Young Bridge

7/27/2019 Young Bridge

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Young, Thomas. Bridge. En: Supplement to the fourth, fifth and sixth

editions of the Encyclopaedia Britannica. Edinburgh: Archibald Constable,

1824. Vol. 2, pp. 497-520, plates 42, 43, 44.


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B R IB rick and brow n, according to the substances w ith w hichU the oxide is combined. We ascribe the yellow co-Bridge. . lo ur o f thGLo nd on b ric ks to th ~ ash e$ o f th e c oa ls,~

B R ~91which , b y u nitin g w ith th e p ero xid es o f iro n, fo rm a B rickkind of yellC lwochre. (J,) ur1L.e.~B RID G E.

1'"'11 mathematical theory of the structure ofbridges has been a favourite subject with m echa-nical philosophers; it gives scope to some of them ost refined and elegant app1iC'ations of scienceto practical utility; and at the same time that itsp ro gre ssiv e im prov em en t ex hib its an e xamp le o f th every sJow steps by w hich speculation has som etim esfollow ed execution, it enables us to look forw ardsw ith p erfect co nfide nce to th at m ore de sir!J.b le stateof human knowledge, in which the calculations ofthe m athem atician are authorised to direct the ope-rations of the artificer with security, instead ofw atc hin g w ith serv ility th e prog re ss o f h is lab ours.Of the origin of the art of building bridges asketch has been given in the body of the Enclfclo-pcedia; the subject has been l'ediscussed w ithin thelast twenty years by some of the m ost leamed anti-q ua rie s, a nd o f th e 1 11 o;,;tle ga nt ;,;c ho la rs o f th e a ge ;b ut ad ditio ns stiJI'm ore im po rtan t ha ve b een m ad e toth e scien tific an d p ractical prin cip le s 0 11w hich th atart depends; and the principal inform ation, that isdem anded on the present occasion, w iII be com pre-h en de d u nd er th e tw o h ea ds o fp hy ~ic o-ma th ematic !tlprinciples, subservient to the theory of this depart-m ent of architectm c, and a historical account of thew orks either actually executed or projected, w hichappear to be the m ost deserving of notice. The firsth ea d w ill c on ta in th re e s ec tio ns , r ela tin g re sp ec tiv e-ly (1) to the resistance of the m aterials em ployed, (;z)to the equilibrium of arches, and (S ) to th e effe cts o ffriction; the second will com prehend (4.) som e de-tails of earlier history and litem ture, (5) an ac-cO llnt of the discussions w hich have taken place re-specting the improvement of the port of London,and (/) a description of s(ll'ne of the m ost rem ark-'able bridges which hnve been erected in mOtlerntimes.

SECTION I.-Of the Resistance 0/ Materials.The nature of the forces on which the utility ofthe su bsta nc es emp lo ye d in arch itectu re an d ca rp en -

A . In a ll lw1I!9geneous so li d bodi es , t he yu is laU61!: sto e xte ns io n a nd c om pr es sio n m us t h e in itia ll!J e qu al,a nd p ro po rtio na l to th e c ha ng e q f d im en sio ns .The equilibrium of the particles of any body re-m aining at rest, depends on the equality of oppositeforces, varying according to certain law s; and thatth ese law s a re co ntin ued w ith ou t an y ab ru pt c ha ng e,w hen any m inute alteration takes place in the dis-tance, is dem onstrated by their continuing little al-te re d b y a ny v aria tio n o f d im en sio ns, in c on se qu en ceof an increase or dim inution of temperature, andm ight indeed be at once inferred.as highly proba-b le , fro m th e g en eral p rin cip le o f co ntin uity o bserv-ed in the Jaw s of nature. W e m ay, therefore, alw aysassum e a change of dim ensions so sm aIJ, that, as iF.a 1l o th er d iffe re ntia l c alc ula tio ns, th e e leme nts o f th ec urve s, o f w hich th e o rd in ates ex pre ss th e fo rce s, asfun ctio ns o f, o r as d epe nd in g o n, th e d istan ces a s ab -sc isses, m ay b e c on sid ered as n ot sen sib ly d ifferin gfrom rig ht lin es, c ro ssin g eac h o th er, if th e cu rv es b edrawn on the same side of the absciss, in a pointco rrespo nd ing to th e p oin t of rest, o r to the distan ceaffording an equilibrium ; so that the elem entary fi-n ite d iff ere nc es o f th e re sp ec tiv e p airs ,o f o rd in ate s,w hich m ust fo rm , w ith th e p ortio ns o f the tw o cu rv es,rectilinear triangles, alw ays sim ilar to each other,w i I I ahvaJ's val'Y as the lengths of the elem ents. ofthe curves, or as the eJem ents of the absciss, begm -ning at the point of rest; and it is obvious that thesed if fe re nc es w ill re pr es en t th e a ctu al m ag nitu de o f th eresistan ce s ex hib ited b y th e su bsta nc e to ex ten sio nor com pression. (Plate X LII. fig. 1.)It w as on the sam e principle that Bernoulli longa go o bs erv ed , th at th e m in ute o sc il1 atio ns o f a ny s ys -tem of bodies, whatever the laws of the forces go-verning them m ight be, m ust ultim ately be isochro-nous, notw ithstanding any im aginable variation ofth eir c om para tiv e e xten t, th e fo rce s ten din g to brin gthem back to the quiescent position being alwaysproportional to the displacem ents; and so far 'as thedoctrine has been investigated by experim ents, itsgeneral truth has been am ply confirm ed; the slight


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B RID G E.98B ridgt>. body to rem ain plane and perpen?icular to the, axis,-v--' w llatever the point may be to, w hich the force IS a~-plicd a supposition w hich w Ill be correctly true, Ifthe pressure be m ade by the intervention of a firmplate attached to each end, and w hich, is perfectlyadmissible in every other case. Now, If the terul1-n al p la te s rema in f? ara lle J, it is o bv ,io us th ,a t , th ~ c om .p re ssio n o r ex ten sIO n m ust b e umfo rm ly d IstrIb utedtb r(} ug ho lit the su bstan ce , w hich m ust b ap pen w he n

the original force is applied in the middle of theblock; the centre of pressure or resistance, collect.ed by the plate, acting like a lever, being then ~o-ipcident with the axis. But when the plates are In-clin ed , th e resista nc e d ep en ding o n th e comp re ssio nor extension 'w iIJ be various in different pr..rts, andw ill alw ays be proportional to the distance from theneutral point, w here .thecom pression ends and thee xte ns io n b eg in s, if the depth of the substance issuH ident to extend to. this point; consequently theforces m ay alw ays be represented, like the pressureof a flllid, at different depths, by the ordinates of atriangle; and their result m ay be considered as con-centrated in the centre of gravity of the triangle, or9 such of its portions as are ,contaiued within thedepth of the substance; and when both extensionand com pression are concerned, the sm aller forcelpay be considered as a negative pressure. to besl.lbtracted from the greater, as is usual when anyutller compound forces are supposed to act on a le-ver of any kind. Now, when the neutral point issituated in one of the surfaces of the block; the sumof ~U t he f!)rces is represented by the area of thetriangle, as 'it is by that of the paralldogram whenthe pla-tes rem ain parallel, and these areas being ineither case equivalent to the sam e external force, itis ob vio us th at the p erp en dic ula r o f th e tria ngle m IJ.S tbe equal to t.w ice tbe height of the paraH elogram ,indicating that the com pression or extension of thesu rfac e in th -e (1 ).e c ase is tw ice as great as th e .eq ua-b le compressio n o r ex ten si< )fi in the o th cr; an dsin cetl:lere is .alw ays a certain degree of com pression ore~t t} nJ )i onwh ic h must b e p re cis el y s uf fi ci eI 1t t .o c ru shor tear that part of the substance which is itnme-d.iately ex po sed to it, a nd sin ce th e w ho le sub stan cem ust in general give w ay w hen any of its parts fail, itf Q U o w s that the strength is only half as great in thefermer case as in the latter. And the centre of gra-vity of every triangle being at the distance Qf O11e-third of its height from the hase,. the external forcem ust be applie!i, in order to pI'Qduce sucb a. ~orn-

cohesive and repulsive resistances of the blcck, and n/'id~~;t11e external force; and it is obvious that, as 111all ~other le~ers, the e~ternal force w ill alw ays be equalto the dJfference of the other tw o forces dependingon the compression and extension, or to the meancom pression or extension of the w hoie, w hich m ustalso be the im mediate com pression or extension ofthe m iddle, since the figure representing the forcesis rectilinear. A nd the effect w ill be the sam e, w hat-ever may, b~ the interm ediate substances by w hichthe force IS Im pressed on the block, w hether conti.nued in a straight line or otherwise. W hen the forceis oblique, the portion perpendicular to the axis w illbe resisted by the lateral adhesion of the differentstrata of the block, the com pression or extension be~ing only determ ined by the portion parallel to theaxis; and when it is transverse, the length of theaxis will remain unaltered. But the line of direc.tion of the original force m ust alw ays be continuedtill it meets tht.: transverse section at any point ofthe length. in order to determine the nature of thestrain at that point.D . The d is tance if the neutralpointftom tlte axisgf a block or beam is to the depth, as the depth totw elve tim es th e d ista nce q f th e J aree , m ea su l"cd in th etransverse scction.CaIlin g th e d ep th a, and the distance of the neu.tral point from the axis z, the resistances m ay be ex-pressed by the squares of k a+ z and! a-z, whichare the sides of the sim ilar triangles denoting thec omp re ss io n a nd e xte ns io n ( Pro p. n .); c on se qu elltly ,thediffercllce of these squares, 2 az , wiII representthe external force (Prop. C.). But the distance ofthe centres of gravity of the two triangles m ust al-ways be fa ; and, by the property of the lever,m aking the centre of action of the greater resistancethe fulcrW D, as the external force is to the smallerresistance, so is this distance to the distance of theforce from the centre of action of the greater resist.

. ( I ) 2!J' ( aa a + Z )nce; or2az.


