centre, 120 ft. at bottom and 33 ft. at top. This batter of the vertical columns is maintained throughout the cantilever bridge. It had been intended to so arrange the sides of the cantilevers that the batter of 1 in 7½ in the central towers should gradually decrease until a vertical position was attained in the endposts and the central girders; but this plan would have led to considerable complications in the junctions both in top and bottom members, and in the intersection of struts and ties, and would have produced a twisted top member.
There can be no doubt that the arrangement of a uniform batter throughout the structure adds materially to its appearance, by giving it harmonious and simple lines, and heightens the impression of stability and resistance to lateral wind pressure.
The investigations and experiments made by Mr. Baker, and extending over several years, have led to the decision that all members under compressive stress should be of tubular form—circular by preference where admissible—this form being the strongest, weight for weight. This rule is, for structural reasons, only departed from in the struts of Bay 6 of the cantilevers and in the struts and top member of the central girders. All members under tensile stress are open lattice girders.
Thus the bottom members-the vertical columns and the struts in cantilevers are always under compression and are tubular in form, while the top members, the inclined ties in cantilevers and vertical ties are invariably in tension, and are of open lattice-girder form. The diagonal struts in the central towers again, although always in compression from dead load or wind pressure, receive an alternate tensile or compressive stress, and vice versa, according to the direction from which the live load or train load enters on the pier. In a similar way the diagonal wind bracings between bottom members, the vertical columns and inclined struts in cantilevers, are exposed to varying stresses according to the direction of the wind, and they are likewise affected to some degree by the position of the sun.
In order to preserve balance so far as dead load is concerned, it became necessary to load the ends of the outer or fixed cantilevers to the extent of half the weight of a central girder. To this end the endposts of these cantilevers are formed in a large box built of plates and filled with dead weight to the required extent. Thus far then the conditions would be alike for all six cantilevers in the state of rest, and in the absence of wind pressure and train load. Any introduction of the latter would at once disturb the balance, and, therefore, additional weight was placed in the ends of the fixed cantilevers large enough to counterbalance any possible train load which is likely to pass over the opposite end and leave a couple of hundred tons to the good. Under these circumstances the ends of the free cantilevers in the Fife and Queensferry Piers cannot deflect except in so far as deflection is due to the elasticity of the steel. On the other hand the fixed end will receive a downward pressure of, in the case of the maximum, the weight of the counterpoise, plus the maximum train load, and in the case of the minimum, the weight of the counterpoise minus the maximum train load, and of course any number of loads varying between the two. It will thus be seen how changeable are the conditions of load in the cantilevers, and the stresses upon the different members.
In the central or Inchgarvie Pier the conditions are different. There the weight of half a central girder is carried at each end, and so far as dead load is concerned the balance is absolute. But every ton of train load introduced from either end will upset this balance at once, and it was therefore essential to provide for every contingency. The worst condition that can be assumed would be for two trains to meet in the central girder at one end. The tendency would then be to form a fulcrum of the two nearest circular granite piers and lift the structure off the two furthest piers. As it was not intended that the anchorage in these piers, that is the holding-down bolts, should ever be brought into play except under the most improbable conditions of hurricane pressure, it was necessary to make the base of the central towers so great that the contingency stated above could not possibly arise. It is for these reasons that the central tower of the Inchgarvie pier has so much longer a base than either the Fife or Queensferry.
The four vertical columns are combined together and are braced in various ways. Longitudinally they are connected at bottom by the horizontal portions of the bottom members, and at top by those of the top members, both of these being carried through in unbroken section. The four corners of the rectangle thus formed are connected by a pair of diagonal struts intersecting each other at the centre.
In order to facilitate the intersection these struts—and for similar reasons the struts in the cantilevers—are flattened throughout on both sides, and at the points of intersection are considerably stiffened and almost doubled in the plates. At this point a horizontal bracing girder is carried across and attached to the vertical columns on either side. In the case of the central tower on Inchgarvie, owing to the greater distance between the piers, the top and bottom members cannot be carried for the whole distance without deflection, and a vertical tie is therefore brought down from the intersection of the diagonal struts and attached to the bottom member, while a vertical supporting column is carried up from the same point to take up the deflection in the top member.
In the lateral sense at the base of the columns there are two horizontal bracing girders and one pair (in the case of Inchgarvie two pairs) of horizontal diagonal bracing girders of great strength and stiffness, thus forming with the horizontal bottom members a very rigid framework immediately over the circular masonry piers. A similar double set of cross-bracings though of much lighter section is placed at the level of the intersection of the diagonal struts, thus bringing these points into direct connection with the four vertical columns half way up the towers. Between the vertical columns are placed four sets of vertical cross-bracings, the lowest of which also assist in carrying the internal viaduct at these points, and horizontal bracings at top between the top members. A similar bracing is placed between top members at the top of the central supporting columns and the vertical central ties on Inchgarvie above described.
