319 



BRIDGE. 



BRIDGE. 



30 



not only is the rainfall upon the former more copious than that upon 

 the latter, but that it runs off with greater rapidity. From this it 

 also follows, that the water way to be given to bridges in districts 

 composed of the non-absorbent strata, must be made greater than that 

 which would suffice for the porous ones. M. de Belgrand, in. an article 

 inserted in the ' Annales des Fonts et Chausse'es,' stated that the 

 granitic rocks, being usually the most precipitous, were those which 

 required bridges with the largest water way ; but that with an equality 

 of fall, the liasic formations required nearly the same, if not rather 

 larger, dimensions ; the clays, whether of the secondary, or post-tertiary 

 series, were considered by him to require bridges somewhat smaller ; 

 whilst the oolites and the chalk admitted the construction of bridges 

 with comparatively speaking small water-ways. It is observed, how- 

 ever, by M. de Belgrand that these theoretical rules must be modified 

 by the distance the water has to flow before it arrives at the bridge. 

 He stated that from the practice of the bridge builders in the valley 

 of the Seine, the proportions of the water way to the area of the 

 feeding ground of the streams, might be reckoned as follows ; but 

 evidently the conditions of the rainfall of the particular district under 

 examination must affect the whole of this question, and the results 

 indicated by M. de Belgrand must only be considered to show the 

 relative proportions prevailing in the bridges of some parts of central 

 Europe. 



Very steeply inclined liasic deposits require a water way, per mile 

 square of feeding ground equal to about 1 yard deep. 



Granitic rocks Ij yard deep. 



Oxford clay 1-1 



Common clays .... '72 



Chalk, or Oolites, only . . . -03 



These dimensions are not quite in accordance with those usually 

 adopted in either very flat, or very mountainous districts ; for in 

 Holland, it is the custom to make the water way of bridges in the 

 proportion of about 0'15 yard superficial for every square mile of 

 back country ; and in many granitic districts the water way is not made 

 greater than in the proportion of 0'45 yard superficial per square mile. 

 M. de Belgrand's observations are, however, the first which have been 

 made in any philosophical or consecutive spirit ; and they may be the 

 more safely adopted, because they would rather lead to an error in 

 favour of the stability of the work than otherwise. 



But in addition to the consideration of the area of water way to be 

 provided, in order to allow the free discharge of storm or flood waters, 

 it u necessary to provide against the possibility of the bed of the river 

 being affected by the increase in the velocity of the stream produced 

 by the contraction of its lateral dimensions. Whatever changes 

 therefore may be introduced in the shape of the water way of a river, 

 in order to admit of the construction of a bridge, it is absolutely 

 necessary to limit the mean velocity of the stream, at the periods 

 even of its greatest flow, within the following limits, according 

 to the nature of the strata it may flow over (Neville's ' Hydraulic 

 formulas ') : 



25 feet per minute in soft alluvial deposits. 



40 , clayey beds. 



60 , sandy and silty beds. 



120 , gravelly. 



180 ,, , strong gravelly. 



240 , shingly. 



300 , shingly and rocky. 



400 , and upwards in rocky formations. 



It is essential also to the stability of a bridge that, even in flood 

 times, the water should not rise to the underside of the keystone; and 

 in settling the dimensions of the water way attention must be paid to 

 the contraction of the fluid vein, produced by the various points of 

 support. The interference those points of support produce upon the 

 onward flow of the river gives rise to a species of heaping up of the 

 water, as it were, on the upside of the bridge, and a consequent increase 

 of velocity on the lower side : both of these phenomena, which depend 

 upon local conditions, require to be taken into serious consideration 

 in every case under observation. It follows, however, from their 

 existence that the fewer the points of support of a bridge are, the less 

 interference it will produce with the hydraulic conditions of the 

 stream ; and that unless very cogent reasons of economy should exist 

 to induce a preference for small arches, large ones should be adopted. 

 In countries exposed to severe frosts and sudden thaws, it is moreover 

 necessary to guard against any danger from an accumulation of float- 

 ing ice on the upper side of the bridge ; and it is desirable that as far 

 as possible the xpringingg of the arches should be kept above the flood 

 line. Thin precaution is more necessary when the shape of the arch is 

 segmental, or semicircular, than when it is elliptical ; but whatever 

 form be adopted, the danger from floating ice must always be guarded 

 against. 