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13 RID G E. 499B '1 "e. p oin t is g re ate r th an th at d is t:m ce its elf, t ha t is , i n in the J irec tio7 ! r f' one 0/ i ts Jia~o1/({ls ,is t w i c e as . Bri~;;~ the r~tio of a + 6 to a, siDce z is to a as a to l~~ ; g rea t a s if the sainefirce 'we/'eapp iedi~ the airection-- .(P ro p. D .) a nd to ~a as a to i'J/J: a nd th e str~n gth IS q jth e a xis. . . threduced in the same pro p o rtio n, as th e p artia l C ?U 1- T his p ro po sitio n a ffa rd s,.a sim ple illu stra tio n o f e, f Iven application of the preceding one.. C alling the length!P res::;ion or extension, by the oper!ltlO n 0 a g,. , "-. h' LI I fi ) of iU ly n ortion of the axis .'1:,begmning nom teiorce, is increased. (Plate X

"

g, 3. middle ,l'a nd n. eg lectiing t he ob liqui ty, the distance ofF. T he cu rva tu re rf' th e n eu tra l lin e q f a b efr1 !za ta ny p oin t, p ro du ce d b y a , g ive n f? rce~ is p ro pa rtz0 1i(ll the force m ay be called I1= n...,and th e compr es -to the distance (If the lme qf dlrectwn qf the lorce sion in the line of the force being everywI1ere asfrom the given point qf the a,'eis, whaievel' that dlrec-' 12y,y , . ,'. d.x d 12nnxx dtion may be. , . 1 + --"-, Its flu xlO n w ill b e + x~ , anS in ce th e d ista nc e z of the neutral pom t from tbe aa ,aa," I h d t f th fior c e and h .li 4n~.i3 h ' 1:. h 1 bX Is IS I nv ers e y as y, t e is ance 0 e .' t e nuent x + - '- , w IC u,W en y = 7Ja, ecomesdie radius of curvature, or the distance of the m ter- aa ,~section of the planes oftbe term inal plates ft'om the x+x, wh ic h is tw ic e 8 '$ g re at a s if yw 'l' e- ah va ys ::::: 0,neutral point, m ust be to the distance z as th e w ho le B ut if th e b read th o th e b lo ck w ere co nsid ec ab le , S olenoth of the axis is to the alteration of that length th at it ap pro ach ed to a c ub e; th e comp ression w ou ld .p ro du ced b y th e comp ressio n o r e xten sio n, it fo llo ws va ry accO l 'd ing t .ua - di ff er en t l aw , each s ec ti onpar al -that tbe radius of curvature m ust be inversely as the le l to th e d ia go na l a ffo rd in g an eq ua l re sista nc e, a nd

distance y, and inversely also as the com pression, the exact solution of tl!e problem would requireand the curvature itself must b~ conjointly as the 1:force and as the distance of its application. If th,e an infinite series for expressing the value of Jn x dr .d irec tio n o f th e fo rc e b e ch an ge d, a nd th e p ,erpe nd l- ;".

., ." "ular faIling from th~ given point of t~e aXIs on the I~. If a sokrl 0 0 ' 1 ' n W D - e ~t$'l lXZScur 'Ded a l tUre !~toline of the force be new caIJed y, th e d istan ce o f the r: c zr cu l~ rf o~m , and an e xt er na l fo rc e iJ e th en :'1!PhedfO l'cc from the axis measured in the transverse sec- m the dtrectzan if t lEe chord , wh il e t he e xi remztws 'Pe -tio n w ill b e in ~l'ea sed b y ~ he ?b !iq uity e xac tly in th e t a in t lEe i~angular pos it ion; t ke , great .e s t c (} 'l f/ pre ss iI J/ ts ame r at io a s I tS e ff ic acy I Sd lm lD ls hed, and the cur - o r extensronqf the suUstll1We ill uit,zm4tely.oet(}ohevature of the neutral line w ill rem ain unaltered ; al- 'm ea n cQmpre ssio n o r e xte nsio n w hich ta kes p l{ [C ~ilzth ou gh -tb e p lac e o f th at H ne w ill b e a little v arie d, . , . ' 4h " 16hhu ntil at last it coincides w ith the axis w hen the force t he dzr ec tzO t!o f t he c hord, a s 1 + - to 1 + ; a'. ',a 15aa,becom es com pletely transverse: and the radIU s of, , . "curvature of the axis w ill always be to that of the h~zng the depi~ qf {he bar, and k the. act/(al verG edneutral line as the acquired to the original length of sm e, or the M zght of the arch. .the axis. (Plate X LII, fig . 4 .) . ~ e. m ust here separate tbe, actJO ns of the forcesG . The m dius cif cU r'V ature q ! the neutral line is r~tam U1g t?e ends of t~e bar l?tot~6 parts, theoneto the distance ql the' neutral point as the original sim ply u rgmg th e ~ ar ,1 11 he d ire ctIO n o f ~ r1 ec ho rd , .length if the axis to the alteration qfthat length; or and the Q t~er, w hich IS of a. m o:e con:phcat~~ na-,a s a c erta in g tt> en qu an tity to th e e xte rn al.lo rc e: a nd , OO re , ke epmg th e a ng ula r d 1r~ ct~ on U 1Ja lte re d; a 11 dth is qu an tity h as b eelz term ed th e M od ulu s q f ela sti. ~'m~ first c alc ula t~ th e v arla t~ on o f t~ e a .n ~la l'city' sltU l,\tlO no f th e e nd s; In c on se qu en ce o r tb e b en dm g. of the bar by tbe nrst portion, and then the strainOr r . z - M :f, an d r - 1\ 1z ::: Maa, as is ob. r eq.u ir e~ toI obd,:iate , that fcblang~ 'd' db lYmfeahns 'bof a fOh1.'~}e. - , - f JW Y actmgmt1e IrectlODo tlem l eo t e ar,w le.

'. '. . the elids are supposed to be fixed. If each haIf ofV lOUSfrom th e p re ce dm g d em on stra tio n; Y bemg th e b ar w ere rec tilin eal' th ese tw o stra in s w ou ld o b-th~ distance of t~e li~e o~ the force f~om the given viou sl:v b e eq ual, an d ~o uJd n eu tralise ea ch o th cl' inp om t, w ha te ve ~ l,t~ dire ctio n m ay b e. '" the m iddle of the halves, w hich ~ight be consideredH. T .l te jl ex zbzl zt y, r if er r~d t o , the dzr ec tz 01zq f t l! e as the meeting of the ends of two shorter pieces,.f~rce, zs expressed b,y u,nzty, tncr.e~sed by tw elvc a ctin g tra nsv ~rse ly o r o bliq ue ly o n e ac h o th er; w ith -tU 'T le sth e sq ua re q f th e d zsta nc e, d z v ! d e d by tltat gf o l1 t a ny stra in ; th e c urv atu re p ro du ce d: b y tIre w Jm le


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BRIDGE.UOBridge. w hich the fluent is p rfx -pb x. In th e s ec on d p la ce ,~ the curvature derived fl'o~ the force acting betweenthe tw o halves w hen the ends are considered as fix-ed points, w ill' be as '1 '- r~x, and the fluent of tht:change of aI!gular situation m ay be called qrx-q).{~; and at the end, when x becom es equal t


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BRIDGE.B rid ge . sy ste n: o r b od ie ~ su pp ortin g ea ch o th er, th e g :e ne ral~ directIOn of theIr mucual pressure; remembermg a].w ays that this cur\!~ is as m uch an im aginary line, asth e ce ntre o f g ra vity is a n im !lg in ary p oin t, th e f orc es 'being no more actual1y coBected into such a linethan the whole weight or inertia of a body is col-lected in its centre of gravity. Indeed, the situa-tion of the curve is even less definite than that of the

centre of gravity, since in many cases it may differa little according to the nature of the co-operationof the forces which it is supposed to represent. Inreality, every gravitating atom entering the struc-ture m ust be supported by som e forces continu~d in$om e line, w hether regular or il'l'egular, to the fixedpoints or abutm ents, and every resisting atom par-takes, in a m athem atical sense, either positively ornegatively, in transm itting a lateral pressure w hereit is required for supporting any part of the w eight:and when we attempt to represent the result of allthese collateral pressures by a sim ple curve, its situ.ation is liable to a slight variation, according to thedirection in which we suppose the co-operatingforces to be' collected. If, for instance, we wishedto determine the stability of a joint, formed in agiven direction, it w ould be necessary to consider.the m agnitude of the forces acting throughout theextent of the joint in a direction perpendicular to itsplane, and to collect them into a single result, andit is obvious that the forces, represented by the vari-ous elementary curves, may vary very sensibly: inth eir p ro po rtio n, w he n w e c on sid er th eir jo in t o pera.tion on a vertical or on an oblique plane; althoug1tif th e d ep th o f th e su bstan ce b e in co nsic:iera]:> le ,h isd iff er eI} ce w ill b e who lly impe rc ep tib le , a nd in p ra c~tice it m ay generally be neglected w ithout i~conve-nience; calculating the carve upon the suppositionof a series of joints in a vertical direction. If, how .,ever, we wish to be very m inutely accurate, w e m ust.attend to the actual direction of the joints in the de~term ination of the curve, and m ust consider, in the.case of a bridge, the whole weight of the stl"Uctureterm inated by a given arch stone~ w ith the m aterialswhich it supports, aB determining the direction ofthe ourve of equilibrium where it meets the givenjoint., instead of the w eight of the. m aterials term i~nated by a vertical plane passing through the pointof the curve in question, which may sometimes bev ery sen sib ly less; th is c on sid era tio n b ein g as n ec es-sary for determ ining the circum stances under w hichthe joints w ill open, as for the m ore im aginary pos.$ibilityof the arch stones sliding upw ards or dow n-

.501and of the w hole weight ot each block. And if we Biidge.im agine the blocks to be divided into any num ber of ~parts, by sections para]Jel to the ends, 'w hich is theonly w ay in w hich w e can easily obtain a regular re;'suIt, it is evident that the force exerted at any ofth ese se ctio ns, b y th e e xte rn al p ortio ns, m us t b e su f-ficient to support' the lateral thrust and the w eightof the internal portions; and its inclination m ust besuch tr,at the horizontal base of the triangle offorces must be to the vertjcalperpendicuIar aithe lateral thrust to the weight of the internalportion;, or, in other words, the lateral thrust reo,m aining constant, the w eight supported w ill be asthe tangent of the inclination. B ut calling the hori.zontal absc is s x, a nd th e v er tic al o rd in ate y, th e ta n..g en t o f t he < in clin atio nw i ll b e ~~.. w hic h, in th e c aseof a paraU elepiped, m ust be proportional to the dis-tance x from the contiguous ends; and x ==:;;consequently xdx: :: mdy, and'i x2 = my, whic h is tlieequa tion of a parabola. . It is u su al in such cases toconsider the thrusts as rectilinear throughout, andas m eeting in the vertical line passing through thecentre of gravity of each block; but this mode ofr ep re sent at ion i s evi dent ly onl y a conveni en t compen -, 'dium. 'I f th e I ;> lo ck sw er e u nite d to ge th er i n th e m id dle , s o-as to form a single bar or lever, the forces wouJd besomew hat d iffe re ntly a rra ng ed ; th e u pp er h alf o f th ebar would conta!n a series of elementary arches,abutting on a series of sim ilar elem entary chains inthe low er half, so as to take off a ll lateral thrust from ,the supports at the ends. 'W ith respect to the transverse strains of levers in'ge neral, it m ay h e o bserv ed, tha t th e m os t co nv en ien tway of representing them is to consider the axis ofth e lev er a s comp ose d o f a series o f e hilIlen tary b ars,bisected, and crossed at right angles, by as manyothers extending across the lever, or rather as far ailtw .o-thirds of the half depth on each side, w here thecentre of resistance is situated. The transversef orc e mus t th en b e tr an sm itte d u na lte re d th ro ug ho utthe w hole system , acting iu' contrary directions atthe opposite ends of e a c h of the elem enta'ry barilconstituting the axis; and it m ust be held in equili-b rium, w ith re sp ec t to e ac h o f th e c en tres , c on sid er.cd as a fulcrum , by the general result of all the cor.,