All these members combined together form a tower of immense strength and weight, well able to take up and resist the enormous stresses resulting from the combined influences of dead load, live load, and wind pressure upon the tower itself and upon the cantilevers projecting from it. All these stresses, however, must ultimately resolve themselves in those portions immediately resting on the circular masonry piers, which are called the skewbacks or main junctions. These junctions are the gathering points of five tubular and five latticed girders, and as their construction will be described in detail further on, it is only necessary to mention here that they terminate at foot in a flat plate called the upper bedplate, which is so arranged that it rests on, and, in some cases, can slide or move on another bedplate, the lower bedplate, which is fixed to the masonry pier.
The functions of these bedplates in resisting and yet partially yielding to the wind-pressure and in taking up the expansions and contractions in the central towers are of so important a nature that they have received a very large amount of care and thought on the part of the engineers. The difficulties were avoided in the original design of Messrs. Fowler and Baker, and were consequent upon the modifications introduced by the other consulting engineers.
It had been the intention originally to make the skewbacks an absolute fixture upon the piers, after having given an initial compressive stress to the horizontal tubes between the piers, also to clothe these tubes inside and outside with some non-conducting material which would practically neutralise the effects of heat or cold upon them. On reconsideration, however, it was decided to only fix one skewback out of the four comprised in each pier, and to allow the other three to yield to a limited and well-defined degree to the influences of temperature, and to the lateral deflections produced in the cantilevers by wind pressure, and to some degree also by the heat of the sun. It suffices for the moment to say that, for various reasons, the south-east pier on Fife, the north-east pier on Inchgarvie, and the north-east pier on Queensferry, were chosen as the fixed points. The arrangements of the bedplates, and the reasons for these arrangements, will be stated further on in connection with the provisions made for expansion and contraction in the main spans, and for distortions produced by wind pressures.
It will be noticed that the bottom member in the cantilevers is not arched or curved, but polygonal in form, each portion from junction to junction being a straight line and passing into the next portion with a nick or kink. Apart from the fact that a piece of straight tube is stronger than a bent one, some consideration was given to the manufacture of the plates for these tubes. Had they been curved, nearly every plate on the circumference would have had to be shaped in a different die a difficulty still more increased by the decreasing diameter of the tube from 12 ft. at the skewback to 6 ½ ft. at the end of the fourth bay, after which the member becomes gradually rectangular in form.
The top member, being always in tension, is straight from the top of the vertical columns to the top of the endpost which closes the cantilever. It is carried uninterruptedly through all the junctions with struts and ties, though its cross section decreases gradually towards the point of the cantilever.
The central connecting girder consists of a top compression member, polygonal in form, and a straight bottom or tension member, with eight sets of vertical cross-bracings to each side, consisting of struts and ties, the struts being, as in the cantilevers, provided with diagonal wind-bracings. The top members are also connected by sixteen sets of diagonal horizontal wind-bracings. From the points of intersection of struts and ties a vertical lattice tie is brought down to carry the bottom member midway between junctions. The bottom members are connected by solid plate girders going right across these carrying the rail troughs; and they are further stiffened by diagonal T bracings and by the solid floor of buckle plates.
The internal viaduct which carries the permanent way of a double line of rails and a footpath on each side, consists in the main of two lattice girders, set 16 ft. apart, centre to centre, and of varying depth, according to the length of span. Both top and bottom booms are trough-shaped, the top booms receiving the longitudinal sleeper and rails. A cross-bearing girder occurs about every 11 ft., and upon this are laid the two inner rail-troughs, leaving the 6-ft. way between them.
The main girders differ in their construction from those in the approach viaducts, in so far as they have vertical struts and diagonal ties. They are also continuous and without break from the end of one cantilever through the central tower to the end of the other cantilever.
A footpath about 4 ft. 6 in. wide on the outside of each outer rail-trough is carried on brackets attached to gussets both to the top and bottom booms of the main girders. The footpaths are formed by buckle plates, and buckle plates are also fixed between the rail-troughs and in the 6-ft. way, thus making up a very stiff flooring. The bottom booms of the main girders are connected by horizontal cross-bracings.
It may be as well to mention that the footpaths are to be used only by the railway officials. The trains are intended to be run over the bridge at full speed, and it would be neither convenient nor safe to admit the general public.
The girders of the internal viaduct are carried between the vertical columns (and in the case of the Inchgarvie pier between the central vertical ties) by a plate-girder reaching right across, and by vertical supports carried upwards from the intersection of the first pair of vertical wind-bracings between columns. The same mode of supporting the viaduct is adopted at the centres of the first and second bays in cantilever, while at the ends of the first, second, and third bays, as also at the centre of tho third bay, trestles, supported by the bottom members, are arranged. At the centre of the fourth bay a cross-girder carries the viaduct girders, and after this, the bottom member closely approaching the line of the viaduct, similar cross girders; are used with short vertical supports. In bays five and six the girders are absent, and the rail trough, stiffer in section, are there carried by cross-girders and by the diagonal wind-bracings alternately.
In the central connecting girders the rail troughs, as already mentioned, are carried by solid plate-girders about every 22 ft.
To each side of the internal viaduct a wind fence 4 ft. 6 in. high, and of lattice construction, is carried from end to end of the bridge, and on the approach viaducts.
The viaduct girders and rail troughs are rigidly fixed to the cantilevers, and form an essential part of the latter, adding considerably to the stiffness laterally of the bottom members. The only breaks
