The Anatomy of Bridgework

by William Henry Thorpe

Fig. 21.

As rail-joints upon a bridge may injuriously affect the floor, so also will a weak floor be very trying to the rails. A remarkable instance of this has come under the writer’s notice, where a bridge ([Fig. 21]) of three 33-feet spans, having outer and centre main girders, with cross-girders spaced 3 feet apart, resting upon the girder flanges, but not attached, and carrying two roads, had the permanent-way in a very bad state. The rails proper, with supplementary angle-plates, rested direct upon the cross-girders, which were decidedly light, and the whole floor had much “life” in it, the ill-effect of which was shown in thirteen breaks in the angle-plates, in each case near their ends, generally at holes.

It appears probable that severe stresses may be thrown upon the parts of a floor, whether placed at the level of the bottom booms or of the top, by changes of length in the booms due to stress. The author has, unfortunately, no direct evidence to offer in reference to this, tending either for or against the contention. If an unplated floor of cross and longitudinal girders of usual arrangement be at the bottom boom of a large bridge, as the boom lengthens with the imposition of load upon the bridge, all the cross-girders from the centre towards the abutments will be curved horizontally, the middle portion being restrained by the longitudinals from moving bodily with the ends. Each cross-girder except that at the centre, if there be one, will thus present a figure in plan, concave towards the abutment to which it is nearest. This will be accompanied by stressing of the connections, and a transfer to the longitudinals of as much of the tensile stress properly belonging to the booms as the stiffness of the cross-girders may communicate.

This in itself will hardly be considerable, and will be the less on account of a slight yielding which may be expected at the end connections of each longitudinal; but the effect upon the cross-girders by horizontal bending will be much marked. If the case be supposed of a 200-feet span in steel at ordinary loads and stresses, carrying one line of way, with cross-girders 20 feet apart, and having no floor-plates, it may be ascertained, neglecting for the moment any slight yielding of the longitudinal girder connections, that upon the bridge taking its full live load there will be the following approximate results: Movement at each end of the end cross-girders of ³⁄₁₀ inch, equivalent to a force of 7¹⁄₂ tons, tending to bend them horizontally, and a mean stress on the outer edges of the girders, 12 inches wide, of 8 tons per square inch due to flexure, which, compounded with the ordinary flange stresses, will seem to give rather alarming results. There will also be a longitudinal stress in the rail-girders, at centre part of bridge, of ³⁄₄ ton per square inch. Normal elongation of the longitudinal girder bottom flanges, and compression of the top, modifies the figures unfavourably as to the cross-girder top flange. Yielding of the connections named before has been neglected in arriving at these stresses. If they are sufficiently accommodating to give freely, to a mean extent, as between the top and bottom of each joint, of ¹⁄₂₉ inch, these results will disappear. It is evident, however, that we cannot rely upon good work yielding without the existence of considerable forces to cause it. In the issue it is justifiable to apprehend that the flexing and stressing of the cross-girders will be considerable.

The most favourable case has been taken; if now it is assumed that the floor has continuous plating, the results would seem to be much more astonishing. It will appear on this supposition that the boom stresses, instead of being taken wholly by the booms, are about equally divided between these and the floor structure, each cross-girder connection communicating its share of boom stress to the floor, which for the end cross-girders will approach 40 tons at each connection—considerably more than the vertical reaction under normal loads.

Palpably, these conclusions must be greatly modified by the yield of longitudinal girder ends, and slip of the floor rivets in transverse seams. If these rivets be 3¹⁄₂ inch pitch and ³⁄₄ inch in diameter, the stress at each, as estimated, would be sufficient to induce shear of about 6 tons per square inch—more than enough to cause “slip.” After making this allowance, it is still evident there must be very serious forces at work about the ends of cross-girders under the conditions supposed, probably not less than one half the amounts named, as with this reduction the floor rivets should not yield, given reasonably good work. It is to be observed that the effect of live load only has been introduced, on the presumption that the longitudinals and floor-plating have not been riveted up till the main girders have been allowed to carry the major part of the dead load; but even this cannot always be conceded. The deduction appears to be that the floor and cross-girder connections should be studied with special reference to these possible effects, either with the object of rendering the communication of these forces harmless, or making the floor so that it shall take little or no stress from the main booms, by arranging joints across the floor specially designed to yield, the ends of longitudinals being schemed with the same object. Where there is no plating, the case is, perhaps, sufficiently provided for by making the cross-girders narrow, and the longitudinal girder connections flexible, or by putting these girders upon the top of the cross-girders, when stretching of the bottom flanges of the rail-bearers under load may be expected, within a little, to keep pace with the lengthening of the main booms.

It would appear that light pressed troughs running across the longitudinals would, by yielding in every section, also furnish relief, as compared with the rigidity of flat plates.

By placing the floor at a level corresponding to the neutral axis of the main girders, the communication of stress to the floor may be avoided; but it seldom happens that there is so free a choice as to floor height relative to the girders. This solution is, therefore, of limited application.

It is obvious that somewhat similar effects must obtain to those considered in detail, when the floor structure lies at the level of top booms, but with forces of compression from the booms to deal with, instead of tension.