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:302 'B RID G E.'B l'id g~ : f ou rth f lnxio ll o f t he o rd in ate . A lso, t he 11uxiono f~ the str~in beinG 'as the whole weight on each side, itI:>

",

1"foHows that when the stram IS a maXImum , ana Itsfluxion vanishes the whole weight, or the sum ofthe po sitive anl negative forces on ei,ther side, m u~ talso vanish; as M r D upin has lately aem onstrated IIIa d if fe re nt m an ne r.M . I n eve ry s tmc tu re suppor i: :d v ,l fabl ltm~n~s ,, th etangent qf the inclinathm qf the Cllrt'e 0/ ~quilzbrzu?nto the hOl'izon is proportiond to the wezght elf ~hep arts in ter po se d b etw ee n th e g iv en 'p ain t a ud d ie n 2Z d~die if the stntcture.T he truth of th is pro position depends on the equ a~lity of the horizontal thrust throughout the stru'c-ture, from w hich it m ay be im mediately inferred, asin the last propositioq. The m aterials em ployed formaking bridges are not uncommonly such, as tocreate a certain degree of lateral pressure on theoutside of the arch; but as there must be it sim ilarand equal pressure in a contrary direction a~ainstth e a bu tm en t, its effec ts w ill b e comp re hen ded 1 ll th ed ete rm in atio n o f th e p oin t a t w hic h th e cQry e sp rin gsftom the abutment, as wen as in tbe direction of thecurv e itself; so that the circum stan ce d oes not affordany exception to the general truth of the law. It is,h ow ev er, se ld om n ec ess ary to . i nc lu de th e o pe ra ti onof su ch m aterials in ou r calculation s, since. their la-teral pressure has little or no effect at the upperpart of the arch, w hich has the greatest influence onthe direction of the curve; and it is alse desirableto avoid the unnecessary employm ent of these softm aterials, becau se they tend to increase the horizon-tal thrust, and to raise it to a greater height abovethe foundation of the abutment. '.W e' hav e therefore generally fwdx = mt = m :~ ,

~v being the height of uniform matter, pressing onthe arch at th e ho rizon tal distance x from the ver~tex, t the tangent of the inclination of the curve ofequilibrium, y its v ertic al o rd in ate, a nd m a quant it yproportional to the lateral pressure, or horizontalthrust. '.N. The radius if curvatu re qf the cur'V eif equili-brium is inversely as, the load on each part, and di-r ec tly a s th e c ub e q fth e se ca nt q fth e a ng le in clin atio nt o t he l to ri zon .T he g eneral expression for tbe radius of curvature. . ( d z ) 3 I h ' .d dx~ r. dx dS r = dxdd ; an< . ere, sm ce m 'Y::: :; w , x.'Y

(Prop. L.) The uniform ity of the load im plies Bridge.that the supcrior and inferior term inations of the ~arch, com monly called the extrados and int;-ados,should be paraJIel: but it is not necessary thateither of them should be parabolic, unless we wishto keep the curve exactly in the middle of the wholestructure. When the height of the load is verygreat in proportion to that of the arch, the


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B RID G E.Brid..e., ,dz zd z~ a nd dy: :: ;; ( ~- ) "" " ;~-'-' - v' 1 + ~~ - 'V (z z + mm), ofwhichthe, zz:f luen~ is .v(z~ + m2), re qu irin g n o fu rth er c orr ec tio nth an to su pp ose y in itia lly e qu al to m; and we have,1


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504 B RID G E.B ridge. out friction, and the parts m ust slide on each other:

'-'v'- this, however, is an event that can never be likel~ tooccur in practice. B ut if -the CU l've, representm gthe general pressure on any joint, be directed to ap oint in its plane beyo~ d the lim its of the su bst~ nce,the joint will open at Its remoter end, unless It besecured by the cohesian of the cemc?ts, and thestru ctu re w illC 'ith er w ho lly faIl, o r c on tm ue to stan din a new form . (Plate XLII. fig. 5.)F rom th is c on ditio n, to ge th er w ith th e d eterm in a-tion of .the direction of the joints already m entioned(P ro p. P :), w ,e m ay e as ily fin d th e, b es t, a rran geme ntof the jom ts ID a tIat ard1 ; the object, Il1 such cases,being to diminish the lateral thrust as m uch as pos-sible, it is obvious that the common centre of thejoints must. be brought as near to the arch as iscom patible w ith th e cond ition of the circle rem ain-ing within its lim its; .and it may even happen thatthe superincum bent materials would prevent theopening of the joints even if the centre were stillnearer than this: but if, 011 the other hand, thearch depended only on its own resistance, and thematerials were in any danger of' being crushed, itw ould be necessary to keep the circle at som e littledistance from its surfac.es, even at the expence ofsomewhat increasin"gthe la te ra l pressure . . .When the curve of equilibrium touches the intra.dos of an arch of any kind, the compression at the$urface must be at least foul' times as great.as if itrem ained in the m id dle of the arch-stones (P ro p. E .~ ,and stiU greater than this if the cohesion of thece-ments is called into action. In this estimate wesu pp ose th e tra nsv erse se ctio ns o f th e b lo ck s in fle xi-ble, so as to cooperate throughout the depth ill re-. s is tin g th e p re ssur e 011any -poin t; but in r ea li ty th iscoop eration w iJI be confined w ith in m uch narro werlim its, and the dim inu tion o f strength w ill p ro bab lyb ec on sid erab ly "g rea te r th an is h ere su pp ose d, w hen -ever the curve approaches to the intradilli of thearch. .The passage of the curve of equilibrium throught11e middle of each block is all that is necessary toinsure the stability of a bridge of moderate dim en-sions and of sound materials. Its strength is by nom eans increased, like that of a fram e of carpentry,or of a beam resisting a transverse force, by an in-crease of its depth in preference to any other of itsdimeniions: a greater depth does, indeed, give it apow er of effectually resisting a greater force of ex-ternal pressure derived from the presen ce o f an)' o c-casionalload on any part of the structure; but the

out, the crown will sink so much as to cause a 1'a. Bridge.pid increase of curvature on each side in its imme- ldiate neighbourhood, w hich w iII bring the intradosup to the curve of equilibrium , or even a'bove it, theform of this curve being little altered by the changeof that of the arch. T11e m id dle rem ain s fil"m , b e-c au se th e p re ssu re is p re tty e qu aJJ y d iv id ed th ro ug h-out the blocks, but the parts newly bent give wayto the unequal force, and chip a little at their inter-m d surface; but being reduced in their dimension"by the pressure, they suffer the middle to descendstill low er, an d are, consequ ently, carried dow n w ithit, so as to be relieved from the inequality of pres-sure depending on their curvature, and to transferthe effect to the parts im mediately beyond them , tillthese in their turn crumble, and by degrees thew hole structure faJls.{Plate X LII. fig. 6.)This explanation will enable us to understandsome observations and experiments which the lateProfessol' Robison has related as somewhat paloa-doxical. He says, that an arch built" of an ex-ceedingly soft and friable ston e," th e arch-stones b e-ing also too short, began to show signs of w eaknessby the stones chipping about ten feet from the mid-dle, and that it afterwards split at the middle, andfifteen or sixteen feet on each side of it, and also atthe abutments. And in some experiments on mG-dels of arches in chalk, he found, that" the archalways broke at some place considerably beyondanother point, whel'e the first chipping had. beeno bse rv ed ;" a c irc um sta nc e w hic h h e h as D ot su cc eetl-e d i n suf fi ci en tl y exp la in ing .

SECTION III,-O fthe Effict qf Friction.The friction or adhesion of the substances; em~ployed in A rchitecture, is of the m ost m aterial con-sequence, for insuring the stability of the worksconstructed w ith them ; and it is right that W P. houldkn ow the extent of its operation ; it is n ot, h ow ev er,often practically necessary to calculate its exactmagnitude, because it would seldom be prudent torely m aterially on it, the accid en tal circum stancesof agitation or m oisture tending very m uch to dim i-nish its effect. Nor is the cohesion of the cementsem ployed of much further consequence than as en-abling them to form a firm connexion, by means ofw hich the blocks m ay rest m ore com pletely on eachother than they could do without it; for we mustalways remem ber, that we m ust lose at least half of


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B RI D G E.:B t- iJO 'e , f g ra vi ty , w iJ I b e r es is te d by th e f ric tio n o r adhe-~ sion of the surfaces w lIen its direction is w ithin thelim its of the angle at which the substances begin toslid e; and it m ay be in ferrt'd fro 111the exp erim entsof M rC ouIom b and Professor V ince, that this angleis constan t, w hatever th e m agn itu de o f the fo rce m aybe, since the friction is ver): nearly proportional tothe mutual pressure of the substances. The ten-

dency of a body to descend along any plane beingas much less than its weight as the height of theplane is less than its length, and the pressure on thep lane bein g as m uch less than th e w eig ht as th e leng this g re ate r th an th e h oriz on ta l e xte nt, it fo llo ws, th at,w hen th e w eig ht begins to overco me the friction , thefriction m ust be to the pressure as the height of theplane to its horizontal extent, or as the tangent ofth e in clin atio n to th e ra diu s.T his pro perty of the ang le of repose afford s a T eryeasy m ethod of ascertaining, by a sim ple experi-m en t, th e f ri cti on o f th e ma te ri als empl oy ec :j. : t a kin g,for exam ple, a C6m mon brick, and placing it, withthe shorter side of its end dow nwards, on another,rhich is graduaIJy raised, w e shall find that it willfall over w ithout beginning to slide; and w hen .thishappens, the height must be half of the horizon-tal extent, a brick being twice as long as it isbroad: in this case, therefore, the friction m ust beat least half of,the pressure, and the angle of reposeat least 80; and an equilateral w edge ofbrick couldnot be forced up by any steady pressure of bricksacting ag ainst its sides, in a direction parallel. to itsbase. But the effects of agitation would m ake sucha w edge totally insecure in any practical case; andthe determ ination only serves to assure us, that avery considerable latitude may be allowed to thejoints of our m aterials, w hen there is any reason fordeviating from the proper direction, provided thatwe. be assured of a steady pressure; and m uch m orein brick or stone than in wood, and more in woodthan in iron, unless the joints of the iron be securedby some cohesive' connexion. It may also be in-ferred fro m tbese co nsid eratio ns, th at the directio nof the joints can never determ ine the direction ofthe curve of equilibrium crossing them , since the& iction will always enable them to transm it thethl'ust in a direction va'y in g very consid erab ly fromthe perpendicular; although, with respect to anyparticular joint, of which we w ish to ascertain thestab ility in depen dent o f th e frictio n, it w ould b e d e-sirab le to collect th e resu lt of the elem ents, o f w bich

