'UTn^: THE FORTH BRIDGE BT B. BAKER RKAD AT THE BRITISH ASSOCIATION MONTREAL 1884 JSonbon : PRINTED AT THE BEDFORD PRESS ao A ai, BEDFORDBUBY, W.C. 1884 l * '1 ■ ' » i» H^> iiii. •.. THE FORTH BRIDGE BY B. BAKER READ AT THE BRITISH ASSOCIATION MONTREAL 1884 IConbon : PRINTED AT THE BEDFORD TRESS 20 & 21, BEDFORDBURY, W.C 1884 %2l THE FOETH BRIDGE. Two years ago I read a paper on the proposed Forth Bridge at the Southampton meeting of the British x\ssociation. Until the other day I had not since glanced at the paper, and a re-perusal was in many respects suggestive ; for during the past two years the works have progressed, and some of the theories advanced in the first paper have been put to the test of actual practice. In one respect the re-perusal was a painful one, for the opening sentence contained a reference to Sir William Siemens, and I was reminded of the loss of a friend who took the greatest interest in the Forth Bridge, and whose vast experience and matured judgment could always be drawn upon in times of doubt or difficulty. Taking up the narrative of the proceedings from the date of my last paper, I may state, in the first place, that five tenders were submitted for the con- struction and erection of the bridge, the amounts varying from £1,487,000 to £2,301,760, and that the contract was finally let to Messrs. Tancred, Arrol, and Co., on the 21st of December, 1882, for THE FORTH BRIDGE. £1,000,000, which was within £5000 of the esti- mated cost of the work as prepared by Mr. Fowler and myself for Parliamentary purposes. The total length of viaduct Included in this con- tract is about 1^ miles, and there are : 2 spans of 1700 ft. each 2 „ G75 „ 15 „ 168 „ 5 „ 25 „ Including piers there is thus almost exactly one mile of main spans, and half a mile of viaduct approach. The clear headway under the centre of the bridge is 1 50 ft. above high water, and the highest part of the bridge is 3G1 ft. above the same datum. Each of the three main })iers consists of a group of four cylindrical masonry and concrete piers, 49 ft. in diameter at the top and from GO ft. to 70 ft. in dia- meter at the bottom. The deepest pier is about 70 ft. below low water, and the rise of tide is 18 ft. at ordinary springs. In the piers there are about 120,000 cube yards of masonry, and in the super- structure about 45,000 tons of steel. Operations were commenced in January, 1883, so the works have now been some twenty months in progress, and about 170,000/. have been expended in plant and temporary works and 200,000/. in the permanent works of the bridge. At South Queens- ferry an area of about 20 acres of ground has been laid out in shops and yards for the manufacture of the 1700 ft. span steel girders .?nd for other purposes. These shops are in direct communica- THE FORTH BRIDGE. tion with the North British Railway, and are con- nected by an incline and winding engine with a temporary timber viaduct 2200 ft. in length and 50 ft. in width, extending from the South Queens- ferry shore to the first of the groups of four cylin- drical iron caissons which constitute the lower por- tions of the main piers of the bridge. At Inch Garvic stores and offices have been built, and as this Ih an exposed island in the middle of the Forth the staging for the pierwork is of iron pinned to the rock. Similarly at North Queensferry, on the Fife side of the Forth, stores, offices, and iron staging- have been erected. The state of the works at the present time is as follows : PIERS. South Queenfifevry Main Piers. — One of the 70 ft. diameter caissons has been sunk to a depth of 16 ft. below low water, a second is in position, and the two others are advanced to the required extent to follow on. Inch Garvie Main Piers. — One of the piers is practically complete, another is well advanced, and the pneumatic caissons for the other two are being constructed. Fife Main Piers. — Three of the piers are built and the remaining one is in progress. Cantilever End Piers.— One of these piers is carried to a height of 66 ft. above high water, and the other to a height of G ft. above X.ovv waie^v THE FORTH BRIDGE. Viaduct Piers. — Eleven out of the total number of thirteen piers are built up to the height at which it is proposed to erect the girders in the first in- stance before final raising into position by hydraulic jacks. SUPERSTRUCTURE. About tons of st-jel have been delivered for the 1700 ft. spans. The first portion to be erected will be that over the Fife Main Piers, and the bed-plates, skew-backs, and 12 ft. diameter tubes for this work are well advanced. A further quantity of tons of steel girder work for the approach viaduct is now in course of erection. PLANT. The plant includes 1 4 steam barges, launches, and other vessels; 22 steam, 12 hydraulic, and 38 hand- power cranes ; 28 single and double engines for shop machines, hydraulic work, air- compressing, electric lighting, pumping, and other purposes ; also gas furnaces for heating the steel plates, a 2000 ton hydraulic press for bending them, and planing machines, nmltiple drills, hydraulic rivetters, and other specially designed tools too numerous to men- tion. Having reference to the novelty and mag- nitude of the work and the amount of preliminary preparations required, it may be considered that fair progress has been made during the past twenty months. THE FORTH BRIDGE. No special difficulties were encountered in founding the viaduct piers, notwithstanding their exposed position. Except in two cases the piers rest on the rock, and they were executed in half- tide or whole tide cofferdams, which call for no special remark. The cofferdam for the south canti- lever end pier was necessarily a very substantial structure, being a quarter of a mile from the shore. It measured 126 ft. by 75 ft. over all, and had a double row of whole timber piles, with 4 ft. of puddle between, and internal struts, chain cable ties, and external raking struts and piles of great strength and solidity. A highly satisfactory bottom on boulder clay of rock-like hardness was found at a depth of 35 ft. below high water. The masonry of the viaduct piers and cantilever end piers consists of an Aberdeen granite facing, averaging a little over 2 ft. in thickness of rock-faced work, backed up with cement concrete or with rubble masonry set in cement, and bonded, about every 12 ft. in height, with courses of large stones carried across the entire area of the piers. The main piers have on the whole, perhaps, given more trouble than was anticipated. On the Fife shore the whinstone rock brttom falls with a rapid slope of about 1^ to 1 to deep water, and it was necessary to step this slope for the masonry. Diamond drills worked from an iron stage were employed for the subaqueous blasting ; but the removal of the rock proved a most tedious affair, and a substantial timber THE FORTH BRIDGE. and clay cofferdam had, after all, to be constructed for one of the piers. With some trouble, the other pier was built within a makeshift half-tide dam, made up partly of the OOft. diameter permanent iron caisson below low water, with a temporary iron caisson attached to it, the whole made tight to the rock as far as might be with concrete and clay filled in between the caisson and a few buckle plates. At Inch Garvie similar delay and trouble were experienced in carrying out the shallow piers. Some of the work could only proceed at low water of spring tides, and it generally happened to blow hard just at that long waited-for moment. Tidal work, and even half-tide work, are proverbially slow and worrying ; but we were all de- termined that, as the rock varied in quality, no foun- dation should be put in until the bottom had been laid dry. By perseverance and patience this has hitherto been accomplished, and we have the satis- faction of knowing that both the rock foundation and masonry are unexceptionable in strength and solidity. In our shallow rock foundations at the Forth we had nmch the same problem to deal with as Stephenson encountered, thirty years ago, when building the tine bridge across the St. Lawrence at this city, and our contractors dealt with it in much the same way. I am not concerned to defend the oj)erations, as such details are usually left to those responsible, namely the contractors. Where speed is required, I am satisfied that in most cases pneumatic appliances ofiier incomparable advantages THE FORTH BRIDGE. over cofterdani work on a rock bottom. French contractors generally