the only difference being that the vane is absent, and P is a fixture in R and cannot turn. The circular disc of course faces west.
It is needless to say that these gauges were not expected to give very accurate records of the wind pressures which occurred since they were put up, but they give a sufficiently approximate idea of what the structure will hereafter have to encounter in the way of wind.
Upon one occasion the small fixed board appeared to register 65 lb. to the square foot, a registration which caused no little alarm and anxiety. Mr. Baker, however, declined to accept the figures recorded, and on investigation found that, with the lever multiplication-pointer, it was not difficult to obtain high figures, owing to the lever acquiring momentum from a suddenly applied force such as a strong gust of wind would produce, thereby overshooting the mark. Thus a blow of about 20 lb. applied smartly to the gauge would register 65 lb., and would probably have registered more but that the pointer could go no further. This occurred in January, 1884, and since then the recording apparatus has been altered, the horizontal lever being done away with, and a vertical bar—suspended directly from the wire of the gauge—being substituted.
Since then the highest pressures recorded have only been 35 lb., 41 lb., and 27 lb. respectively.
A gale on March 31, 1886, gave the following results:—
| Upon the small fixed gauge | 31 | lb. to the sq. ft. |
| Upon the„ revolving gauge„ | 26 | lb. to the sq. ft.„ |
| In the centre of the large board | 28½ | lb. to the sq. ft.„ |
| In the„ upper corner of the large board„ | 22 | lb. to the sq. ft.„ |
| All over the large board | 19 | lb. to the sq. ft.„ |
These figures seem to indicate that the higher wind pressures come more in gusts and sudden squalls than in a steady and even pressure extending over a large area.
After the central towers had been carried up to the full height, two additional revolving gauges—one at the north-east and one at the south-west corner of each tower—were put up and records taken and compared with those given by the other gauges. The records confirm most distinctly the results of the smaller gauges inserted upon the large board—for the pressures recorded vary as much as 10 lb. and 12 lb. between the different piers—sometimes the one, sometimes the other, showing the higher registration.
Experiments on Wind Stresses.
The scanty information existing on the very important subject of the action of wind pressure on the surfaces of structures, whether flat or curved, induced Mr. Baker to make a series of experiments, upon the results of which it would be possible to form some definite conclusions. These experiments are so interesting, and the appliances by which they were obtained were so ingenious, that no apology is needed for their repetition here. Realising the difficulty of working with models in actual wind, which is never, so to speak, of the same intensity or direction for two consecutive moments, and labouring under the disadvantage of not having an instrument which would reliably indicate the actual pressure at any time, Mr. Baker simply reversed the order of things by making the wind stationary and the apparatus movable. The latter then consisted of a light wooden rod, suspended in the middle, so as to balance correctly, by a string from the ceiling. At one end of the rod was attached a cardboard model of the surface the resistance of which was to be tested, be it a portion of a round tube, a flattened strut, a piece of top member, or of the internal viaduct, or even of a whole cantilever. On the opposite end of the rod was placed a sheet of cardboard facing the same way as the model, so arranged that by means of another and adjustable sheet, which could slide in and out of the first, the surface at that end could be increased or decreased at the will of the operator.
The mode of working this contrivance is for a person to pull it from its perpendicular position towards himself, and then gently release it, being careful to allow both ends to go together. If this is properly done, it is evident that the rod will in swinging retain a position parallel to its original position, supposing that the model at one end and the cardboard frame at the other end are balanced as to weight, and that the two surfaces exposed to the air pressure coming against it in swinging are exactly alike. Should one area be greater than the other, the model or the cardboard sheet, whichever it may be, will be lagging behind, and twist the string. By now increasing or diminishing the area of the cardboard sheet and repeating the experiment over and over again, a point will be reached when the whole mass will swing without twisting being produced. The area of the cardboard will then represent the exact area of the model which is affected by wind pressure.
The experiments carried on in various ways by different people and at different times are generally in agreement with each other, and not very different from those arrived at by scientists with most complicated apparatus, and by laborious and painstaking processes.
The points on which reliable information was more particularly wanted were in respect of surfaces more or less sheltered by those immediately in front of them. In the case of any box lattice girder, for instance, assuming that the wind was blowing fully square at it, it might also be assumed that the side nearest the wind would cover the side of the girder lying behind; but if the wind blows at an angle to the girder, it is certain that the second surface receives its proportion of full pressure of the wind; and in cases where two lattice box girders are close together—as, for instance, in the top member—all four surfaces will receive a proportionate amount of wind pressure.
It may easily be understood that the distance from each other of these surfaces has a great deal to do with the amount of wind stress they receive, and it was with a view of obtaining some useful data with regard to this question that Mr. Baker's experiments were carried out.
Information exists about flat surfaces and curved surfaces, and also about cubes—that is, two or more sides of any rectangular box or girder upon which the wind acts in a more or less diagonal direction. In all these Mr. Baker's experiments agreed with those of other observers, and obtained with different apparatus; but in the case of sheltered surfaces the results were somewhat different. On the whole, however, Mr. Baker satisfied himself that in no case was the area affected by the wind in any girder which had two or more surfaces exposed more than 1.8 times the area of the surface directly fronting the wind. As the calculations have been made for twice this area, the stresses which the structure will receive from this cause will be in all cases less than those provided for.