505serv es, th at the arch w as generally co nsid ered as the B ridge.invention of D em ocritus, a Philosopher w ho lived ~som e centuries before Christ, but that, in his opi-nion, the sim plicity of the principle could not haveescaped the rudest architect; and, that long beforeD em ocritus, th ere m ust have b een both b ridg es an ddoo rs, in both o f w hich structu res the arch w as com -monly employed. There do indeed appear to besolitary instances of arches m ore ancient than t]1eep()ch assigned by M r K ing to their invention. W efind arches concealed in the walls of some of theoldest temples extant at A thens; the cloacre aresaid to be arched, not at the opening into the Tibero nly , b ut to a g re ater d ista nc e w ith iI\. it th an is lik elyto have been rebuilt at a later period far ornam ent;and the fragments of a bridge, still remaining at. R om e, bear an inscrip tio n w hich refers its erectio rito the latter years- o f the Commonwealth. But itseem s highly probable, that alm ost all the coveredw ay s, con stru cted in th e earlier tim es of G reece an dR om e, w ere e ith er fo rm ed b y lin te ls , lik e d oo rw ay s,o r b y sto ne s o ve rh an gin g e ac h o th 1'!r, i n h oriz od ~a l,strata, and leaving a trian gular ap erture, o r b y b othth ese arran gem ents com bined, as is exem plified inthe entrance to the treasury of A treus. a t. Mycen re ,w here the lin tel has a triangu lar apertu re o ver it, b ywhich it is relieved from the pressure of the. w allabove; and this instance serves to show how differ-ent the distribution of the pressure on any part ofa structure m ay be, from the sim ple proportions ofthe height of the materials above it. Some othero ld bu ild in gs, w hich h av e b een su ppo sed to b e arch-ed , h ave been fou nd, o n fu rth er exam in ation, ratherto resemble domes, which may be built w ithoutcentres, and may be left open at the summit, thc>horizon ta l cU1" lra tu reproduc ing .a t ransverse pressure ,w h~ch supports the structure w ithout an ordinarykey"stone. And this has been suspected to be theform of the roofs and ceilings of ancient B abylon.,w here S trabo tells us that th e b uilding s w ere arch ed, ov er or " c am era te d," fo r th e p urp os e o f sa vin g tim -ber: and the bridge of Babylon, which must haveb ee n o f c on sid era ble a ntiq uity , is e xp re ss ly ,s aid ,b yH erod otus, to h ave co nsisted of p iers o f ston e, w itha road formed of beams of wood only. It may how-ever be rejoined, that though a dom e' is not sim plyan arch, yet it exceeds it in contrivance and m echa-nical com plicatio n; it g enerally exerts a thru st, andrequ ires either an abu tm ent, or a circular tie; and it., .is sc arc ely p oss ib le th at th e in ve nto r o f a d om e sh ou ld !


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506 BRIDGE.B rid ge . th e mos tim po rta nt o pe l'a tjo ns , th at a re g en era lly re -

"""""'-quired to be performed in it, may be found in thenumerous Reports of the ingenious M r Smeaton,published ~ince his de~th by th~ Society of. CivilEngineers m London. 1 hey contam a body of m for-m atitm con~rehending alm ost every case that canoccur to a w orkm an, in the execution of such struc-tures; and even where they have to record an acci-d ental failu re; the instru ction they afford is not less,valuable th an w here th e su ccess h as b een m ore corn .plete.R especting the general arrangem ent of a hridge,and the number of arches to be employed, in thecase of a wide river, M r Sm eaton has expressed hisapp rob ation of a few w ide an d flat arch es, supp ortedb y g oo d abutm ents, in p referen ce to m ore numero usp ie rs , w hic h u nn ec essa rily in te rru pt th e w ate r-w ay .In a case where a long series of sm all arches w as re-quired, he has made them so flat, and the piers soslight, that a single pier w ould be incapable of w ith-standing the thrust of its arch: but in order toavoid the destruction of the w hole fabric incase ofan accident, he has interm ixed a n um ber of stro ngerpiers, at certain intervals, am ong the w eaker ones.W here several arches, of different heights, w ere re-q ui re d, h e c ommon ly r ec ommended d if fe re nt p or ti on softhe.sam e circle for all of them ; a m ode w hich ren-dered the lateral thrust nearly equal throughout thefabric, and had the advantage of allow ing the sam ecentre to be em ployed for all, w ith som e little addi-tion at the end!; to adapt it to the larger arches.H e records the case of Old W alton bridge, in whichthe w ooden superstructure .had sunk tw o feet, so asto becom ~ part o~ a circle 700 feet in diam eter, andthe thrust, thus increased, had forced the piers con-siderably out of their original situation: a strildngproof ,that the principles of the pressure of archesmust not be neglected, even when frames of cllr-p en tr y a re c on ce rn ed . ' ,M r Sm eaton particularly describes the inconve.niences arising from the old method of laying thefoundations of piers, which was introduced soonafter the Conquest, and which is particularly ex.em plified in Ll>ndon B ridge.. The m asonrycom .m ences above low water m ark, being supported onpiles, w hich w ould be exposed to the destructive al.ternatio n o f m oist'llre an d dryn ess, w ith th e access ofair, if they w ere not defended by other piles, fO l'ln-in g pro jectio ns partly filled w ith ston e, and denomi-nated sterlings; w hich, in their turn, occasionaJIy

decay, it has happened, according to late reports Bridgethat the rep airs of L ond on B rid~ e hav e often am ou nt~ '--,~ed, for m any years together, to L. 4000 a year, whileth os e o f We stm in ste r a nd B Ia ck ti'ia rs B rid


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BRIDGE.Dr idge .wh i ch had been bui lt in c of fe r- dams,w ith t he a ss is t- .~ ance of some piles, withstood the violence of theflood; and it is remarkable, that the whole bridgehas been rebuilt by a provincial architect w ith per-fect success, having stood w ithout any accident formany y ea rs .It seem s, therefore, scarcely prudent to trust anyvery heavy bridge to a foundation not secured by

piles, unless the ground on which it stands is an ab-solute rock; and in this case, as well as when pilesare to be driven and saw ed off, it is generaJly neces-sary to have recourse to a coffer-dam. In the in-stan ce of th e bridg e at H arraton , for exam ple;w herethe rock is nine feet b~low the bed of the river, M rSm eaton directs that the piles form ing 'the coffer-dam be rebated into each other, driven dow n to ther oc k, a nd sec ur ed by in te rn al s tr etc he rs , . bef or e t hewater contained within them is pumped' out. Insome cases, a d ou ble row o f p iles, w ith clay b etw eenthem , has been em ployed for form ing a coffer-dam ;but in others it has been found more convenient todrive and cut off the piles under w ater, by m eans ofpro per m ach in ery , w itho ut the assistance o f a coffer-dam.Piles are em ployed of various lengths, from 7 to16 feet or more, and from 8 to 10 inches in thick-ness, and they are com monly shod with iron. Sm ea-ton directs them to be driven tilJ it requires from 20to 40 strokes of the pile driver to sink them an inch,according to the magnitude of the weight, and thefirmness required in the work. He was in the habitof freq uen tly recommend in g the p iles surrou nd in gtile piers to be secured by throw ing in rubble stone,so as to form an inclined surface, sloping grl!duallyfi'om the bridge upwards. and downwards. In thecase of C oldstream B ridge, it w as also found neces-eary to h ave a p artial d am , or artificial sh oal, throw nacross the river a little' below the bridge, in orderto lessen the velocity of the water, which was cut-ting up the gravel from the base of the piles. Butall these exp edients are atten ded w ith con siderableinconvenience, and it is better to avoid them in thefirst instance by leaving tbe w ater-w ay as w ide andas deep as p ossib le, an d by m ak in g the fou ndatio ns asfirm a nd e xte nsiv e a s th e circ um sta nce s m ay re qu ire .The angles of the piers, both above and underw ater, are common ly rou nd ed off,' i n o rder to facili-tate the passage of the stream , and to be less liableto accidental injury. Mr Smeaton r~commends acy lindrieal surfh ce of 60 as a pro per term inatio n;

507the abu tm en ts, as w dl DSa tl'a I)sv el's e th ru st a ga in st \> 'rid ~.the side w alls. For the inclination of the road pass- "-"',----ing ov er th is b rid ge, M r S llleaton th ou gh t a sl.o pe o f1 in 12 not too great; observing that hprses cannottro t ev en w hen th e ascen t is m uch m ore grad ual than .th is, an d that if they w alk , they can d raw a 'carriag e.u p su Ch a ro ad as this w ith ou t c::lifficu lty : an d, in -deed, the bridge at N ew castlc, appears, for a shortdistance, to have been much steeper. But it hasbeen m ore lately arg~ ed , on ano th er o ccasio n, thatit is a great in conv enience in a cro wd ed city , to haveto lock the wheel of a loade(l waggon; that this is'necessary at all tim es on Holborn H ill, where theslope is. only 1 in 18; while in frosty w eather thisstreet is absolu tely im passable fo r such carriag es:.a nd th e d es ce nt o fL ud ga te H iJl, w hic h is o nly 1 in 3 6,is c on sid ere d a s mu~h more d esira ble , w he n it is p os-s ib le t oc on st ru et a b rid ge \y ith a n a cc liv it y s o g en tle ~SJiCTION V.-Impro'Vcments if the P ori q f L on ao u.From the study of M r Sm eaton's diversified, la-bours, w e proceed to take a cursory view of the Par-l iamen ta ry I nqui ry r es pe cti ng t he imp rovemen t o f th ePort of London, which has brought forw ards a va~.r ie ty o f impor ta nt i nf orma tio n, a nd s ugge st ed am ll1 -tip licity o f ing eniou s desig ns. T he prin cip al part ofth at w hich relates to o ur p resen t su bject is co nta!n -ed in the Second and T hird R eports from the SelectCom mittee of the H ouse of Commons, on the"im-provementof the Port of London; ordered to beprinted 11th July 1799, and 28th July 1800.W e find in th ese R ep orts some in te re stin g d eta ilsrespectin g the h isto ry of L ondo n B ridg e, w hich ap -pears to have been begun, not, as H um e teJls ifS, b yW illiam R ufu s, w ho w as k illed in 1 100 , b ut iD 117 6.under Henry n.; and to have been completed in83 years. The piles are principally of elm, andthey h ave rem ain ed fo r six centuries w itho ut m ate-rial decay; although a part of the bridge feU, andwas rebuilt about 100 years after it was begun.R och ester, Y ork, an d N ew castle B ridg es w ere alsobuiltin the tw elfth century, as w ell as the B ridge ofSt Esprit at Avignon. About DO years ago, themiddle pier of London Bridge was removed; thepiles were draw n by i1 very powerful screw, -com -monl y u se d f or lif tin g th e whe el s o f t he wa te r- 'Yo rk s;and a single arch was made to occupy the place oftw o. In co nseq uen ce of th is, the fall'w as som ew hatdim inished, and . it' w as necessary partially to ob-