resort to pneumatic caissons of ordinary type in depths exceeding 15 ft., but have employed, with great advantage, modifications known as the caisson -hatardeau, the hateau-plon- gcur, &c., in depths as little as 6 ft. The six weeks required to build a pier with the aid of pneumatic appliances may often be taken up in stopping the leaks of a cofferdam on rock bottom. English contractors are not much accustomed to pneumatic appliances, other than an ordinary diving dress, and rarely resort to them. A diving-bell with shaft of access and air lock was provided and mounted on traveller complete at the Forth, and compressed air drills were fitted in the working chamber, but no use has hitherto been made of the apparatus. The lower part of the South Queensferry main pier consists, as already stated, of a group of four pneumatic caissons 70 ft. in diameter. In the con- tract the option was allowed of sinking open-topped caissons by dredging inside, but, after experiencing the extreme hardness of the boulder clay, we were all agreed that it would be i)referable to resort to the pneumatic process. Owing to the slope of the clay the four caissons will be sunk to varying depths, ranging from 6b ft. to 88 ft. below high water. The caissons, which were built on shore, launched and floated into position, are 70 ft. in diameter at the cutting edge, and taper I in 4G to facilitate sinking. At 1 ft. above low water, which is the top of the 10 THE FORTH BRIDGE. permanent caisson and commencement of the granite- faced masonry, the diameter is 60 ft. A working chamber 7 ft. high is provided at the bottom of the caisson, the roof of which is sujjportcd by four strong lattice girders 18 ft. deep, and cross girders 3 ft. deep spaced 4 ft. apart. An internal skin 7 ft. distant from the external skin, and vertical diaphragms, form pockets which can be filled with concrete at any point where, owing to the slope of the ground and the varying hardness of the silt and clay, a heavier pressure is desired to force down the caisson. Three shafts, 3 ft. in. in diameter, with air locks at the top, pipes for admitting water and ejecting silt, and other of the usual appliances, are provided. The air locks for passing out the clay and boulders as designed by Mr. Arrol and myself have, instead of the usual hinged doors, two sliding doors like horizontal sluice valves, across the 3 ft. G in. shafts, which are worked by little hydraulic rams, or by hand, and arc interlocked like railway points and signals, so that one slide cannot be opened until the other is closed. Mounted on the side of the air lock is a steam engine which, by means of a shaft passing through a stuffing-box in the side of the air lock and a drum inside, winds up the excavated material in skips containing one cubic yard. The operation of hoisting, opening slides, and discharg- ing, is raj)idly performed, so the two locks have a large working capacity. A third air lock, with side doors, ladder, and hoist, is also provided for the men. THE FORTH BRIDGE. 11 The air-compressing' plant consists of three engines with 16^ in. diameter by 24 in. stroke s^Pim and air cylinders, ample power being furnished by boilers of the locomotive type erected on the staging. Reference has already been made to the two shallow piers at Inch Garvie, but there are also two deep piers which, being on a very irregular and sloping rock bottom, have required much consideration. It was finally decided to level a bed roughly with bags of sand, and to float out pneumatic caissons, and excavate the rock until a level bed was cut. Pro- bably Mr. Fowler and I would not have adopted this precise plan if we had been contracting, although we might have resorted to the pneumatic process, but as M. Coisseau, a contractor of great experience in such work, offered to sub-contract for the sinking of the caissons at fair rates, we did not object. These caissons are 70 ft. in diameter at the bottom, and the rock slopes from 14 ft. to 19 ft. in that length, the lowest point being 75 ft. below high water. All of the pneumatic caissons will bo filled with concrete up to low-water mark, the mixture being 27 cube feet of broken whinstone, 7 cube feet of sand, and 5| cube feet of cement, which together make a full yard of concrete, having a crushing resistance of about 50 tons i)er square foot. Above low water the cylindrical piers, which are 49 ft. in diameter at the top, 55 ft. .at the bottom, and 36 ft. high, consists of the strongest masonry, the hearting being flat-bedded Arbroath stone with 12 THE FORTH BRIDGE. both horizontal and vertical bond, and the facing Aberdeen granite, the whole set in two to one cement mortar, and built in the dry within tem- porary wrought-iron caissons. In the shallow piers where the rock is stepped the masonry is carried down to the rock itself, and wrought-iron hoops 36 in. by 1^ in. bind the bases of the piers. At the top of all the piers 18 in. by 1^ in. hoops, and midway down 18 in. by | in. hoops, are also built in, and it is believed that these cylindrical masses of masonry are as completely monolithic as can be attained or desired. In each cylindrical pier there are forty-eight steel bolts 2^ in. in diameter and 24 ft, long to hold down the bed-plates and super- structure of the main spans. A few words now as to the manufacture of the superstructure. About 42 miles of plates have to be bent for the tubular compression members, and the best method of doing this became a question of great practical importance. Bending cold did not answer, as the true curvatures could not be so attained. Theoretically, a 10,000 ton hydraulic press would be required to bend, truly, our 16 ft. by 1^ in. thick steel plates, and practically a 2000 ton press was of no use. Heated in a gas furnace, the plates bent readily, but distorted considerably and irregularly in cooling. Covering with ashes, packing up, and a variety of expedients were tried before the proper method was hit upon, which was to bend the plates hot and to THE FORTH BRIDGE. 13 give them a straightening squeeze afterwards when cold. Uniform heating is secured by admitting the gas near the door and mid-way along the furnace, and an important incidental advantage of the use of tubular compression member.; thus is that every plate gets relieved from any internal strains which may have been setup by shearing or improper usage at the steel works, which is of the greater moment as steel having the comparatively high tensile strength of 34 to 37 tons per square inch is used for the com- pression members. Some alarm was occasioned at the works by certain 1^ in. thick plates breaking like cast iron on being bent cold to the flat radius of 6 ft. I felt certain, however, that the Landore steel was not at fault, as our inspectors test a shearing from every plate by bending it round a radius of 1^ in. after being made red hot and cooled in water. On investigation I traced the cause of the fracture in the local damage the plates received from shearing. What the damage consists in is an unsolved riddle. It cannot extend more than ^^ in. from the edge, because planing to that extent re- lieves the plate and yet it affects the entire width, for the 4 ft. 6 in. plate snapped as readily as the 1 in. wide strip sheared from it. Neither can it arise from " nicking" by bad shearing, because making the plates red-hot cures the evil, though the "nicking," if previously existent, remains as visible as ever. Practically, the important point of 14 THE FORTH BRIDGE. interest to bridge buildci'.s is that with planed edges and drilled holes we have had no mysterious fractures, but the Foitli Bridge plates have behaved as a material having as the higher limit a tensile strength of 37 tons per square inch and an elonga- tion of 17 per cent, in 8 in. should behave. Our specification for steel in compression is 34 tons to 37 tons with an elongation of 17 per cent., and for steel in tension 30 tons to 33 tons with 20 per cent, elongation. The strength rarely varies as widely as the stated limits, and the elongation averages some 3 per cent. more. One of the plates which fractured from sheared edges when bent cold was tested by me in a variety of ways. A specimen made red-hot and cooled in water at 80 deg. stood 38.3 tons per square inch and elongated 21 per cent. Another specimen made hot and allowed to cool in air stood 36.6 tons and also elongated 21 per cent., whilst one planed from the plate direct with- out heating failed with 34.3 tons, but extended 25 per cent. For practical purposes, therefore, it mattered little how the plate was treated, provided the effect of the shearing was eliminated by planing or by heating. When bent, the plates are planed at the edges in the usual way, and at the curved ends by a specially designed radial machine. They are then, with the internal stiffeners, temporarily built into a tube round a mandrel, and drilled through plates, covers, and bars at one operation. Four specially-designed rilE FORTH BRIDGE. 