Ml 



RltlDOK. 



HIIIDOE. 



of UM extradcs or of the intrados; for if this abould Uke place, the 

 rauh itMU is liable to be overthrown, under one or other of the con- 

 diUon. indicated in the previous article, Amca. It U tolerably well 

 known at present that the theoretical and practical rule* adopted by 

 glniiH lor flsjmilrtjng the thickness of archea,and for settling the 

 form of the extndoa, give raralU which are in exceed of thoee rigo- 

 rously required ; and ML Yvon de Villarceau ha* era taken the pain* 

 to indicate the mob* degree of waste, to be discovered according to 

 hi. theoretical rule*, in the mat celebrated bridge* actually executed. 

 In a memoir, 'Bar rtttabaaraent dec Arches de Pont,' Pan*, 4to, 



1854, the* eminent mathematician ha* treated the investigation of the 

 form* and thirs-nsss** to be given to the vault upon a different system 

 to the one usually adopted; for he take* a* the unknown quantities in hi* 

 investigation* precisely those quantitie* which are assumed in the ordi- 

 nary theory . and be atk* to determine the fornu of intndu* and extrodog 

 which would aecur* the greateat stability of a vault intended to support 

 a load whoa* weight and mode of distribution are previously fixed ; as 

 also be suppoen* that the span and the rise of the arch are fixed. The 

 reasoning upon which he support* hi* opinions is of the most elaborate 

 description, but it involve* the discussion of problems of such extreme 

 complication, that it would be impossible to condense them within the 

 limit* of this article. The reader is therefore referred to the original 

 Usstisu; and for the present it may suffice to gay, that H. de Villar- 

 ceau has arrived at the conclusion that, theoretically, the rise of 

 complete arches should be made to vary between 1 and J of the span, 

 without attaining either of those limits; and that the rise should 

 approach the proportion of in arches of small spans, and of J in 

 arches of larger span*. Semicircular arches, he considers, ought only 

 to be adopted in case* when, as in tunnels, the load may be considered 

 infinite. A series of tables are appended to the memoir, in which are 

 stated the value* of the quantitie* applicable to the elements of the 

 calculations required in the case* of segments! arches, or in semi- 

 elliptical ones ; and a section of an arch of the latter form, of 200 feet 

 span, and 53ft SJ in. rise, with a thickness of the keystone not 

 rtonxding 6 ft. 2 in., is also given. Such an arch would indeed exceed 

 in boldness anything hitherto attempted ; but it is to be observed, that 

 the whole of M. de Villaroeau's theory depends upon the correctness 

 with which the surfaces of the joints of the voussoira are originally 

 reduced to their element which meets the curve of the centres of 

 gravity, and the contact is subsequently restored upon equal portions 

 of the plane of the joint on either side of that primitive element, so 

 that the pressure must finally be distributed over the whole of the 

 new joint These conditions are only attainable with extreme diffi- 

 culty, for defects of execution, or in the quality of the materials, 

 would materially affect them ; and indeed the movements which take 

 place after withdrawing the centre* of a bridge, are often of so serious a 

 nature as to render it inexpedient or unwise, to adhere to the results 

 of even the most rigorous mathematical investigations. 



In the execution of an arch it is desirable, and indeed almost 

 necessary, that the vouasoirs should be in uneven numbers, disposed 

 symmetrically upon either side of the keystone ; and if there should 

 be simply a band of ashlar voussoira upon the edge, filled in with 

 mailer rubble, or brickwork, the joints of the Utter must range 

 with those of the bands. Of late years, some very large bridges, 

 such as the Maidenhead bridge of the Great Western railway, or the 

 Pont aux Doubles, at Paris, have been executed entirely of small 

 materials, which, in fact, do not act in any way whatever as arches ; 

 for the adhesion of the cement employed converts the whole moss into 

 solid body, which retains its form through the inherent powers of 

 nuisranoB of the cementing matt-rials themselves. But whether the 

 arch be composed of vouasoirs able to move upon their beds, or of 

 what may be styled artificial monoliths, the construction of the centra 

 upon which the arch U to be formed, must always command serious 

 attention on the part of the engineer. The principles upon which 

 then ceuties are constructed, are much modified by local circumstances ; 

 for according to the facilities these may present for establishing inter- 

 mediate point* of support, it may be necessary to adopt particular 

 description* of framing. The essential conditions of a centre may, 

 however, be very briefly stated ; they being in fact simply, that they 

 should not be susceptible of deformation under the influence of the 

 partial loads they will have to support, and that they should rigorously 

 conform to the projected outline of the intrados ; they must also be 

 susceptible of being removed, after the completion of the work, without 

 disturbing the arch itself. The centre* are usually composed of timber 

 framing, or trusses ; either bearing upon the extremities of the opening, 

 or upon intermediate points of support. Until within a few yean the 

 frames were made to rest upon wedges, and when the vault* were 

 completed, these wedges were loosened by being driven back with 



braced, so as to hinder anything like lateral displacement of the trusses. 