Mr. Baker also tested models of girders built of metal, both in air and in water, and although some slight differences with the former result were found, yet on the whole they fully confirmed the general conclusions arrived at.
The observations now made on the completed structure will no doubt help to throw further light on this subject of great importance to engineers, since in large structures the wind stresses are of considerably greater moment than the train loads, and should therefore, for economical considerations, be reduced to the narrowest limits compatible with absolute safety.
General Description of the Structure.
(See Plate III., Figs. 1 to 29).
From the general view of the bridge in profile it will be seen that it consists of two approach viaducts and of the cantilever bridge proper. The viaducts only differ in extent; the height above water and the lengths of the spans being the same. It will also be seen that a similar viaduct which forms the railroad or permanent way is carried through the cantilevers and central towers at one uniform level.
Commencing at the south end there are four granite masonry arches which terminate in the abutment for the South Approach Viaduct. Here the girder-spans commence—10 in number—the end of the last being supported in the south cantilever end pier. On the north shore there are three similar masonry arches, terminating in an abutment, and five girder-spans to the north cantilever end pier.
The bridge proper consists of three double cantilevers and two central connecting girders. Each double cantilever consists of a central tower supported on four circular masonry piers—a cantilever projecting from each side of it. The two outside piers the—Fife and Queensferry—have, in addition to the four supports of their central towers, a further support, inasmuch as their outer cantilevers rest in the cantilever end piers. No such additional support was available in the case of the Inchgarvie pier, and the length of the base has here been nearly doubled. The reasons for this are given further on.
The length of the cantilever bridge is 5,330 ft., consisting of the central tower on Inchgarvie, 260 ft.; the Fife and Queensferry central towers, 145 ft. each; the two central connecting girders, 350 ft. each; and six cantilevers of 680 ft. each. The cantilever end piers are apart 5,349 ft. 6 in. from centre to centre. The South Approach Viaduct is 1,978 ft. long from centre of cantilever end pier to end of arches, consisting of ten spans of 168 feet each; four arches of 66 ft. each centre to centre, and 34 ft. made up by abutments. The North Approach Viaduct is 968 ft. 3½ in. long to end of arches, consisting of five spans of 168 ft. long; three arches of 37 ft., 31 it., and 46 ft. centre to centre respectively, and 14 ft. 3 in. made up by abutments. The total length of the structure is therefore 8,295 ft. 9½ in. The two main spans are 1,710 ft. from centre to centre of vertical columns, made up of two cantilevers of 680 ft. each, and one central girder 350 ft.
The waterway to be crossed is about 5,700 ft., extending from the south circular piers on Fife to Viaduct Pier No. 3 at Queensferry. The rail level has been fixed at 157 ft. above high water, which leaves for a total length of 500 ft. in the centre of each channel a clear headway of 151 ft., no train load being on the bridge. The ordinary load of two trains is not expected to diminish this headway by more than about 3½ in.
The Fife and Queensferry Piers are alike and identical in every respect, and only reversed with regard to their outer cantilevers. All six cantilevers are the same in length—namely, 680 ft. from centre of vertical columns to centre of endpost—and are also of the same height and width, namely, 330 ft. high at the central towers, by 120 ft. wide at bottom, and 33 ft. wide at top, and 34 ft. high at the endposts, with a width of 32 ft. at bottom and 22 ft. at top. The only difference in the cantilevers lies in the arrangements of the endposts, and further in the fact that the two outside or fixed cantilevers of Fife and Queensferry are somewhat heavier in construction than the others. Each cantilever consists of a bottom member, or compression member, and a top member, or tension member—these being braced together vertically by six pairs of cross-bracings on each side, and being closed at one end by the vertical columns, at the other end by endposts. The space occupied by each pair of side-bracings is termed a bay, of which there are six in each cantilever. The bottom members are connected together by twelve sets of horizontal diagonal bracings intersecting in centre line, and further by the trestles and cross-girders, which carry the internal viaduct. The side bracings connecting top and bottom members consist each of a strut or compression member and a tie or tension member intersecting one another, and being connected at the intersections by strong gusset-plates and other stiffening. Each pair of opposite struts is connected by diagonal wind-bracings both above and below the internal viaduct, and by a cross-girder at top between the top members. From the intersection of struts and ties in the sides of the cantilevers, lattice girders, called vertical ties, are carried downwards and attached to the bottom members, relieving the latter of deflection between the junctions. Cross-sections of the cantilevers at each pair of struts and each pair of vertical ties are given in Plate III., Figs. 11 to 29.
Each central tower is formed of four columns, each column resting on a circular granite pier. Transversely all these piers are 120 ft. from centre to centre, or 60 ft. on each side of the centre line of the bridge. Longitudinally these piers are 155 ft. apart from centre to centre in the Fife and Queensferry Piers, and 270 ft. in the Inchgarvie Pier. It follows that the central tower on Inchgarvie is much heavier in construction and different in several features from the other two.
All the circular granite piers are carried to a height of 18 ft. above high water, and the height between the centres of bottom members and top members is 330 ft., measured vertically, which gives an extreme height of the central towers above high water of 361 ft.
The vertical columns—so called for distinction—are vertical only in one sense; that is, when looking broadside on. In the other sense, looking along the centre line of the bridge, they have an inclination of about 1 in 7, being apart, centre to