16 annular drill frames, surrounding the tubes, and fur- nished each with ten traversing drills, capable of attacking every hole, travel along lines of railway in the building yards, so laid out that four lengths of tube, each of about 400 ft., can, if desired, be dealt with at once. In a IG ft. length of 12 ft. diameter tube there are about IGOO holes to drill through from 2^ in. to 3^ in. thickness of steel, which operation takes about 52 hours' working of the drills. Con- tinuous working is, of course, not possible, as the machine has to be advanced every 8 ft., which is the shift of the butts in the plating of the large tubes. Over the piers the arched tubular lower member forms a connection with the upper bed-plates, the vertical and diagonal tubes, and the lateral and vertical cross bracing, so that considerable thought had to be given to the details at this point. A full- sized model was prepared, and different modes of arranging the junctions were set out and modelled. Finally it was decided to gradually change the tubular lower member into a box form with one rounded upper corner, where it meets the skewback or part over the pier, and by internal vertical and horizontal diaphragms, to make the latter a cellular structure of enormous strength and stifthess, offering facilities for attachments in any required direction. Several layers of plates form the bottom of this skewback, and constitute what may be termed the ** upper bed-plate" of 16 THE FORTH BRIDGE. the bridge. The " lower bed-plate" consists of similar layers of plates rivetted together and bolted to the pier ; and the two bed-plates are free to slide on each other within certain limits to be referred to more particularly hereaftor. The layers of plates run longitudinally and transversely, to meet the different stresses ; and, after the edges are planed, the plates are fitted together, clamped between girders, and drilled by special machines through their whole thickness. About 1000 lineal feet of l^ in. holes have to be drilled in each bed-plate, which in practice with the 8 -drill machine, takes about eighteen days, including stoppages. In the upper bed-plates holes about 1 1 in. square, with corners rounded to a 3 in. radius, are required, in some instances, to clear the nuts of the holding-down bolts, and these are cut readily by a simple tool devised by Mr. Arrol. In other cases, 12 ft. diameter recesses, 2 in. deep, have to be bored for what may be termed a huge key or dowel, which will connect the upper and lower bed- plates, but allow a slight rotation ; and this also requires a speoial tool. The tension members and cross bracing generally consist of box lattice girders which are drilled by travelling machines of similar type to those already referred to in connection with the tubular members. All of the rivets are of steel, having a tensile strength of about 27 tons, an elongation of aboul 30 per cent., and a shearing resistance of from 22 tons to 24 tons per square inch. It is hardly THE FORTH BRIDGE. 17 necessary to state that, hydraulic rivetting will be used throughout. The nuts and washers of the holding-down bolts and some other parts are of cast steel, having a tensile strength of 30 tons per square inch, and an elongation of 8 to 10 per cent. It may be interesting to mention that the con- tractors have used steel in preference to iron in some parts of the temporary works, and that at their request the 168 ft. span viaduct approach girders were changed from iron to steel with a view to save expense. The two years' additional consideration given to this bridge since the date of my first paper, has led to no modifications of importance in the design, or in the weight of steel required for the construction, a satis- factory result which is largely due to the care and ability of my colleague Mr. Allan Stewart, who has had charge of the detailed calculations and designs from the inception of the undertaking. Originally the cantilevers had a varying batter towards each other from 1 in 7^ at the piers to vertical at the ends, where they meet the central girder. We have now made the central girders slope inwards and maintained the batter of 1 in 7^ throughout, thus getting rid of the previous " winding" which some- what complicated the details of the cantilever, and at the same time preserving and emphasising the pyramidal form of cross-section characteristic of the design. In models of the bridge a feeling of great solidity results from this feature, as will be the case 18 THE FORTH BRIDGE. no doubt in the bridge itself, of which a geome- trical elevation necessarily gives but a poor idea. We have also modified the attachment of the superstructure to the piers. Formerly the inten- tion was to put an initial stress upon the 12 ft tubes between the double piers as described in my first paper, ant! vj bolt the superstructure rigidly to the masonry. Now we secure the superstruc- ture to one only of the four cylindrical piers in each group by the great circular key already re- ferred to, and permit a certain amount of sliding on the others. Owing to the enormous size of the structure elastic deformations which may be neg- lected in ordinary cases have to be provided for. A veTj great deal of consideration has been given to this important point, and the calculations have neces- sarily been complex and tedious, but we think we have now made the best disposition attainable to resist all possible and improbable hurricanes striking the bridge locally or throughout the whole span, and all variations of temperature likely to be met with at the Forth. The question of clothing the tubes between the piers with some non-conducting material will be left for future settlement after the movements under changes of temperature have been registered by the tube itself. Fortunately we are not troubled with Canadian variations of temperature and the correspon- dingly great changes of form in metallic structures. At the new Clyde Viaduct in a length of 37G ft., the THE FORTH BRIDGE. 19 observed annual range is 2 in., or a fraction over half an inch in the 100 ft., and this is an open lattice con- struction, whilst the Forth Bridge horizontal members between the piers are closed tubes. Obviously during the early stages of erection, before much weight comes on the bed-plates, the tube will be practically free to expand and contract. Ultimately, when the whole weight of the completed structure rests on the piers, the friction between the two surfaces of the upper and lower bed-plates will probably be sufficient to prevent movement except under extremes of tem- perature and heavy wind pressure of rare occurrence. The attachment of the superstructure to the piers par- takes thus of the character of a safety friction clutch. Movement will not occur under ordinary circum- stances, and if an excessive shock from some unfore- seen cause arise on the superstructure, it san only be transmitted to the masonry of the })ier through the sliding surface of the upper and lower bed-plates. Should a wave of deflection from the impact of a tornado pass along the great cantilever, as some critics suggest, then it would be arrested by skidding as an express train is arrested, and not by running into a buffer stop. Provision is made for lubricating the surfaces, and as the result of experiments made by myself during the past two years, probably some crude petroleum will be applied to the bed-plates every time paint is applied to the rest of the bridge. Calculations have been made of the extent of sliding 20 THE FORTH BRIDGE. and of the stresses on the piers under the twisting action of a hurricane blowing on one cantilever, whilst the balancing cantilever is in a dead calm, and various coefficients of friction have been assumed. During erection sliding can, if desired, be made prac- tically free by carrying one cantilever further out than the balancing one, and so relieving two out of the four bed-plates of weight. In the completed bridge the position of the bed-plates could be ad- justed by temporarily loading the end of a cantilever. Experiments on friction vary considerably, but when such large surfaces as 2200 square feet, which is the joint area of the four bed-plates of each main pier, are concerned, there would no doubt be an equalising effect which would make the proper coefficient of friction for the bed-plates approximate to the mean of the results obtained with a number of experiments on small areas. The coefficients obtained by Morin for iron on iron greased ranged from .09 to .115, and with the grease wiped off, .16 to .19, the pressure being about 27 tons per square foot, or considerably greater than that on the Forth Bridge bed-plates. On a large scale, the mean values of coefficients for different surfaces are derivable from launching WFys of ships, brake ex- periments, and other data. In launching ways the coefficient must be singularly small, for with de- clivities of ^ in. to 1 in. in the foot, ships not only start, but acquire a velocity of ten miles an hour or more very quickly. In some of Mr. Denny's THE FORTH BRIDGE. 