 It U equally important that the frames should not be allowed to rise 

 under the action of the partial load ; and, therefore, the crown of the 

 centre must be tied down to the springing, and the crown itself must 

 be weighted whilst the vault is being brought up symmetrically on the 

 sides. As all wood framing is liable to some description of compres- 

 sion under the action of great loads, and as the materials of which every 

 arch is composed are susceptible also of some degree of compression, it 

 U customary to give an additional height to the centre beyond that 

 which would rigorously be required if its outline were made to 

 correspond exactly with the curve intended to be given to the intrados. 

 There does not appear to be any rule for settling the height to be 

 thus allowed; and evidently it must depend mainly upon the 

 skill and attention of the workmen; but from the following table 

 of the settlements of some arches, recorded by CUudel (' Formules 

 a 1' usage des Ingcnieurs,' Paris, 1854), it will at once be seen 

 that there is an absolute necessity for observing the precaution in 

 question : 



but in the construction of some of the modern railway 

 bridges of France, a system of placing Ugi filled with dry sand under 

 the poinU of rapport, has been introduced wiUi success. This inge- 

 nious .ytem obviate* the danger of jarring the fresh masonry in 

 driving Wk the wedges, and H has the advantage of enabling the 

 workmen to stop the descent of the centre* at any time they ma; 

 think proper. A description of it will be found in ' Lei Annales das 

 Poote et ChaiwseVV for November, 1 849. 



Winterer be the form, or the mode of bearing adopted, in executing 

 the centre* of a Urge bridge, H U necessary that it should be cross 



The principles which must be applied in the construction of centres 

 have been ably discussed in Kobison's ' Mechanical Philosophy ' (vol. 

 i. p. 661, ed. 1822), and it will be necessary to revert to the sub- 

 ject in the article on CARPENTRY. For the present, then, it will 

 suffice to say that, in fact, the framing of a centre must be itself an 

 arch able to support the weight of the vault ; and that it is essential 

 to convert all the strains upon the various parts of which it is com- 

 posed, as far as possible into efforts of compression. Cross strains 

 must be carefully avoided, and it is not even desirable to trust to the 

 timber to any great extent, as furnishing ties to the rest of the 

 framing. 



Timber bridges have been used very frequently in countries wherein 

 that particular material is abundant, and where neither the import- 

 ance of the traffic nor the wealth of the country would justify the out- 

 lay required for the erection of a permanent structure of masonry. Thus 

 in Switzerland, Germany, America, and in our own colonial possessions 

 wooden bridges ore commonly met with; but the very perishable nature 

 of the material must always render its use objectionable in tho great 

 majority of cases. When, however, local considerations render it 

 desirable to resort to the use of wood, the principles which should 

 guide the engineer in designing the bridge must be substantially thv 

 some as he would adopt in designing any other piece of carpentry, but 

 perhaps it is more essential that he should guard against the effects 

 of atmospheric action upon the various parts of the framing he uses, 

 than it would be necessary to do in ordinary cases. Thus it should be 

 established as a rule that the piers and abutments of wooden bridge* 

 must be of masonry of impermeable materials ; that no important port 

 of the framing should be bedded in the masonry in such a manner as 

 to prevent the free circulation of air around it; that no water should 

 be allowed to lodge in the joints, or to remain in the bearings, of the 

 framing ; and that all the movements which naturally take place in 

 the wood should be allowed to take place without interference from 

 the mode of construction. Tho framing itself must be put together 

 upon the ordinary mechanical principles adopted in carpentry ; but it 

 may bo desirable here to state, that in the earlier bridges the timber 

 was used simply as girders or straight horizontal beams ; then Pallodio 

 and the Italian architects introduced a system of trussing with tie- 

 beams; the German and Swiss engineers habitually resorted to trusses 

 without tie-beams, and in which tho thrust was carried down to the 

 feet of masses of masonry by means of inclined strutts, a system 

 which has been applied with infinite modifications by the engineers of 

 other nations; and latterly, the American engineers have resorted 

 to the use of what may be called built beams, applied, in fact, as 

 s^sflsn, 



Of course the use of timber baulks as girders, can only be admitted 

 when the openings are small, and the loads to be carried are not very 

 great In such cases tho girders must be considered to be beams 

 resting at each end on fixed supports, and loaded with a weight 

 dependent upon the purposes the bridge is intended to fulfil. The 

 resistance of a beam under such circumstances is directly proportional 

 to it* breadth multiplied by the square of its depth, and inversely 

 proportional to the distance between the points of support In most 

 books upon construction are to be found tables of the multipliers to be 

 used for ascertaining the transverse strength of the different kinds of 

 wood, and in practice these tables are applied upon the supposition 

 that the safe load should not exceed from J to J of the breaking weight 

 ascertained thus : 



tab. No. x breadth x depth 1 _ 

 length. 



