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DISCUSSION.

Mr. C. Bender. Responding to the kind invitation of the Canadian Society of Civil Engineers, the writer ventures to make some remarks regarding Mr. Findlay's paper on Cantilever Bridges.

The author agrees with the writer on many points, but on several others the views are much at variance.

In the first instance, the writer holds it to be of great importance that a clear idea should be had as to what a cantilever bridge really is, for this reason that a continuous bridge with hinges, and that other designs of the solitary beam, fixed with the minimum expense at its ends, and provided with an independent middle span of suitable length, are entirely different structures, and have to be designed for essentially different conditions. He at once excludes such bridges, which for the sake of one fixed span are provided with one or even two heavy outside spans over dry land. Such structures have no reason of existence, and are the more objectionable, as the entirely erroneous idea has crept in that it is economical to make long cantilevers, and consequently very great moments of flexure at the piers. If continous bridges must be built, there must be good reasons for making several spans, there must be deep water to be crossed.

Perhaps it will not be out of place to trace the scientific development of this class of bridges in general, which form the subject of Mr. Findlay's paper.

At the end of last century the French savant, Pierre Simon Girard, translated the theory of flexure, which the immortal Leonard Euler had given in 1744, and extended this theory, which to-day goes by the name of Navier, to the beam fixed at the ends. About 10 years later Poyet, in France, proposed what the writer termed stay-bridges, consisting of two pairs of masts, anchored back, and carrying the floor by inclined tension rods or stays, and compression-members abutting against each other at the feet of the masts. His idea was taken up in Germany, and in 1825 the first modern cantilever bridge was built over the Saale at Nienburg. The designer had already a tolerably clear understanding as to economy. The span was 240 feet in the clear; the wooden towers were 40 feet high, the anchorage bars were manifold, but inclined in the average at an angle of nearly 30 degrees. A short drawspan in the middle was added to accommodate the passage of

ships. The bottom chords were of wood, abutting against masonry; the stays were of iron. This bridge, however, had but a short life. It only cost 8,000 dollars, inclusive of abutment and anchorage arches, and though it stood its tests, for some unknown reason, though unloaded, it fell several months later. As a peculiarity of this structure, it may be mentioned that the suspension stays were kept in straight lines by a system of light distance pieces or struts, which in concentric lines intersected the stays and back-stays at nearly 90 degrees, in the same manner as was proposed for a similar design by Messrs. Flad and Pfeiffer in 1875, for the projected Blackwell's Island bridge in New York.

In 1865 C. de Bergue in England patented continuous girders with hinges, but properly speaking this patent was an extension of designs proposed by Joseph Langer in Austria. At that time so little attention was given to this novelty, that in 1866 it could be reinvented by the practical bridge engineer Gerber in Germany, and a year later by the writer in the United States.

In the year 1873 the writer had occasion to make estimates for an intended bridge over the Niagara river, and the idea struck him to utilize the cantilever principle of erection already proposed by Pope of New York, then by Telford in 1811, and executed by the Engineers of the St. Louis arch-bridge, by making the material necessary for such an erection a permanent and necessary part of the bridge. The arch should be very deep, hence broad at the base, and not wider at the top than necessary for the floor. The outcome was the writer's arch bridge with five hinges.

The design, however, is not simply a three-hinged arch set upon the ends of two cantilevers, but it is entirely different in principle from the cantilever bridge. It is a bridge with but one pair of chords, a real arch, but with five hinges. If the whole arch is uniformly loaded this bridge will act as a theoretically perfect arch. The two hinges between the crown and the abutments are so placed that they must be fixed in position, in such a way that in certain cases of loading the bridge they cannot move upwards or downwards. The unloaded bridge again is an arch, and has hardly any strains in the anchorages.

In order to prevent reversal of strains in the anchorages, so as to permit the use of tensile members instead of tie-struts, also to make the middle arch deeper, hence more economical for very large spans, the writer afterwards added the arrangements which Mr. Findlay mentions, consisting of the provision by which the protractions of the end

tangents of the middle arch pass sufficiently underneath the abutments of the whole arch.

For moderate spans, the arch is more in place where the question is to erect a deck-bridge. If a through bridge were intended, a difficulty would arise how to carry the wind strains from the arch above down to the floor below, and yet how to leave a way for the passage of trains. Arches being in an unstable equilibrium must be thoroughly braced together. This problem indeed arises with all through bridges, only that they have tensile chords on which stiff frames can be erected, holding the joint points of the top chords in position. However, not many through girder-bridges are at all properly braced transversely at their entrances. Such bridges, especially pin jointed structures, which not only have a smaller number of stiff members in their webs than rivetted lattice girders with stiff members throughout, and therefore should be fitted with especially stiff and carefully calculated ends, are frequently found, and are still constructed with loose suspenders instead of posts, entirely out of place where the tensile chords consist of eye bars. These loose hangers are nowhere more out of place than at the first panel points from the end-bearings of a bridge, and with the parsimoniously designed portals are among the causes why it is so easy to push such bridges from their piers.