21 experiments it would appear that even with this flat slope the velocity acquired was fully half that which a body would attain falling freely, so the retarding friction during motion must be very small. Again, the coefficient of friction at starting could not exceed .OG, but of course in ordinary launching ways the pressure per square foot and the character of the surfaces are different to those in the Forth Bridge, though the total weight of the moving mass may be the same, and the facts are worth mentioning on that account. Brunei's broadside launch of the Great Eastern in 1857 affords, however, valuable data directly applicable to our sliding bed-plates, for the weight of the ship was 12,000 tons, and the launching ways were iron on iron somewhat rough on the surface, and imper- fectly lubricated or not lubricated at all. As a result of experiments with a small section of the launching ways, the inclination was made 1 in 12, as it was thought a small force would then start the ship, and a similar force restrain it from acquiring undue velocity, the observed coefficients of friction ranging from .125 at starting to .067 at moderate velocities. On commencing the launch an estimated force of about 500 tons was required to assist gravity on the 1 in 12 incline, hence the starting co- efficient with the 12,000 ton load would be about .125 as in the model. Again, when started, the 1 in 12 was more than sufficient, for the vessel ran on some 3 or 4 ft., and, spinning round the 22 THE FORTH BRIDGE. handles of the winches, injured five men. Subse- quently, however, owing to want of rigidity in the ways, rusting of the rails, or some other disturbing cause, considerable trouble was experienced, and successive additions had to be made to the hydraulic presses during the three months occupied in the launch. For the last 30 or 40 ft. Brunei estimated the power required, inclusive of gravity, at one quarter of the weight, or double that which started the ship at the top of the launching ways. Railway trains are not as heavy as ships, but afford valuable data as to the coefficient of friction of steel on steel under severe pressures, such as must obtain at the point of contact of the tyre with the rail. Captain Galton's experiments show that the coefficient varies widely with the speed and other elements, being sometimes as little as .05. With dry rails the adhesion of the driving wheels indicates a coefficient of about .20 to .25, and with wet rails, .15 to .20. Probably with "greasy" rails it would not exceed the .10 arrived at by Morin fifty years ago as an average. Calculations of the stresses on the piers have been made upon the hypothesis that coefficients of .10 and .25 obtain on different bed-plates at the same moment in the manner most unfavourable to the structure. A variety of other assumptions and test calculations have been made. As a final result we are of opinion that the maximum stress on the masonry of the main piers will be something be- THE FORTH BRIDGE. 23 tween 9 tons and 12 tons per square foot. To attempt a closer approximation would only serve to advertise our incapacity to appreciate the complex character of the problem and the uncertainty of some of the data. So far as compression is concerned, our con- crete, which has a crushing resistance of 50 tons per square foot, would thus give a factor of safety of at least four. The solid Arbroath stone piers are, of course, of far greater strength both as regaids compression and the shearing and possibly tensile stresses to which the piers may be subject under the extreme hypotheses made as to force and distribution of wind. Very valuable data as to the ability of a massive rubble pier in cement to resist a heavy lateral force were afforded by the experimental arch of 124 ft. span and 7 ft. rise built in Paris some fifteen years ago. The thrust of the arch was about 1400 tons, and, treating the abutment as an elastic solid, the stress upon the masonry would range from 14.7 tons com- pression to 8.7 tons tension per square foot. To ascertain the ability of cement concrete to resist heavy shearing and tensile forces I tested a number of con- crete beams having different proportions of cement. Such concrete as that used at the Forth developed a tensile strength under transverse stress of about 10 to 12 tons per square foot, so that it was from no in- herent weakness in the concrete that masonry was substituted for it in the 36 ft. upper length of the main piers. Our reason for its adoption was that we 24 THE FORTH BRIDGE. believed by using natural flat-bedded Arbroath stone set in two to one cement mortar, with both hori- zontal and vertical bond, we made certain of obtain- ing practically a monolith, whilst with concrete, however careful the inspection, there might be cleavage plaiios of perhaps dangerous extent in places. The special stresses on the piers arising from the cantilever system of construction have received, as I have already said, our most close consideration, and we doubt not that the desired factor of safety of four will be obtained as regards all shearing, tensile, and compressive stresses to which the masonry may be conceived to be liable under any reasonable hypothesis which can be framed. Happily, we are relieved from all anxiety as to the foundations, since the piers rest either on rock or on a boulder clay, which for all practical purposes is as hard as rock. It may be mentioned, however, that the heaviest load at the base of any of the 70 ft. diameter caissons, including the tilting action of a 5G lb. per square foot wind, is about 24,000 tons, or at the average rate of a little over six tons per square foot, deducting nothing for the water displaced by the pier. As it is impossible to produce the working drawings of the bridge on the present occasion, a short tabular statement of some of the leading fea- tures may be desirable. Steel in main cantilevers ... ... 40,000 tons. „ centre girders ... ... ... 1,000 „ „ viaduct approach ... ... 2,800 „ THE FORTH BRIDGE. 25 Cantilevers — 680 ft. projectior ; 343 ft. and 40 ft. deep. Bottom Member of Cantilever, a pair of tapering tubes : Diatance apart centres at piers ... 120 feet. „ „ „ ends ... 31.5 „ Tube at piers, 1 2 ft. diameter, 1 \ in. thick, 830 sq. in. area. „ ends, 5 ft, „ fin. thick, 120 sq. in. „ Top Member of Cantilever, a pair of tapering box lattice girders : Distance apart centres at piers ... 33 feet. „ „ „ ends ... 22.25 „ Girder at piers, 12 ft. x 10 ft. ... 50G sq. in. net area. „ end, 5ft. x 3 ft. ... 