 tons for wrought iron or steel.

a = a constant depending on the section and method of fixing 3000 for rectangular sections.

=

b the buckling stress per square inch.

=

Then, by Rankine's and Gordon's formula—