The forms to be given to the piers and to the arches of a bridge will 

 depend upon several practical considerations. With respect to the 

 former, it may be stated that they will depend principally upon the 

 opening of the arches, and the description of resistance they themselves 

 (the piers) are required to offer to the stream, or to the dynamical 

 action of the arches. Upon the up-side of the stream in non-tidal 



rivers, and on both sides in rivers susceptible of tidal actipu, the piers 

 must be terminated by what are technically called cut-waters, rising to 

 the extreme height of ordinary floods ; and from direct experiments it 

 would appear that the most advisable horizontal section to be given to 

 such cut-waters is that of an equilateral spherical triangle, whose apex 

 is presented to the stream. In so much as the piers alone are affected 

 by the openings, their dimensions and form must depend upon their 

 being made equivalent at least to the vertical effort they must sup- 

 port; and it is only in extraordinary cases that they are made of 

 sufficient dimension to resist the lateral thrust of the arches. In fact, 

 there are few important bridges in existence, erected over large rivers 

 especially, in which the piers would remain upright, if the thrust of 

 the respective arches were not carried over, as it were, through the 

 whole series to the abutments ; and if one arch in such bridges were 

 withdrawn, all the others would most probably follow. As to the 

 shape of the arches, that may often depend upon mere economical 

 considerations. Semicircular or segmental arches are executed with 

 the least expense, because, if stone be employed, all the voussoirs can 

 be worked from the same mould, or if brick be employed, the labour 

 of laying can be performed by even the commonest description of 

 workmen. But, on the other hand, arches of either of these descrip- 

 tions require, as we have seen, that the whole structure of the bridge 

 should be kept at a considerable elevation ; and in the case of seg- 

 mental arches the lateral thrust upon the abutments is greater than 

 in any other form. jEsthetically, a semi-ellipse, or a segment sub- 

 tending an angle of 60, are unquestionably the most elegant forms ; 

 and in large semi-elliptical arches it is desirable that the outline should 

 be struck from a sufficient number of centres to ensure the flowing 

 regularity of the curve. The arches of the bridge of Neuilly were 

 struck from eleven centres. 



The most important considerations to be borne in mind in designing 

 a bridge are, that the foundations of the piers and abutments should 

 be sufficiently strong to resist the weight .brought upon them, and any 

 accidental effort to which they may be exposed from floods or other 

 extraneous causes. As the functions of the piers and abutments are 

 merely to support the vertical pressures of the arches, and to resist 

 any tendency towards a movement of rotation on their own edges, 

 arising from the lateral thrust of the arches, it follows that the lighter 

 they are, and the greater the area over which they distribute the 

 effort, the less will they load the foundations, and the more satis- 

 factorily will they perform the duty required of them. The positive 

 effort to which they may be exposed is ascertained first by calcu- 

 lating the extreme passing load ; then that of the structure above the 

 arch ; that of the arch itself ; and finally, the dynamical efforts of these 

 various loads. As to the passing load, it is customary to calculate upon 

 240 Ibs. per foot superficial of the whole area in ordinary bridges ; and 

 in railway bridges, exposed to the action of rolling loads travelling at 

 great velocities, it will be safer to quadruple this calculation. As to 

 the weight of the superstructure, that is of course ascertained from its 

 mere density and cubical contents ; and it may be assumed, practi- 

 cally, to be distributed equally over the arch. The weight of the arch 

 will of course also depend upon its density and its cubical contents ; 

 and these may practically be ascertained by making the depth of the 

 crown or keystone equal to from 53 to ^5 of the clear span, and tracing 

 the extrados of the arch upon the principle that the vertical depth 

 over any particular point of the intrados shall be equal to the depth of 

 the keystone, multiplied by the cube of the radius, and divided by the 

 cube of the height of the point considered above the chord line. The 

 sum of the above partial weights will act upon the resisting points of a 

 bridge with an effort equal to its total weight multiplied by the 

 leverage ; and, consequently, the moment of resistance of those points 

 must be sufficiently in excess of the destructive effort exercised by the 

 load to support its continuous action. In order to secure this con- 

 dition, the resultant of the ultimate thrust should fall within the 

 vertical line drawn from the foundations of the abutments through 

 then- centres of gravity ; and the moment of resistance of the abut- 

 ments, from its gravity alone, should be at least equal to three times 

 the maximum effort to which it may be exposed. Of course, in 

 such cases, the resistance to lateral displacement will be increased by 

 the friction of the materials of the abutments upon their beds ; and 

 the tendency of the piers to turn over upon their inner edges will be 

 also resisted by the adhesion of the cement, or mortar, employed. It 

 is essential to observe that the above reasoning pre-supposes that the 

 foundations themselves are able to sustain the whole of the weight 

 thrown upon them ; but as the importance of this detail of bridge- 

 building is so very great, it will be essential to dwell hereafter some- 

 what at length on this part of the art. 



The above remarks are made upon the supposition that the arch is 

 in itself an arch of equilibrium, and that it has been constructed with 

 sufficient care and skill to allow of its retaining its form when the 

 temporary support, or centerint/, upon' which it was built, shall have 

 been withdrawn. They would hold with equal correctness, however, 

 if the materials of which the arch is composed were of such a nature 

 as to render the assemblage equivalent to a solid beam; and this 

 actually occurs when brick-work set in hydraulic mortar, or in cement, 

 or any other analogous-small materials, are used. In either case, the 

 load ultimately thrown upon the arch must never attain such limits as 

 to bring the lino of pressure beyond the vault itself, either on the side 