60 Columns over Piers, 12 ft. diameter, 368 to 468 sq. in. area. Diayonal Struts (tubes), 8 ft. to 3 ft. diameter, 198 to 73 sq. in. area, and 337 ft. to 74 ft. long, Diayonal Ties {\iox\a.tiice), 8 ft. to 3 ft. deep, 163 to 67 sq. in. not area, and 327 ft. to 82 ft. long. Horizontal Wind Braciny (box lattice), 11 ft. to 3.5 ft. deep, 88 to 20 sq. in. area, 142 ft. to 40 ft. long. Vertical Wind Braciny (box lattice), 4.75 ft. to 2.5 ft. deep, 84 to 28 sq. in. area, 160 ft. co 60 ft. long. Central Girder, 350 ft. span, 51 ft, and 41 ft. deep ; bottom members, 32 fe;!t apart centres, 142 sq. in. net area ; top members, 22.25 ft. and 19 ft. centres, 139 sq. in. gross area. Internal Viaduct, lattice girders with spans of 39 ft. to 145 ft Floor, buckle plates and trough girders. Wind Fence, close lattice work 4 ft. 6 in. high. Viaduct Approach, lattice girders, under rails continuous over two 168 ft. openings, 22,5 ft, deep, 16 ft. apart; floor and wind screen as for internal viaduct. Masonry piers 25 ft. x 8 ft. at top, and 50 ft. x 20 ft. at base. Rolling Load: (1) trains of unlimited length on each line of rails, weighing one ton per foot run ; (2) trains on each line made up of two engines and tenders, weighing in all 142 tons, at the head of a train of 60 short coal trucks of 15 tons each. Wind. A pressure of 56 lb. per square foot, striking the whole or any part of the bridge at any angle with the 26 THE FORTH BRIDGE. horizon, and acting square or obliquely upon an area equivalent to twice the plane surface of the front girders, with a deduction of 50 per cent, in the case of tubes. The total wind pressure so derived amounts to 2000 tons on the 1700 ft. span, and 7900 tons on the whole superstructure included between the two cantilever end piers. The following table shows the magnitude and intensity of the heaviest resultant stresses in tons on some of the principal members from dead load, live load, and wind, distributed as already described : Bottom member Top „ ... Vertical „ Diagonal struts . . . „ ties Hor. wind bracing Ver. „ „ Central girder top „ ,, bottom Deau. Live. Wind. Total, i Gross Stress. Stress per sq. in. Gross Stress. Stress per sq. in. 51 Stress per sq. bi. II 7.5 2282 2.8 1022 1.2 2920 3.5 6224 1 2253 4.4 997 2.0 j 544 1.1 3794 7.5 1550 3.3 705 1.5 1024 2.2 3279 7.0 802, 4.1 167 0.8 414 2.1 1383 7.0 754 4.6 186 1.2 194 1.2!ll34 7.0 80 0.9 5 .1 265 3.0 350 4.0 42 0.5 169 2.0 108 1.3; 319 3.8 337 2.4 303 2.2 182 1.4 822 6.0 330 2.3 301 2.1 247 1.8 878 1 6.2 Owing to the batter of 1 in 7\ of the main gir- ders and the adoption of double piers, not merely at Inch Garvie, but for the main piers on either side of it, the calculation of stresses involves some interest- ing and complicated problems. It is fortunate that from the nature of the ground no unequal settlement can occur in the foundations or some of the stresses THE FORTH BRIDGE. 27 would be indeterminate by reason of the double piers which, I may add, were not a feature of the original design. At the centre cantilevers any unequal loading is supported by the double bracing between the piers at Inch Garvie, but at the north and south canti- levers, the support is twofold, namely, the resistance of the bracing, and the pull on the holditig-down bolts at the cantilever end pier. The first problem that arose, therefore, was to ascertain how much of the load would be supported by each of these reactions. But the weight of each part was not known, and in a structure of this magnitude, it required to be ascertained with accuracy. This could only be done by the method of trial and error, and as the stresses produced by the weight of the structure itself are very considerable, and as the secondary bracing is an important item, detailed drawings had to bo made and carefully measured several times before the stresses could be determined. The inward slope of the cantilever gave rise to forces of sensible amount from the component of the vertical forces square to the plane of the cantilevers. A much more diflficult problem, however, was presented by the stresses produced by wind. Thus, for example, a force acting horizontally on the cantilever near the 350 ft. girder, and at right angles to it, pro- duces at the main pier a downward pressure on the leeward side, and an upward action on the windward side, together with a twisting action. 28 THE FORTH BRIDGE. and vertical and lateral pressures on the cantilever end pier. All these forces had to be traced through the diiferent members and bracings, and the same had to be done for a wind force acting as a moving load at every point of the cantilever. It was also essential to consider the wind as blowing not only at right angles to the line of the bridge, but also at such other angle as would impose on each member the greatest amount of stress. By a reference to the diagram it will be seen that the stresses produced by wind are very severe, and, therefore, exactness was required in order that no part might be unnecessarily heavy, nor on the other hand be strained beyond the allowed amount. After all the stresses as a framework structure arising from the dead load, a travel- ling train, and from wind had been ascertained, a new set of problems arose, chiefly from the magni- tude of the work, and the weights of the difl^erent members themselves which cause local stresses of considerable importance in some instances. An all-important point was, of course, the stress per square inch admissible upon the several tension and compression members. The only limit practically imposed upon us by the Board of Trade was that the stress should not exceed one-fourth of the ultimate strength of the steel without reference to the question of the relative proportions of live and dead load, or the character of the stress. In settling the sectional areas we did not bind our- THE FORTH BRIDGE, 29 selves to any formula derived from Wohler's or other experiments on the fatigue of metals, but con- sidered each member separately and had reference to the whole of the circumstances, including the character of the rivetting and other details of con- struction. As many competent engineers are of opinion that the rational way of proportioning structures is to assume varying ultimate resistances of the metal for different proportions of dead and live load, and adopt an uniform factor of safety of 3, we tested the actual areas of the Forth Bridge members by the following rules, and found in all cases an excess on the requirements : a. For a constant load assume the ultimate tensile strength to be 30 tons per square inch. h. For a load varying from nil to a maximum assume the strength to be 20 tons per square inch if the alternation of stress is frequent, and 22.5 tons if it is seldom, as in the case of a hurricane, c. For alternate tension and compression as- sume the ultimate strength to be 10 tons if frequent and 15 tons if seldom. The above apply to tension members and are to be divided by 3 for the working stress. For struts the working stress equivalent to the above, from the results of my own experiments and from other considerations, I take to be 40 per cent, of the stress causing first flexure, as given by the following empirical formulae : 30 THE FORTH BRIDGE. /=(.44-.002 r) (< + 18) for tubes . /=(.40-.004 r) (<+ 18) for lattice where r = ratio of length to diameter and < = tons per square inch, as set forth in paragraphs a, b, and c, but increased in all cases in the ratio of 34 to 30, which are the specified minimum strengths of the steel used for compression and tension members respectively. I have no doubt that any structure proportioned by the above rules would have an ample margin of safety, but as already stated the stresses in the case of the Forth Bridge are lower than indicated. The diagram of stresses shows that the lower tubular member is the most affected by wind, and, in fact, under the conditions assumed the leeward tube does the work and the windward is almost relieved of stress. Looking at the huge 12 -ft. tubes as they now lie at the Forth Bridge works, with their ten longitudinal T bars 12 in. x 7 in. x f in., having double angles rivetted to the web of tlie T, and with annular stiffeners every 8 ft., certainly nothing could appear better adapted to resist stress and fatigue, and I should not feel the least anxiety if they were subject to double the stress which will ever be imposed upon them. I may add that the preceding formula for struts is based upon my ex- periments with steel ranging from 26 to 56 tons in tensile strength, and fairly represents the average results, though in this instance, as in all others where columns are concerned, individual experiments differ rather widely, owing to initial stress, unequal bear- THE FORTH BRIDGE. 