All such bridges should be well provided with carefully designed endposts, which should be stiffly connected at their feet as well as above the open space for the passage of carriages.

Thus it is seen, and it is illustrated by the many accidents occurring to scantily braced through bridges, that it is not very easy in case of a small or a moderate span of through arch, to comply with these conditions of transverse stiffness against wind. In reality it would be necessary to build for every panel a thoroughly stiff frame which would hold the arch points above the floor in position, and would have to receive its basis from a couple of continuous chords in the plane of the floor, thoroughly braced to receive the whole windstrains. On this basis stiff frames or diaphragms would have to be erected to hold the joints of the arch in position.

But all these preparations combined with the abutment masonry would destroy the economy of the arch, so that only the erection on the cantilever principle would remain, and perhaps the graceful appearance of the design.

In the case of very great arches, however, the question of safe and scientific bracing is not offering any great difficulty, and for deck-arches there is none whatever.

The through cantilever bridge of Girardot, of 328 ft. span, designed in 1879, and the arch-bridge at Honda with five hinges designed in 1833, comply with the conditions of transverse stiffness against wind, and the manner in which these conditions are fulfilled is illustrated in the writer's book, kindly mentioned by Mr. Findlay. These two examples at the same time show how the writer thought a better appearance might be given to such structures, and, having discussed the conditions which limit the use of the arch bridge with five hinges, he returns to its merits as regards economy.

If engineers have an opportunity of utilizing the advantage offered by locality towards dispensing with tensile chords, by abutting curved top chords against firm rock or economical artificial abutments, or if a railway or a city bridge exceeds 250 feet in span, a considerable weight is not only entirely saved, but it no longer loads the bridge which at the same time receives a more graceful appearence.

For all these reasons the arch is very well adapted for spans of extraordinary lengths, and the only improvement necessary is to secure its easy erection.

By anchoring the two end-parts of the arch with five hinges backwards, just enough material is obtained to dispense with false works, and at the same time the moments of flexure of the arch under a onesided load are reduced to about one-half of what they would be in case of an arch with three hinges, so that again material, which otherwise would load the bridge, is removed from it, and it is utilized to make the anchorage which is thus obtained at no cost at all.

Up to spans of about 550 feet, single span bridges require the least quantity of material. For very large bridges, and where the locality permits it, for moderate spans also, arches are more economical. On account of the high strength (nearly 300,000 lbs. per square inch) and great lengths (in coils of one piece up to a hundred weight) of steel wire, now so cheap, and on account of the very great facility of erection, suspension bridges with suspended well braced stiffening girders, which we now know how to calculate and to proportion properly, compete with great arches.

Continuous girders with hinges, where in place, offer all the advantages claimed for the theoretical continuous girders without their disadvantages.

Cantilever bridges will remain only for localities where erection is difficult and where the arch with five hinges can not be applied. Extraordinary economy can hardly be claimed for them.

According to careful estimates of spans of 1,700 feet, the arch with five hinges was found to be about one half as heavy as the cantilever bridge.

A cantilever bridge, defined by the writer as the single span fixed at the ends, must be designed so that the span itself, plus its anchorages, contains a minimum of material. The quantity of material on the whole forms the basis for comparison, for admitted that eyebars cost more per ton than bars of equivalent strength obtained by adding pairs of joint plates rivetted to them, there remains the difference of dead load important for great spans.

With a continuous bridge, however, the question of anchorage is only of secondary importance, because the outside spans by their own unavoidable weights counterblance the moments at the main-piers.

What Mr. Findlay says about the proportions of cantilevers refers to this class of bridges, not to the real cantilever bridge or the single span fixed at the ends.

He also says that the theories hitherto given towards proportioning cantilver bridges are all vitiated by not considering the non-uniformity of the permanent loads of cantilevers.

This objection, which, if true, would overthrow the writer's own, investigations as published in his book, however only holds good, if the cantilevers were to be designed long and the central span short. This design is only admissible for certain continuous girders, not for the single span fixed at the ends. Of such a bridge the moments at the roots of the cantilevers must be kept moderate in order to make the anchorages economical. In fact, these end moments must be not greater than necessary to erect the whole bridge safely without false works. And thus it is at once seen how the distinction between continuous girders and beams fixed at their end leads to the proper design of either class of

structures.

It seems to the writer that Mr. Findlay has perhaps underrated the importance of moderate moments at the piers, and overrated the impor. tance of unequal dead loads. If the permanent load of a cantilever at the root is 6 tons and at the end 1 ton, and if the movable load corresponding with it is two tons per lineal foot, the theoretical quantity of this cantilever is only 20 per cent. in the average, less than if the weights were all uniformely distributed.

That with cantilevers of the modern fixed girder, the permanent loads at the piers are still greater than at their ends is an advantage which is not overlooked, but the cantilevers becoming short is of no such importance as to alter the leading principles.

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