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.508 B RID G E .B rir1 g~ . pm'ch ase o f p re mises, 'w as ab ou t L . 26 0,0 00 ; th at o f~-- the buHding only was L. 170,000. W e;;tmin~terBriag'e, built in the beginning .of the century, costa bo ut L . 4 00 ,0 00 .The com mittee had received an im mense varietyo f p la ns a nd p ro po sa ls fo r d oc ks , w ha rf s, a nd b rid ge s,and many of these have been pubJished in the Re-ports, together, w ith engraved details on a very am -ple scale. T hey finally adopted three resolutions re-sp ectin g th e reb uild ing o f L on do n B ridg e."1. That it is the opinion of this CQ mm ittee, thatit is essential to the im provem ent and accom moda-tion of the port of London, that London Bridgesh .o uld b e re built u po n su ~h a co nstru ct,io n as to p er-ullta free passage, at all tIm es of the tide, for ships'ofsucb a tonnage, at least, as the deptb of the riverw ould adm it of, at present, betw een London Bridgeand BIackfriars Bridge. ." 5 2. T I-.at it is tbe o pin io n of th is C omm ittee , th atan iron bridge, having its centre arch not less than

65 feet high in the clear, above high-w ater-m ark,w -iIlansw er the intended purpose, and at r.he leastexpense." 3. T hat it is th e o pinio n o f th is C omm ittee "th atth e.mos t c ?u ve nie nt s itu atio n fo r th e N ew B rid ge , w illb e .Immedl at el y aB ()Ve'8 t S av io ur 's Chur ch , ,a nd 'u pGna ,hne fpom thence to the R oyal E xchange."Jp a subsequent Report, ordered to be printed

3d. J une 1801, w e find a plan for a m agnificent ironbrIdge of 600 feet span, w hich had been subm ittedto the Comm ittee by M essrs Telford and Douglas.M r Telford's reputation in his profession as an en-g in ee r. d es erv ed ly a ttra cte d th e a tt.e ntio n o f th eC om -m ittee; but m any practical difficulties having beens?ggeste~ to them , they,circulated a num ber of que-,nes relatm g to the proposal, am ong such persons of,sc ie nc e, an d p ro fe ssio nal arc hitec ts, as w ere th e m ost,l ik el y to h av e a ff on le d .th em s ati sf ac to ry i nf ormat io n.But tbe .results of tbese inquiries are not a little hu-m iliating to the adm irers of abstract reasoning andof geom etrical evidence; and it w ould be difficult tofind a greater discordance in the m ost heterodoxprofessions of faith, or in the m ost capricious varia-ti~ns of taste, than is exhibited in the responses ofOU l'~ os t c ele bra ~e d p ro fe ss or~ , o n a lmos t e ve ry p oin tsubm Itted to theIr consIderatIO n. It w oultJ be use-less to "dw ell ,o p :th e numero us errQ f.S w it-h w hichmany of the answers abound; but the questions wiUafford us a very convenient clue for directin.,. our~ tte ntio n to su c~ s ub je ct~ 0 : ? elib era tio n a s a re !e ally

e re ct ed upon t lt e a rc lt es 0/ s tone bridg es. 01' does th e E' .'. )h I fi ' ., 'If, ~~,W a e act 'as one. rame qj lron,~vlllch can only be de. -.:..-s tr ay ed by e ru sl lin g it s p ar ts ? 1The ~istributio? of the resistance of a bridge m aybe considered as 111som e m easure optional, since itm ay be transferred from one part of the structure toan oth er, b y w ed gin g to gethe r m ost firm ly th ose p artsw hich w e ~ vish to be m ost m aterial1y concem ed in it.

But there IS a lso a natural principle of adjustm entby w hic.h the resistance has a tendency to be throw ~w~ere It can best be supported; for the materialsbem g alw ays m ore or less com pressible, a very sm ItHchange of form ? 'm p~oged to be equal throughoutth e stru ct.u re , W JIIrelIev e th ose p arts m ost w hich areth,e m ost strained, and the accom modation will bestdl m ore effectual w hen the parts m ost strained un-dergo t~le greatest change of form. Thus, if theflatter nbs, seen at tile upper part of the proposedst.ru cture, su pp orted an y ~ ate rial p art ? f its w eig ht,th ey w ou ld u nd ergo a c on sid era ble lo ng Itu din al com.p re ssiO !~ , an d b ein g s ho rte ne d a little , w ou ld n atu ra l-ly descend very rapidly upon the more curved, andco nseq uen tly stron ger p arts b elo w, w hic h w ou ld so onreliO \'e them fi'om the load jm properly a!Iotted tothem ; the abutm ent w ould also give w ay a little, andbe fOl:ce? out, by the greater pr~ssure at its upperpart, w hIle the low er part rem am ed alm ost entirelyunchanged.It is, however. highly important ,that the workshould, in the first instance, be so arranged as best tofu lfil th e inten ded p urp ose s, an d e sp ecially th at suc hparts should have to ,support the weight as are ableto do it w ith the least expense ,of lateral t.hrustwhich is the great evil to be dreaded in a work ofthe se g ig an tic d im en sio ns, th e m ate ria ls th em selv esbeing scarcely ever crushed, when the arch is of aproper form ; and the failure of an ironbridO 'e byh f I " b

,t e want 0 u tUllate resIstance of its parts to a com.pressing force, being a thing altogether out of ourcontem plation; and it is obvious that the greater thecurvature of the resisting parts, the stnaller w ill bethe lateral thrust on the abutm ents.W e m ay, therefore, sufficiently answ er this ques-tio n, b .y sa yin g, th at .th: w ~ole fram e of thepropo-sed brIdge, so far as It lIes m or near the longitudi-n al d irection o f th e arc h, m ay o ccasio na lly c oop eratein affording a partial resistance if required; but thatthe principal part of the force ought to be concen-trated in the lower ribs, not far rem ote from the in-


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B RID G E. 509B li< lg e. th at th e o rd in ates o f th is c urv e a re a lto geth er d if fer -~ ent from the Ol'dinates which have hitherto beenconsidered by theoretical writers. It m ay be im a-f.1:inedhat this difference is of no great im portancein practice; but its am ount is m uch greater than thedifterence betw een the theoretical curves of equili.brium , determ ined by calculation, and the common-est circ ular o r e llip tic al ar ch es.W ith respect to the alternative of com paring tIJebridge w ith m asonry or w ith carpentry, w e m ay sa)',that ,the principles on which the equilibrium ofb rid ges is ca lcu la te d, a re altQ ge th er elem en tar y, a ndin de pe nd en t .o f an y fig ur ativ e ex pr essio ns o f strain sand mechanical purchase, which are employed inc on sid erin g m an y o f th e arr an gem en ts o f ca rp en try ,and which may indeed, when they ar~ accuratelyanalysed, be resolved into forces opposed and com -bined in the sam e manner as the thrusts of a bridge.I t is, th er efo re, w ho lly u nn ece ssar y, w he n w e in qu ireinto the strength of such a fabric, to distinguish thethrusts of m asonry from th e strains of carpentry, th elaw s w hich govern them being not only sim ilar butidentical; except that a strain is com monly under-stood as im plying an exertion of .cohesiye force, andw e have seen that a cohesive force ought never to becalled into action in a brid ge, since it im plies a greatand unnecessary sacrifice of the strength of the m a-terials em ployed. If, indeed, .w e w anted to cross am ere ditch, w ithout depending on the firm ness of thebank, we might easily find a beam of wooa or a bar.of iron strong enough to afford a passage over it,

unsupported by any abutment, because, in a sub-stance of inconsiderable length, w e are sure of hav-in g more strength than we require. f3ut to ~sertthat an iron bridge of 600 feet span I" is a level' ex-erting a vertical pressure only on the abutm ents," isto pronounce a sentence from the lofty tribunal ofrefined science, w hich the sim plest w orkm an m ust.teel to be erroneous. But, in this instance, the er-ror is not so m uch in the com parison with the lever,as in the inattention to the mode of fixing it,: for alever or beam of the dimensions of the proposedb rid ge, ly in g lo ose ly o n its ab .u tm en ts, w ou ld p ro ba-b ly }} eat least a hundl'ed times weaker than if itw ere firm ly c on nec ted w ith th e ab utm en ts a s a b rid geis, so as to be fixed in a dete1'nJinate direction.And the true reason of the utility of cast iron forbuiJding bridges, consists not, as has often been sup-posed, in its capability of being united so as to actlike a frame of carpentry, but in the great resist-

from a circular or parabolic arc, in consequence of .Bridge.the greaf inequality of the load on the different-~parts; and there seem s to be no great difficulty inform ing a firm connexio n betw een a nm "row b ridgean d a w id er a bu tm en t, w ith ou t th is. in co nv en ien ce.The lateral strength of the fabric, in resisfing anyh oriz on tal fo rce , w ou ld b e amply su fficie nt, w ith ou tthe dilatation at the ends. Perhaps the form wassuggested to the in ventor by the recollection o f thepartial failure of an earlier w {)rk of tbe B am e kind,wh ic h h as b ee n fO! ln d t o d ev ia te cOl1s id er a: bl yf ro l1 lt he v er ti ca l p la ne i n'wh ic h i t was o ri gi na JJ y s it ua te d:but in this instance there seem s, if we judge fromthe en grav ing s w hich have be~n published, to havebeen a total deficiency of oblique braces; and theab utm ents appear to have been. som ew hat less firmth an cou ld h av e b een d es ire d, - since one of themc on ta in s a n a rc h a nd s ome war eh ou se s, i ns te ad ' o f b e-ing com posed of m ore solid m aso nry. (P late X LlI~f ig . 9 .)QUESTIONnI. In ' .,h at p ro po rtio ns 8 ko uld th ew ei gh t b e d is tr ih u te df to 7l l t he t en tr e t o t he abu tm ent s;to m ak e t h e a rc h u nifo rm ly s tr on g?This q ue stio n is s o comp reh en siv e, th at a c omple te .answer to it would involve the whole theory ofb rid ge s ;ttn d it w ill b e n ece ssa ry to lim it o ur in vesti-g atio ns to a n in qu ir y w heth er th e stru ctu l'e ,r.e pre -sented in the plan, is actually such as to afford auniform strength, or w heth er any alterations can bem ade in it, com patible w ith the general outlines ofthe proposal, tQ rem edy any im perfections w hichm ay b e d isc ov er ab le , in th e a rra ng em en t o f th e p res.sure.There is an oversight in som e of the official an-sw ers to th is q uestio n, fr om q uarte rs o f th e 'v ery .first'resp ecta bility , w hic h r eq uire s o ur p articn la r a tten .tion. The weight of the different parts' of tIleb ri dg e h as b ee n s up po 's ed t o d if fe r s o mat er ia ll y f romth at w hich is re qu ire d f or p ro du ci'n g an . e qu ilib riumin a circular arch of equable curvature, that it baabeen thought im possible tQ apply the principles ofthe theory in any m anner to an arch so constituted,at the sam e tim e that the structure is adm itted to .'beto le rab ly w eB ca lcu la te d to stan d, w ben co nsid eredas a frame of carpentry. The truth is, that it is byno m eans abso lutely necessary, nor often perfectlypracticable, tbat the m ean. curve of equilibriumshould agree precisely in its form w ith the curves li-m itin g th e e xtern al su rfa ce s o f.th e p arts b eaT in g th ep re ss ure, e spec ia lly when they a re suf fi ci en tlyextef l-