31 ing, or other cause. In proportioning the rivetted joints of the tubes and other members, the shear- ing area is generally made one and a half times the net sectional area of the plates connected if in tension, and half that for planed and butted joints in compression only. In my first paper I said that the maximum wind pressure upon the 1700 ft. span had been assumed to be equivalent to a pressure of 56 lb. per square foot upon the double surface, and I regretted that such assumption necessarily involved many matters of pure conjecture, which rendered it impossible to state with precision what factor of safety would belong to the Forth Bridge. The same remark of course applies even now with equal force to every other bridge, because there exists a lamentable lack of data respecting the actual pressure of the wind on large structures. Mr. Fowler and I have spared no pains during the past two years to contribute some- thing to the general fund of information ; and other engineers, doubtless, are experimenting, — for experi- ments, and not speculations, are wanted. We have had now for two years, on the island in the middle of the Forth near the centre pier of the bridge, three wind gauges or pressure boards; the large one, 300 square ft. in area, is fixed square to the east and west winds, and of the two small ones of 1^ square ft. area, one is fixed as above, and the other is free to swivel square to the wind in any direction. When speaking at the 32 THE FORTH BRIDGE. Institution of Civil Engineers on the subject of wind pressure, previous to the erection of these gauges, I ventured to prophesy that, contrary to the opinion of many, the large board would show a smaller ave- rage pressure per square foot than the small ones. I have summarised the readings of the gauges for the past two years, and find them to fairly bear out my anticipations. In preparing the following table, the mean of all the readings of the revolving gauge between and 5 lb., 5 lb. and 10 lb., &c., have been taken, and the mean of the corresponding readings at the same time of the small fixed gauge and of the large fixed gauge for easterly and westerly winds have been set forth opposite. Revolving Gauge. Small Fixed Gauge. Large Fixed Gauge. Mean PresHure. Easterly. Westerly. Easterly. 1 Westerly, 1 lb. lb. Oto 5 3.09 lb. 3.47 lb. 2.92 lb. 2.04 lb. 1.9 5 to 10 7.58 4.8 7.7 3.54 4.75 10 to 16 12.4 6.27 13.2 4.55 8.26 15 to 20 17.06 7.4 17.9 5.6 12.66 20 to 25 21.0 12.25 22.75 8.6 19 25 to 30 27.0 28.6 18.25 30 to 36 32.5 38.6 21.5 Above 66 41.0 36.25 (One observation only above 32.5.) I do not myself, nor does Mr. Fowler, place im- plicit faith in the registrations of our own or anybody else's anemometers, although we test the working of the gauges in the most careful manner, THE FORTH BRIDGE. 33 but at the same time I think it is pretty well established by our two years' experiments, that the effective pressure per square foot on a large and comparatively heavy board averages only about two-thirds of that indicated by an ordinary light anemometer. It will also be noticed that the heaviest gales have been from the west, and that the revolving gauge then indicated much the same as the fixed gauge. Some critics were of opinion that our 300 ft. gauge would be of little use, as it could not swivel square to the wind, but remembering the experiments made with a fan blast on oblique plates which showed that the resultant pressure was normal to the surface, I felt sure that having reference to the pi'evailing winds swivelling was of no practical importance at the Forth, and the results justified my anticipations. The two heaviest gales occurred in the early morn- ing of December 12th, 1883, and January 26th, 1884, respectively. On the latter occasion much damage was done throughout the country, and there was conclusive evidence from the extent as well as the intensity of the storm, that it was a very exceptional one in character. At Inch Garvie the small fixed gauge was reported to us as registering 65 lb. per square foot, but on inspection I found the index pointer could not traverse further or it might, perhaps, have indicated much higher. At Valencia very strong squalls covering short periods were stated to have attained a rate of upwards of 150 34 THE FORTH BRIDGE. miles per hour. At Holyhead lengthened squalls of 120 miles and short squalls of higher rates were reported. At Alnwick we were told that several instances of 10 miles in five minutes, or 120 miles an hour, and squalls of 150 miles occurred. Now if we assume, as is common, the pressure of wind to be equal to .005 V^, and accept the velocity of 150 miles as correct, we shall have to believe that pressures of 112 lb. per square foot were reached at Valencia on the west coast of Ireland, and at Alnwick on the east coast of England, on the 26th of January last. I confess I find it much easier to believe that the records of anemometers as at present obtained are utterly misleading and value- less for all practical purposes. I entirely mistrusted our own G5 lb. record, even before I knew that the index was at the end of its travel. On finding out the latter fact, however, I experimented with the gauge, and finally in the presence of the inspecting officers of the Board of Trade, made it register 65 lb. by the sudden application of a pressure not exceeding 20 lb. The momentum of the light index needle, and not that of the pressure plate which was bridled back, sufficed to cause the error. I look upon the record of 65 lb., therefore, as valueless so far as regards the specific maximum pressure attained during the great storm, but of considerable value as evidence that the highest pressure, whatever it might have been, partook of the character of a smart jerk of too instantaneous THE FORTH BRIDGE. 35 duration to affect a structure of any size or weight. From the records generally and from my own watch- ing of the movements of the three gauges, I have come to the conclusion that uniform velocity and pressure in a wind, whether it may prevail or not at cloud heights, can never obtain near the surface of the earth or in the neighbourhood of any bridge or other structure capable of causing eddies. Un- steady motion must be the rule in air as in water, and the threads of the currents moving at the highest velocity will strike an obstruction succes- sively rather than simultaneously, so that the mean pressure per S(j[uaro foot on a largo area must be less than that on a small surface from that cause alone, irrespective of possible differences in the partial vacuum at the back of the planes. In the spring of this year, when running into Dublin Harbour during a heavy broadside gale, I took occasion, when in still water but in the full blast of the wind, to measure the heel of the vessel and from her elements to calculate subsequently the mean pressure rc(|uired. My pressure board in this case was about GOOO square feet in area, and the de- duced mean pressure was 12 lb. per square foot. From other data I estimated the corrosj)onding anemometer pressure at fully double the preceding amount, and this was perfectly rational because the vessel kept steady at the constant heel, whilst heavy local gusts of very small area struck different parts of her in a distinctly recognisable manner. 36 THE FORTH BRIDGE. In short, the large area and heavy mass of the hull equalised the jerky action of the numerous small blasts of high intensity, and a similar action doubt- less takes effect in ordinary railway structures, and will to a still greater extent in such a large and heavy structure as the Forth Bridge. Mr. Fowler and I are of opinion, therefore, as a result of our two years' further consideration, that the assumed pressure of 56 lb. per square foot over the whole of the bridge is considerably in excess of anything likely to be realised. It is another question whether the method of estimating the effective area exposed by the bridge, namely, double the plane surface with a deduction of 50 per cent, in the case of tubes, is right or wrong. We think it is a sufficiently near approximation to the truth, for reasons which I will briefly set forth. As all engineers well know, one of the results of the panic caused by the fall of the Tay Bridge was the appointment by the Board of Trade of a Com- mittee to consider the question of wind pressure on railway structures, wliich Committee advised the adoption of certain rules. Shortly stated i/hese were : (1) That a maximum wind pressure of 56 lb. per square foot should be provided for. (2) That the effective surface upon which the wind takes effect should be assumed at from once to twice the front surface according to the extent of the open- ings in the lattice girders. (3) That a factor of safety of 4 for the ironwork, and of 2 for the whole THE FORTH BRIDGE. 