These bridges, however, are supposed to carry two traction engines, each weighing 16 tons, on two wheels 10 feet 4 inches apart, so that they are not unnecessarily strong, as would at first sight appear.

If such a bridge were constructed with pine timber beams, they would require to be spaced closer together across the bridge, or the span reduced.

The following table shows the sizes of girders used in the Roads and Bridges Department, New South Wales, for bridges, similar to the above:

As a second example, take a timber railway viaduct for a single line of way constructed over a considerable length of low-lying ground liable to floods near a river, which form the approaches to the main bridge over the river. If the foundations are fairly good, and the height of the rail-level above the

ground is about 8 feet, a series of spans of 10-feet centres, such as shown in Figs. 110 and 111, will be found to be most economical.

If the height of the rail-level above the ground be from

15 to 20 feet, it may be found to be cheaper to design for spans of 24-feet centres, such as shown in Figs. 112, 113, and 114.

In each case an open deck is used, similar to the deck so largely used on American bridges. The sizes of the timber sleepers, if Australian timber is used, must be decided with reference to the most convenient sizes obtainable; thus it is easier to obtain a good durable sleeper 12 inches wide by 7 inches deep from ironbark trees than one 8 inches square.

Fig. 115 shows an American deck with ironbark sleepers suitable for the type of viaduct illustrated, and Fig. 116 shows a similar deck in which a central beam is used. The former would be suitable for an iron or steel bridge in which the plate web-girder stringers take the place of the main timber beams, we will therefore consider it more fully.

The strength of the deck may be calculated as follows for Fig. 115: The maximum load on the driving-wheels of a locomotive does not generally exceed 16 tons per pair of wheels, therefore the weight on each wheel is 8 tons; but since this weight may be increased on one side, and correspondingly reduced on the other, from the oscillation and plunging of the engine produced in various ways, it is assumed that the total maximum effect may reach 10 tons per wheel.

At least three sleepers will take part in carrying the weight brought on any one of them, the sleeper immediately under the driving-wheel taking one half of this weight, and the sleepers on each side taking one quarter each, so that the maximum value for W, Fig. 115, is 5 tons.

The bending moment is 7.5 foot-tons, or 90 inch-tons.

The moment of resistance for ironbark, where f= 14,000 lbs. per square inch since the section is comparatively small, is—

If Oregon timber is used, f will be about 7000 lbs. per square inch, and the section must be increased to 10 inches.

square with 10 inches space between sleepers, or 20 inches.

centre to centre, in which case

The sizes of sleepers have been calculated on the assumption that only three sleepers carry the load on the driving-wheel; this assumption is on the safe side, as the iron guard-rails and the timbers very probably distribute the weight over more than three sleepers.

This kind of deck in America is usually constructed with 8 × 8 timbers spaced 16 inches centre to centre, thus leaving an 8-inch space. The advantages of this deck over the ordinary close timber deck are as follows: The sleepers are spaced sufficiently close to allow the wheels of a carriage to run without sticking in the case of derailment; and they are exposed on four sides to the air, and therefore dry uniformly and last a much longer time; moreover, any defective sleeper can be readily seen and replaced. The timber guard-rail is a precaution against the effect of derailment, and serves to some extent in assisting to distribute the weight of the driving-wheels. The spacing is large enough to allow hot material from the engine to fall between the sleepers. The number and strength of the sleepers gives considerable lateral strength and stiffness to the structure, enabling it to resist wind pressure and oscillations. The 8-feet spacing of the main beams ensures an elastic road and easy running.

The strength of the main beams in the 10-feet spans of the viaduct will now be considered.

Fig. 117 shows the position and loads produced by the three wheels of a heavy consolidation, mogul, or other engine