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Distance:1:. ,- crseds ine of Vc rs ed s in e o f Ordinate y.the'intrados. the c i rcu la r a r c.50 1.73 1.71 1.34lOO 6.94 6.82 5.g8]50 15.66 15.43 13.00

!lOO 28.13 27.70 24.5025 0 44.42 43.81 41.01300 65.00 64.00 64.00

510 n RID G E.Brjd~f.'.grea test p O E & i 1 > J e security; and if this security is not~ deem ed sufficient, the w hole arrangem ent m ust bealtered. .' 1C onsidering the effect of the dllatatl(:~n at t.leends in increasing the load, we l11ay estim ate thedepth of the m aterials causing the pressure at theabutments as about three times as great as at thecrow n; the plan not being su!fici~ ntly m in~te ~ o a f-ford us a m ore prec.ise determmatlO n; and It W Ill bequite accurate enough to !ake w = a. + UX 2 (Prop.S.) fot the load, w becomIng = 3a when x IS3001fe et, w he nc e 9 0,0 00 b = 2a , an d b = 45,000 a; weI h 1 2 + 1 a ,4 fo r th e v alu elave t en m!J = 2 ax '540,000 .1:o f th e o rd in ate . Now the obliquity to the h?rizonb ein g in co ns id era ble , th is o rd in ate ~ ill n ot u ltIm ate -ly be much less than the whole helg~t of the arch;and its greatest value m ay be called 64 feet; conse-quen tl y w :hen x - 300, we have 64 nt = ~ a X90,000 + t a X. 90,000, and the radius of curva-

?n . h ' l hture at the vertex l' = - = 937.5 feet, w let earadius of the intrados ia 725 feet, and that of acircle passing through both ends of the cur~e ofequilibrium , as w e have supposed them to be situa-ted , 7 35 feet. H en ce,?J b ein g= 1:75 x2 (1 +-2 - X2 ) ', w e m ay calculate the ordinates at dif-270000ferent points, and com pare them with those of thec ir cu la r cu rve s.

Hence it appears that, at the distance of 200 feet

its form , if the load were of necessity such as has Bridge.been supposed. ~QUESTION4. Wha t p ressu re w ill ea ch p art rith ebridge 1.cceive,supposing-i t divided in to a n y p:i,Jennumber if equal .sections, the weight qf the middlesection bein!f given. A/ld on what part,~, and witltw /w t force , ': 'w iL tl te whole ac t ' upon t lt e abutmen ts?It appears from the preceding calculations, thatthe w eight of the" m iddle section" alone is not sur.ficient for determining the pressure in any part ofthe Jabric ; although, when the form of the curve ofe qu ilib rium h as b ee n fo un d, its ra dilis o f CU l'v atu re a tthe summit must give at once the length of a sim i-lar load equivalent to the lateral thrust; and bycom bining- this thrust w ith the w eight, or w ith thedirection of the curve, the oblique thrust at anypart of the arch may be readily found. Thus, sinceat the ab utment w = a + bx 2 = 3a, an d bx 2 = 2a , -1 a Q 1 b X4 dyw e h av e y = ---x. + - - , a nd-d ' t he t an ge nt .2 In 12 'In Xa 1 bof th e inclination , becom es = - x + - _:;;3=3max 2 ax 5 x 5 3 00 S--, - + - - = - -= -. -- -- = ~ = .5333;conse.nt ;) m


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B RID G E.B rid ge . D is ta nc e fr .~ 10 FEETf2 025304050

Ordinate y..7G3.125.137.7115.8131.00

M iddle of theArch-Stones.,.go3.726.128.7516.8131.00Hence it appears that the greatest deviation isabout 30 feet from the m iddle, w here it am oUnts toa little more than a foot. But if we suppose thisdeviation divided by a partial displacem ent of thecurve at'its extrem ities, as it w ould probably be inreality, even .if the resistance w er~ confined to t~earch-stones, It w ould be only about half as great Inall th ree places; and even this d ev iatio n w ill redu ceth e stren gth of the ston es to tw o-thirds, leav ing th emhow ever still m any tim es stronger than can ever benecessary. The participation of tIle w hole fabric,

in supporting a share of the oblique thrust,' m ightm ake the pressure on the arch-stones som ew hat lessunequal, and. the dim inution of their J3trength lessconsiderable; but it w ould be better that the pres-sure should be confined alm ost entirely to the arch-s tones , a s t end ing les s to inc re as e the hor i~ontal .t hrus t,wh ic h i s h er e c omp re ss ed b y 'I ll :: :: :4 36 , Im .p l; v:mgt~eweight of so m any square feet of the 10ngItudmalsection of the, bridge; while, if we determined itfrom the curvature of the intrados, it w Quld appeart o'b e only 56a ::: ::36 8. .In . this calculatiol), the obJique directipn of thej oi nt s, a s a ff ec ti ng t he l oa d, 1 16 sn ot b ee n c on si de re d;b ut its e ff ect m ay be e stim ate d b y mer ely su pp osin g th espe ci fi c g ravi ty :o f the ma te ri al s to be somewha t inc re as .ed. Thus, since tlle back of each arch-stone is abouto ne -e ig hth w id er th an its lowe r e nd , th e w eig ht o ftllem aterials pressing on it w iIJ be ab out o ne.~ ixteenthgreater than w ould press on it, if it w ere of unifonnthickness; and this increase w ill be very nearly pro-p or ti on al t o ~v , the whole load at each part; so thatit w ill only affect the total m agnitude of the thrust,

w hich, instead of 436, m ust be supposed to am ,ountto about 463. If also great accuracy w ere required,it w ould be necessary to appl'eciate the. differentsp ec ific g ra vitie s o f th e v ario us m ate ria ls c oI istjti1 t.i1'!gthe load; since they are not altogether hom o-geneous; but so m inute a calculat}on. is x;ot neces-sary in ord(:r to show the general dlstnblltlop of the

511pressure to be supported at each poin~ or t11e curve J\ridge.must obviously be equal to the weight of the mate- ~,rials interposed betw een' it and this D ew summit ofthe. curve. N ow , in order to find w here the'thrustis horizontal, w e m ust divide the arch into tw o suchport ~' 0 ,s, that their difference, actipg at the end of alever f the length of half the span, that is, of thedista ce from the abutment, m ay be equivalent tothe given w eight, acting on a lever equal to its dis-tance from the other abutment, to which it isn ea re st; c on se qu en tly th is d if fe ren ce must b e to th ew eight as the distance 9f the w eight from the end tohalf the span; and the distance of the 'new sum mit,of the curve from the m iddle m ust be such, that thew eight of m aterials. intercepted betw een it and them iddle shall be to the w eight as the distanc.e of thew eight from the end to the w hole span; and. the tan~g en t of the in clin atio n m ust ev eryw here b e increas-.ed or diminished by' the tangent of the angle atw hich th e lateral thrust ,w ou ld sup port the w eig ht o fthis 'po rtion 'of the m aterials; ex cep t imm ed iatelyunder the weight, where the two' portions. of thecurve w ill m eet in a finite angle, at least if w e sup-pose the w eight te be collected in a single point.. If, for example, a weight of 100 tons, equal tothat of about 10 feet of the crown of the arch, beplaced half-way between the abutment and themiddle; then the vertex of the curve, where theth ru st is h or iz on ta l, w ill b e r emov ed fGAee t towar dsthe weight ; but the radius being 937.5 feet; thetangent of the additional inclination w ill be 29 ,57 ".a= -71 , a nd e ach o rd in ate o f th e CUi'vew ill be in-S 5creased 2- of the absciss, ~ckoning from the place-87 5of the w eight to the rem oter abutm ent ; but betw eenthe w eig ht an d the nea,rest ab utm ent, the add itio nalpressure at each point w ill be 10 - 2.5 = 7.5feet,consequently the tangent w ill be 2-, and the addi-, . U5 ,tions to' the ordinates at the I\butm ents w ill b,e :~~an d 15 , e ac h eql1alto a foot, and at t!ie summit1 f G 5 ~ .