37 bridge overturning as a mass when gravity alone comes in, should bo adopted. In the case of the Forth bridge we took, with the approval of the Board of Trade, the highest ratio for the surface, namely, twice ; but I must admit that I had not at the time the slightest idea whether the twice ought not to be thrice and even more, and the recommendations of the Committee did not assist me, as they were founded on no special experiments, and did not accord with my own experience so far as it then extended. Under these circumstances the necessity of further experiments was clearly indicated, and we have made them. The tension members and the bracing of the Forth bridge, as already explained, are lattice box girders and the main compression members are tubes. Thus, in the case of the top tension members near the piers, we have the front surface of the girder witli channel bars and projecting flanges, making it essen- tially different to the flat anemometer plate, and three corresponding surfaces, situated respectively about 7 ft., 33 ft., and 40 ft. to the rear of the front surface. In the case of the tubes we have the tube itself, then a couple of box lattice cross braces, with channel bar members, and finally another tube. No theory exists which could enable us to estimate even ap- proximately the equivalent flat surface of such a network ; and I felt until my scheme of experhnent by models was realised with satisfactory results, that our calculation of stresses from wind pressure 38 THE FORTH BRIDGE. rested on anything but a logical basis. The problem to be solved was how far the eddies caused by the front surface affected the surfaces to the rear. In the recommendation of the "Wind Committee" a front plate girder was considered to give complete shelter to any girders to the rear of it, but I think anyone who has walked " Indian file " in a gale of wind will have noticed that unless he locked up pretty closely to the front man he felt practically the full force of the gale, and similarly unless the rear plate girders of a bridge be relatively close to the front girder the latter will not afford anything like complete shelter. It is obvious, therefore, that the depth of the girders, and the distance apart enter into the problem, as well as the question of their being plate or lattice ; and I may add further that the position and character of the floor between the girders also materially affect the wind stresses. My original idea was to prepare models and test them in actual wind at Inch Garvie, but the irregularity of the results, even with the flat boards, precluded the possibility of any useful data being so obtained. I determined, therefore, to abandon the attempt to measure actual resistances, but to arrive at the same end by getting the equivalent area in flat surface of the diflerent bridge members and cross bracing, and for this purpose devised a very simple pendulum arrangement, consisting in eftect of a cross bar with a model at one end and an ad- justable flat surface at the other of exactly equal THE FORTH BRIDGE. 39 weight, which bar was suspended at the centre, so that the only resistance to turning was the torsion of the suspending string. On oscillating this pendulum, if the flat surface were not the exact equivalent in resistance of the model, one or the other would advance, and the sensitiveness was such that different observers would rarely vary more than 3 or 4 per cent, in their results. To test the sufficiency of this simple apparatus I contrasted the resistances of thin flat surfaces and cubes, and my results agreed within 2 or 3 per cent, of those obtained in the most elaborate manner by Dubuat many years ago. Similarly, the results obtained with cyliadrical surfaces and inclined planes were in strict accord with those obtained by previous observers and other apparatus. When experimenting with sheltered surfaces, however, my results differed considerably from previous experi- mental ones, which I must say are singularly few in number, having reference to the vast importance of the subject to engineers. Thus, according to Thibault, the resistance of the rear plate of a pair set at a distance apart equal to the diameter is .7 of that of the front plate, whilst in my experiments I found no such excess until the distance apart was 3^ diameters. I experimented with discs placed at from 1 diameter to 4 diameters apart, and the resistance of the two discs in terms of that of the single one was in round numbers 1.0 for I diameter; 1.25 for 1^ diameters; 1.4 for 2 diameters ; l.G for 40 THE FORTH BRIDGE. 3 diameters ; and 1.8 for 4 diameters. An increased number of discs placed intermediately between the front and rear discs little affected the resistance. For example, by reducing the 4 diameters to 3.6 diameters, an extra disc could be introduced without increasing the resistance of 1.8, and by still further reducing the distance to 3.5 diameters 4 discs could be employed. This result is of great importance in its bearing on railway bridges where a succession of lattice bars may occur one behind the other, which would offer a very large surface to the wind if the proper way of estimating that surface were to take a slightly angular view of the bridge and measure up all that was visible. It has been already mentioned that in the " Wind Committee's" report no addition is made for shel- tered surfaces in the case of plate girders, whilst it might appear from the foregoing experiments that as much as 80 per cent, allowance should be made where the girders are four depths apart. This would, however, be a very fallacious deduction, for it omits all consideration of the floor of the bridge. Reasoning from the observed resistance of cubes it may be inferred that the resistance of a tubular girder, such as the Britannia Bridge, would be only 80 per cent, of that of a single flat girder, and clearly the floor of a girder bridge, if close plated, makes the conditions a[)})roximate to that of the tube. As a matter of fact I found that two plates connected by a floor plate at the bottom offered no more THE FORTH BRIDGE. 41 than 90 per cent, of the resistance of the single plate. Summarising my conclusions, for it is im- possible to give details here, I should say that the effective surface of a plate girder bridge would range from 90 per cent, to 180 per cent, of that of the front surface according to the distance apart of the girders, the degree of openness of the floor, and its position relative to the main girders. In many respects the preceding remarks apply to lattice girders, but the varying extent of the open spaces between the bars introduces an additional complication. When the openings were one-fourth of the whole area, I found for a distance of one diameter apart, an increased resistance of 8 per cent, from the second disc, whilst with openings of double the size, the increase was 30 per cent. At two diameters the respective amounts were 40 per cent, and 06 per cent., whilst at four diameters the more open lattice reached 94 per cent. In other experi- ments, sometimes with a small flat plate in front of a lattice, and sometimes in the rear, I obtained at four diameters distance resistance exactly equal to the sum of the two specimens tested separately. The top member of the Forth Bridge consists as I have said of a pair of box lattice girders, or as may be said equally truly, of four single-web lattice girders. Models of these single-web girders, tested in pairs, gave 20 per cent, increase from the rear girder when the distance apart was equal to the depth ; 50 per cent, for two depths ; 70 per cent, for three depths, 42 THE FORTH BRIDGE. and 80 per cent, for four depths. When three gir- ders were placed one behind the other, the middle girder gave rise to a further increase of about 4 per per cent, for three depths and for four depths ; in short it mattered practically little whether two, three, or four girders were used. Two models of a complete bay of the top member were made, one as light as possible and the other somewhat heavy. The re- sults were in accord, the resistance averaging 1.75 times that of the plane surface, whilst that of each of the lattice box girders tested separately was 1.15. As a factor of 2 instead of 1.75 was used in the wind calculations, the pressure on the lattice mem- bers has been somewhat over-estimated, but on the other hand that on some of the other members of the bridge, judging from the results of the experi- ments, has been somewhat underrated. The bottom member and the main struts of the bridge consist of a pair of tubes braced together by box lattice girders. I tested a complete bay of the bottom member, and found the resistance of the two tubes, placed seven diameters apart, together with the two box lattice braces, of a depth equal to the dia- meter of the tubes, to be 1.1 times that of the plane surface. Substituting plate girders for the lattice braces the ratio was still only 1.24, so the tube evidently acted as a sort of a cut water, and by clearing a path for the flat surfaces lessened their resistance. This was further proved by removing one of the tubes and testing the single tube and THE FORTH BRIDGE. 43 cross lattice bracing. Tube in front the resistance was but 80 per cent, of that obtained when the lattice was to the fore. The lattice bracing tested alone had a resistance equal to 00 per cent., whilst when in position between the two tubes, it only increased the resistance about 5 per cent. This perhaps was to me the most re-assuring of all the experiments because, looking at a complete model of the bridge, it appeared as if the intricate mass of cross bracing must offer an enormous resistance to the wind. As a matter of fact, so far as my experiments extend, it would seem that the eddies caused by the front surface extend to a great dis- tance in all directions, and in a complex structure the innumerable and conflicting eddies would almost appear to neutralise each other as regards some of the sheltered surfaces. On the other hand, in simple isolated structures, such as a pair of bars or tubes, the shelter is practically nil at distances equal to about six diameters, and the members might as well be abreast. This was well demon- strated in the experiments by arranging the models on the skew so as to imitate the eff'ect of a wind blowing at an angle to the horizon, when constant results were obtained with widely different angles. In the approach viaduct at the Forth the lattice girders are under the rails, and there is a wind fence on each side. Testing a model of this class of con- struction, I found that the resistance of the parapet and of the railway carriages was only two-thirds of 44 THE FORTH BRIDGE. the corresponding plane surface, a result due no doubt to the eddies thrown up by the girders. It would appear therefore that current estimates of the wind pressure required to overturn railway carriages on exposed viaducts should be further considered, for although an average carriage might overturn with a uniform pressure of 40 lb. per square foot, a 60-lb. wind may be necessary to produce the equivalent of that pressure. In our model of a pair of lattice girders with floor, wind fence, and railway carriage on the top, the total resistance was but 93 per cent. of that due to the plane surface. As by the present rules engineers would in such a case estimate the equivalent at about 150 per cent., it follows that in many recent and presumably future bridges the actual wind stresses may be considerably less than estimated. The leading constituent parts of the Forth Bridge were tested, as described, by models of single members and of comjjlete bays, but we proceeded a step further and tested both in air and in water a complete metallic model of two pairs of cantilevers with cross bracing, internal viaduct, and wind fence, together with the intermediate part over the Inch Garvie piers. The total resistance so ascertained was 9 per cent, greater than that obtained by calculation on the basis of taking double the plane surface with a deduction of 50 per cent, in respect of tubes. With the models of different parts tested separately the excess was 4 per cent. This THE FORTH BRIDGE. 46 excess would not apply to the moment of the wind pressure, because the highest parts of the bridge are lattice structures, the resistance of which was over- estimated. If a 56-lb. wind ever occurred as a mean over such an area as that we are dealing with, it would be something greater at the high level of the lattice top member and something less at the level of the bottom tubes. Personally, therefore, I am satisfied that the assumption originally made by ourselves and the Board of Trade officers was a sufficiently close ap- proximation to the truth for all practical purposes. I do not attach undue importance to the results obtained by the models, nor to the records of our large and small pressure boards at the Forth, but at the same time to me they have thrown a little day- light on many obscure questions respecting the actual wind pressure on railway bridges and other structures. Mr. Stewart and I would sometimes attempt to calculate the resistance of a model upon hypotheses of our own, and differ most widely in our results, as others who have attempted the same thing have generally done. A single swing of the long pendulum would solve all our doubts and diffi- culties. In arranging the experiments, I had re- gard to Froude's principles as to velocity relative to the scale of the models, and believe the eddies md interferences to be similar in kind in the models and bridge. Of course what is wanted is the measured resistance of actual bridges in actual 46 THE FORTH BRIDGE. storms, but this I have not yet been able to under- take. Such experiments as I have been able to make have at least served to show how little is known about wind stresses, and how necessary it is that every engineer should seize such opportunities as may offer for contributing something to the general store of information. Two years ago I said I should have preferred to have postponed any communication on the subject of the Forth Bridge to the British Association " until the many points of interest and difficulties insepa- rable from so gigantic an undertaking had manifested themselves." I am in much the same position now, for it will be gathered from the present paper that no real strain has yet been put upon the resources of the contractors, or the capacities of the executive officers. Two years hence I may, perhaps, have a more thrilling tale to tell. Much interest in the work has been evidenced by Continental and American engineers, and the criticism on the whole has not been unfavourable but appreciative. Occasionally it has been suggested that the appearance will not be as elegant as could be desired, but I retort, mentally, in Lord Bacon's words, " Houses are built to live in, and not to look on ; therefore let use be preferred before uniformity, except where both may be had." We aim at getting both, and our granite faced piers, with their simple but bold mouldings, certainly look better than cluster-columned metallic THE FORTH BRIDGE. 47 piers, however scientific. Thus far we have suc- ceeded in satisfying our masters, and very keen critics, the directors of the North Eastern, the Midland, the Great Northern, and North British Railways, and the officers of the Board of Trade both as regards the quality and appearance of the executed work. If I were to pretend that the designing and building of the Forth Bridge was not a source of present and future anxiety to all concerned, no engineer of experience would believe me. Neces- sarily, where no precedent exists, the successful engineer is he who makes the fewest mistakes. We cannot wait for precedents, and therefore as successive points of doubt or difficulty arise, we reason them out on the best data attainable, and then in the land of Burn's we act up to Burn's favourite motto, "On reason build resolve — That column of true majesty in man !" B. Baker. Montreal, September, 1884. Sli'cAseA- fhcm the LU'e Load alcme Maauniwi total •Vj'yy.v.yc.v ai LmMnni (ni,i,(v\, — Fort DIAGRAIVIS OF Gl ^^^jH^^^^j£;_y^2^ ScivU 200\ Scale VO.OOOt c ij/ruun Mai i)'U\.w*'.\'(>fi Wmiitvtini CanUlPAtr Forth Bridge — m OF GREATEST STRESSES ,^'a ^ ^OFe^-X to Vnc. hu^ Scal<. 20,000 Tom to Oru^ Jnehy i/tfi- id aloTte. rd/ CanUlpA'i'r' Ma.anuun toM .yf^,:s;s;:y .'// A^-m^/r/ ^W/A- tiSO QUEENSFERRY PlER. • 160 Ecxxxxy^r^if 2lPf^S^;^r'«f^r=^«^ UPPER TENSION MEMBER. J ^ -^i/-:^i ENLARGED CROSS SECTIONS BOTTOM COMPRESSION MEMBER. IF®m!FM B1,IjE)©]E SESS1():N 1882. 9 r ,. I JOHN FOWJ.ER.Jiiigiiieer iu Chief. gfiV ^rgXKXXXXX^, HIGH WATER ; :r:r> Inchgarvie Pier. •■WO 1 110 r - * \J f "'Wi:'*v*9 ' ^y^- '^ ELEV AT ION. ■^'^nX'/i w>VPV'^", '^^' h7--=f^=^lK^ TTOM COMPRESSION MEMBER. SECTIONAL PLAN AT RAIL LEVEL SchJ». Fnt * V y J^ I I I CROSS SECTION at CENTRE fSL -'■»»* - ^ [ ' Fife Pier. m , us 680 > ■ CROSS SECTION «t PIER law MilK tM"* KEII * «<'M 1 ITM *' KIN'l STHkri 'UVKNI