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.512 B R ID G E .Bridge. dim inish its strength; w hile, on the opposite side,~ immediately under the weight, the ordinate 13 -

15 0 = 1~.6 w ill be reduced to 12.45, and the curve37 5raised between six and seven inches, which is ac han ge b y..n o m ea n! 1 to b e n eg le cte d in c on sid er in gthe resistances required from each part of the strac-ture. We ought also, if great accuracy were re-quired, to determ ine the effect of such a weight inincreasing the lateral th rust, w hich w oul~ affect in f1slight degree the result of the calculatIOn; but Itwould not amount, in the case proposed, to morethan one-eightieth of the whole thrust. . ."It is obvious that the tendency of any additIO nalweight, placed near the middle of a bridge, is. t.ostraighten the tw o branches of the curve of eqU Ili-b rium , an d that, if it w ere su pposed infinite, it w ouldconvert them into right lines; provided, therefore,that such right lines could be drawn without c.om-inO ' too near the intrado s at the haunches, the b ndgewguld be in no danger of giving way, unless eitherthe m aterials w ere crushed, or the abutm ents w ereforced out. In fact, any bridge well constructedm ight support a load at least equal to its ow n w eight,w ith less loss of strength than w ould arise from som esuch errors, as have not very uncommonly been com ~m itted, even in w .orks w hich have on the w hole suc-ce ed ed to le ra bly w ell.QUESTION6. Suppos ing the b ridge e :r :e cl~tedn ~hehest m anner, W hat horizontal firce w zlt zt requzre,w he n a pp lie d to a ny p a1 "tic ula r pa rt, to Q vertu rn it, o rpress it out if'th evcrtical plan e?. I f ilie bridge be well tied together, it m ay be cotr~sidered as a single m ass, standing on its abutm ents;its m ean breadta being about 80 feet, and its w eight10,100 t011S; and such a m ass w ould require a late.ral pressure ,at the crow n-of the arch of about 7000tons to overset it. Any strength of attachment tothe abutm ents w ould, of course, m ake it still firm er,and any w ant of connexion betw een the parts weak"er ; and since the actual resistance to such a forcem ust depend entirely on the strength of the obliqueconnexion between the rib, it is not easy to de-f in e its m ag nitu de w ith ac cu ra cy :, b ut, a.< ;P ro fe sso rR obison has justly rem arked, the strength w ould beincreased by causing the braces to extend acr6S S th ewhole breadth of the .hafr arch. The single ribs, ifw holly unconnected, m ight be overset by an incon.

h e m a de ill th efO rtI! o f a n ellip tic al m "ch , Wha t 'Wou ld Blid"e.h e th e d iffe re nc e in d fec t, a s to stre ng th , d ura tio n, c on - \.,r."""ven ienc ;, and expense s?The question- seem s to suppose the weight of them aterials to rem ain unaltered, and the parts of thestructure, that w ould be expanded, to be m ade pro-p ortion ally lig hter; w hich cou ld n ot be exactly true,though tnere m ight be a com pensation in som e otherparts. Granting, however, the weight to be thesam e under both circum stances, if the oruinate!l atthe. end be increased in the proportion of 64 toabout 75, the curvature at the vertex will be in-creased, and the lateral thrust diminished in thesame ratio, the 9470 tons being reduced to 8800.The additional thrust occasioned by any foreignweight w ould also be lessened, but not the verticaldisplacem ent o f the cu rve derived from its pressu re;and since the whole fabric might sarely be madesomewha t lig hte r, th e lig htn ess w ou ld a ga in d im in ishthe strain. The very least resistance that can beattributed to a square inch of the section of a blockof cast ir911; is about 50 tons, or somewhat morethan 100;000 pounds. It is said, indeed, that 1\:11"W illium R ey nolds found , by accurate exp erim :en ts,that 400 tons were required, to crush a cube of aquarter of an inch, of the kind of cast iron calledgun-metal, which is equivalent to 6400 tons for asquare inch of the section. But this result so farex.ceeds any thing that could be expected, either-from expedm ent 01' from analogy, that it w ould be-im prudent to place m uch reliance on it in practice;the streng th attributed to th e m etal b eing equivalent.to th e pressu re.of a colum n 2 ,280 ,000 feet in h eigh t,w hich w ould com press it to about four-fifths of itslength, since the height of the m odulus of elasticity(Prop. G.) is about 10,000,000 feet. The greatestcohesive force, that 11as ever been observed in iron-or steel, does not exceed 70 tons for a square inclrof the section, and the repulsive force of a hom oge-neous substance has not been found, in any other in-stance, to be m any tim es greater 01' less than the co-hesive. There cannot, however, be any doubt thatthe oblique thmst, which amounts to 10,730 ton&,would be sufficiently resisted by a section of 215square inches, or, if' w e allow ed a load am ounting toabout one-third only of the whole strength, by. asection of 600 square inches ; and since each .ftot ofan iron-bar, an inch square, weighs three pounds,and the whole length of the arch nearly a ton, the


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n RID G E.BJicJge.n the "crew as 1 to rn , Hnd the: pressure on the~ screw to the actual pressmcon the substa.nce as rtto h ,~ aU in g t hi s p re ss ur e x, the pr'es6ure on the

d fi " nx b I '~ crcW 'w ill b e n:c, an the nctlOn --; ut t J lS re-1n . .s!sta .m :e w ill tak e fr om th e g ro ss u ltim ate p res su re fH force: w hich is to the friction itsc!l~ as the veloci-ty of the pal'tf; slidin.g ~n each otb~er is to the velo.cll)' o f th e part prOCl;Jcm g t he ultlllli:te p r,zssure, aprop~r~ion w ~ich we m ay can 1) to 1; and the for~eremall1mg will be the actual pressure; that IS,p~. m . .f - - = x, and:!= - f. In t he se exper !-m m+pnroents, the gross force}; as supposed to be exertedon the iron, was 10tons; the friction ~, wa s p ro ba bl yabou!; i, the screw not having been lately oiled; thedistance of the screw from the centre of m otion w asto the length of the whole vice as :3 to 4, whence nwas :} , a nd p was 8.1


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514 B RID G E.Bridge. any gt!1eral com parison w ltl~ tha.t 'of the m odelo~There is an Es,~ay of Buler m the Ne tt ) Conznu :: n~taries qf the ]loyd Academy ?f Petersburgk (Vol.XX. p. 271.), relating expressly to the mmle of'judg in g o f t}1e strength o f a brid ge ft'om ,1.1 w od el..bU ,t it c on ta In s o nly a n e leme nt ar y c al cu la tIOn , a pp h-cable to ropes, and sim ple levers, and by. r.o m eanscOI I\p .r eh en din g a ll th e cir cumstan ce s th at re qu ir e te )

h e ,c on s~d\ ') re d.i n th e s tr uc tu re o f a n a ~'C ;l ,QU;Ji:STION0. B y w ltr.t m e a i ! s m ay ~ h i 'P s be tes td ir ec te d i n t he m id dl e s tr eam, o r p rc 1)e nt ed fr om d ri u-inp , to the , gide , and ,~t ri lc i17ghe m 'ch; and what . 'Wou ldbe the co~e{j1J.etl(.e ,qf'sucha stroke?For the direction. of, ships, Professor R obi~on'ssuggestion seem S the sinlplest and best, that. theym ight be guided by m eans ora sm all anchor, dragg eqalong the bottom of the rivel'. ,The stroke of a shipm ight fracture the outer ribs, if they w ere too w eak,Qut. could scarcely affect the whole fabric in anym aterial degree, supposing it to be firm ly securedby oblique bars, crossh1g from one side of the abut-m en t to the o ther side of the m idd le; and if still great-er firm ness w ere w anted, the braces m ig ht cross stiJI.m ore ob liquely, and be rep eated fro m space to space.. A ..$hip Il1{Ivicg w ith a velocity of three. m iles inanho.u:r, or ab.out four ieetin.~ second, would bestop ped .by a force equal to her w eig11 t,w hen she hadadvancecl tJvee incl~ es w ith a l'etarJed m otio~ ; andtl1ebridge could not very ea.sily w ithstand, at any'onep9int, aforce mucngre.ater than such a shockofa, ~gp ship, if it W ere direct, without being dan~geroul!lystraineu. But we must consider that 11.larg cf;h.ipcouJd nev :er strike the bridg e w ith its fullforc.eL aM thflU he m !ist w ouM be m uch. m ore cil$ilybr~kep. than the bridge. T he inertia of the ,pa-l'tsofthe, br.i4ge, and of. the heav,'m aterials laid on it,~oLlld-en8ble it to resist the stroke of a sm all m asswi thg~eat ,1 J) .e cAa I1 ic it l. a dvan tage .. . Thus the ine rt iaof. a1;13J,1.vi!.aid O I;\.a ~an's chc>!t,enabl,cs him to8!1BP9J:t,.a:Jiow..o ,n t he .. R l) ,v il ,wh ic h wouh l.b e ~ fa ta lwitJlQ~;. ,$~han iI1 terpQJ:>it ion , the mGlJ ,len tum com~'m uui~ c:;d to: the..g r~ atel' w eigh t, bein g alw ays lesstb~ twice th e; m ~rne:n.tum of the sm aU er; and ;th issl:)J~ 1m cre ~e o t'.m c.n peJ:lt\lID b ein g. atte nd ed b y aD;LUchg re at~l ' d~crea l! e, o f. .c nc rgy o r impe tu s, .which ,,is expr.essed by thepl:oduct of the m llss into thes q~ ar e o f t he ~'e }o cit y, .\ 1] (1wh i~h .i s s ome time s c al l-ed t1)c asc,ending, orp~netrating fm 'cc, since theheig ht o f ascen t. or d epth of peneU 'atio .n is l)ropo r-

S ince this q UeR tiO lll'dates entirely to tbe !ccal' cir- B ridge.c umst an ce s u f t he : b an ks o f t he Th! J.me s, t he p~~non8 , -- y" "I ft J,jto w hom it h as b ee n r ef en ed , h av eg :e ne ru .H y l1 pp e:d edto th e stab iJity o f S t S av ia ur 's C hu rc h, in a n eig hb ou r.ing s ituat ion , J I .Sa prol lf "f the aH hm ati';e. A nd it, do e~ ;not appear that there hav e been any in stan ces of a fail."re ( )f ni le s wei l d ri ve n, i n a mode ra te ly f av on ra bl ,~ s oi l.Profe;wr Rubison, irideeJ, asserts thvJ the flrm estp ilin g w i!! ;:ie hi in tim e to a p re ssu re c () ntin ~] (idw ith .out interruption; but a consideration of the ger",ratnature of friction and lateral adhesion, as w en as theexperience of ages in a m ultituue uf structures actll-aH y erected , w ill 1 10t a H ow us to adop t the ass~rtionas univer~aH y true. W hen, in{leed; the earth is ex,.tremely soft, it would be a4visable to unite it intoone mass for a large extent, perhapg as far as 100yards in every direction, for such a bridge as thatunder d is cu ss ion, b y b eams r ad ia tin g f rom th e a b! .!t-m cnts, resting on short piles, w ith crn8-'>pieces in-terpcl'sed; since w c m ight com bin e, in this m annei",the effe,ctof a w eight of 100,000 tons, ~hich couldscarcely eyer p rod uce a lateral adh es.io n. o f less thanS'w ,OO O,eveu if the m aterials w ere sem ifitiid; fQtthey would afforu this resistance, if they were ca~pab.1e o f stana t d iff ic ulty ill th j;),.c ()n ,struction of sllch a C~l1tre. When the bridge atWe -/ irmou th wa s e re ct ed ".. t he c cp tr ew .a ~ s up pc ,'I I't edby pU es and standards, w hich suff~red ships tQ pl.\.SSb e,tw ee.n th em . w ithout interruptio n, an d a sim iI:!-J:'ar ra ng em en t m it;h t b e m ad e in th e p re se nt:ca sewithequa \ faejJj ty .


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n R ID G E .~ r i d g e . jn dg e-s ,:a s ( ;n :b in in g,in tb e g re ate st d eg re e, t?C~ propertles of I;ardness a~dtoughness; the whItebeing eonsid'Jred as too brIttle, and the grey as toosoft.Dr Hutton> however, and M r Jessop, prefer,the grey; lind if we allow tho strength of the gunAncta! to be at all comparable to that ,which ,MrR eyn olds attribu tes to it, w c m ust also acknow ledg ethat a m uch w re ve ry p ra ct ic al p ur po se , :


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516 "'0 R I D '" 'e . ..D ~.itJ.Bridge. c u m s l a n c e s q f i l t e c a se , a g re e a b le to tIle Rewlutio7!s'if~ the Comm ittee, as sttZted at the conclusioa qf their

Third R eport, is it gonr .(Jpillio.n, tlw .t (J1!?rch if 60 0.f ee t~ in t he .s pa n, a s e xp re ss ed li t tile drtl'WzngsprtJdlt~ced hy Mes. !r s Te lf tn 'd and Doug lr l. !, @r the s il ln cp lan ,'Withany i11lpro~'emento u m a y b e .w g o o d as.to pointou t, i s p ract icab le and ad~. is ab te , tmd - capab le :4' beingmade a dur ah le e di fi ce ?T he answ ers that h av e been returnE :.> do this qu es~tio n ar e a lm ost u niv er sa l!y in th e af firma tiv e, th ou ghd ed uce d'f rom v er y d isc or da nt a nd in co nsis ten t v i2wsof tbe subject. The only reasonable ,(loubt relatesto tbe abutments; and with the precautions whichhave been already m entioned in,the answer to the11 th que3tio p,. there.w ou ld b e no ,insu perable d iffi.c ul ty ,i n ma .k in gt he a b.u tme nt s s uf fi ci en tl y f irm .Q qE sT ioN 2 1. Does t ll e e st ima te , cO'f /! !1 !u ni ca te dherewith, according to your judgment, grea tZIJ,xceedor fall shQ Tt if th e p ro ba ble ex pe ns e q f e xe cu tin g tlte

plan proposed: specif9ing tlte general gt'O u nds qr youropi1tion 11"T he etJtim ate am o.unts to 14.~6Q,289; and it hasg eDerA11y,b e~ I) ,o ns id er ed a s b el ow . t he p ro ba bl e e x~pense. ,The abutm ents are set dow n at.L . 20,000:;but they would very possibly require five' tim es asm qchi to ,.be 'properly .executed; w hile som e otherp art3 of tbe w qrk, by a m ore jud icio u!\ distribu tio n ofth e f Pr,ce s c on ce rn ed , m ig ht ,s af ely . b e m ad e so muc h~ jg hter, as co nsid erably to lesse;n th e ex pense of thew ho le f ab ric " w ith ou t... a ny d im in utio !\. eith .e r o f its

b eauty 9 r, o ri ts , st a. bi1. iJY ,~EC'1 'ION'VI , .Modern l listor;1JqfBri ilges ..

The w hole series of the questians, w hich w e haveb een con siderin g, are. fully as in teresting , at the pre-~ent moment, 'as they were at the tjme when theyw ere circQ.lated by the. Com mittee of the House nfCOro~8. The practice of building iron bridgesh as b ee n p ro gr .e ss iv el y g ai ni ng g ro un l,l , ever. s in ce i ts:6l'8t introduc~ion..in 1779, by M r A biah D arby ofColebrook.D ale. M r WUson, indeed, w ho assisted~{r BurdQ ~in the erection


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B RID G E..B rid ge.. afterw ards in a brid ge o f abo ut 18 0 feet sp an, w hichI.,-..~ was erected on the Tees at Yal'm . In 1802 Ol~1803,

an elegant iron bridge, of 181 feet span, and 16trise, was erected at St!1ines. Its general form re-sembled that of the brIdge at W earmouth, but them ode of connexion of the parts w as som ew hat differ-ent. In a short time after its completion, it beganto sink, and so,m e of the tranverse pieces broke, in'consequence of the change of form . U pon exa~ina-iion it was found that one of the abutments hadgiven way: and when this was repaired and madefirm er, the other failed. The abutm ent was pushedo utwa rd s h or iwn ta ll y, w it ho ut a ny ma te ri al .d er an ge -m ent of its form or direction ;. a circum stance w hichcould not have happened ifits weight had been suf-ficiently great: but .the architect seems to havetrusted to the -firmness of the iron, and the excel-,Ience of the w orkm anship, and to have neglected the"c alcu latio n. o f th e la ter al th ru st, w hic h it is o f so muchimpo rta nce to d ete rm in e. .M r R ennie has executed several iron bridges w ithsuccess in 'L incolnshire; one at Boston. over theW itham , of which the span is 86 feet, and the rise 5~(lnly: but the 'abutm ents being w ell .constructed, it11as stood securely, notw ithstanding the fracture ofsome of the cross pieces of the frames, which hadh-een' weakened by the unequal contraction of -them ~tal in co oling . .A t B ristol, M essrs Jessoperected'two iron bridges, of 100 feet span, rising 15;, eachof them contains 150 tons of grey iron; and the ex-p en t! e o f e ac h was a bo utL .4 00 0. The co ns tr uc ti on .a p-pears to be sim ple and judiciou s. (P late X LII. fig. H ..)M r T elford h as been em plo yed in the constructionof several aqueduct bridges on a considerable scale.One of these w as cast by M essrs Reynolds, and com -pleted in 1796. near W ellington in Shropshire: it isJ 80 feet long, and 20 feet above the water of the'r iv er,_ be in g 'S up po rted OR iro p p illa rs. A no th er, s tilllarger, was cast by M I" Hazledine, for carrying theE llesm ere canal ov er the river D ee, at P on tcy sylte, inthe neighbourhood of Llangollen. It is supported,126 feet abQve the surface of the river, by 20 Stonepillars, and is 1020 feet in length, and 12 feet w we.(Plate X LII. fig. 12.) ,In France, a light iron bridge, for foot paSsengersonly. was thrown across the Seine, opposite to thegate of the Louvre, in 1803. It is support~d 'bystone piers, which arc too narrow to withstand theeffect 9f an accident happening to any part of the

5.17m ore elegant, and it has theadvantsge of a; greatet Bri~g~-so lid ity in th e b Io ck s su pp or tin g th e p rin cip al p art o f~ ,the 'pressure. (PIate X LIII. fig. 2, 3.)T his ad va nta ge ch ar acte rize s a lso 'v er y- stro ng lythe m asterly design of M r R enhiefor tbe structureabout to be erected at the bottom of Queen. Street,C heapsid e, opp osite to G uildh aH , und er the nam e o fthe Southwark Bridge., It exhibits an exceHentsp ec im en o f f irmn ess o f mutu al ab utm en t in th e p ar tsconstituting the chief strength of the arch,w hicnhas been show n ill this essav to b e 8 0 essen tial to tIlesecurity of the w ork, and 'w hich the architect hasprobably been in great measure induced to adoptfrom his practical' experience of the com parativemerits of different arrangements. A plan of thebridge w as in February last m ade public in theR e-pertory of A rts; a w ork w hich am ply desei.'vestheencouragement o f aUthose who wish to p,romot~thediffu sion of useful inform ation : an d' th e m agn itu deof the object i$ such, as to justify our entering'm tG 'some det ai ls o f cal cu la ti on respect ing the p re ss tt reand strength of the different .parts of the fabric.foundea on a pal 't ic ularac count o fthe ir 'we igh ta .a iJ ddim ensions, w hiehhas not yet been m ade public.(Plate,XLIII. fig.4, 5,6.) . . . .';An act of Parliament fur the erection "Of thisbridge was passed in J:811 ; but it'w as notbi!guatill 18 14 ; th e act h av ing directed that n e op eratio nssh ou ld b e c ommen ce d, 'u ntil'L ;.3 00 ;0 00 ~! )u t o f th e'required L .400,000, should berrosed by subscrip-tion. T he subscribers are allo wed to receive teJi pe rcent. annually on their shares,and the rem ainder ofthe rece ip ts is to be l aid by ,and to accumula te , un ti lit sh all b ecome su ffic ie nt to p ay of f to th e p ro pr ieto rsthe d oub le am ou nt of. th eir sub scrip tions, arid afterthis tim e the bridge is to. rem ain. open, w ithoU t anytoU. A c on sid era ble .'p ar t o f th e' ir on wor k is a lr ea qycast; by M essrs W alk ers of R ot her h am . T hem id dlearch is to be 240 feet in ii!pan, the side arches 21:0feet each. T he abutm ent is 'of ':firm . masonry, con-n ec te d b y d ow els ,. t o p l:e ve nt its slid in g; ,an d re stin gon gratings of tim ber, supported by oblique piles.The p ie rs s ta l1d .o n fo un dlltio ns n in e o r'te n fe et b elowthe present bed .of the river, in otder to 'provideaga'instanya1terations w hich m ay hereafter takeplace in its channel, from the operation of :vari...ouscauses: and they are abundantly secured ,by. a .flooring of tim ber, resting on a great .num ber 'ofpiles.;


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x. y. Middle ofthe Blocks .30.2 1.4,1 1.4060.8 5,65 5.6791.0 13.02 ]2.89121.6 23.00 23.00

518 BRIDGE.'Bl'id~E'."'-',..-1 (B roug11 t fo rwa rd ,)Covt> ring-p la te s -Co rn ic e a nd p al is ad esR oa dw ay a nd p av em en t

Total.t. cw t.u4315152 077 5650 0Whole weight 1523 0Springing plate 1310Abutment 11,000 0Span 240 feet. Rise 24. Depth of the blocks orplates at the crown 6 feet; at the pier 8 feet.It is evident from the inspection of this statem entof the w eights, that their distribution is by no m eans

-capable of being accurately expressed by anyoneform ula; but it will be amply sufficient for the de-term ination of the thrust, to em ploy the approxim a-tion tounded on the supposition of a parabolic curve(Prop. T .); and if we afterwards wished to find theeffect of any local deyiation from the assum ed law ofthe. w eight, w e m ight have recourse to the m ode. ofca)culation exemplified in the answer to the fifthQuestion. But, in fact, that answer may of itself beconsidered as sufficient to show , that the effect ofavariation of a few tons, from the load appropriate toeach p art; w ou ld be w ho lly u nim portant.W e m ust, therefore, begin by finding the weigbtora portion of tbe arch corresponding to a quarterof the span; and the whole angle, of which the tan-. '. 24 b . 0 Itgent IS120 = .2, emg 11 18.2, its sine is .lg61;and the angle, of w hich the sine is .09805, being50 S7i, w e have to com pute the w eight of 6337.5, or78.5~.~1,o f th e a ng ula r e xte nt, b eg in nin g from th e m id -dle of the arch. A p.d this w ill b e 4S~g + 88 its+95 H + (S7lo) X .7345 = 297 tons. Now, thewe ig ht of th ec ov er in g'p la te s, c or ni ce , p aJ is ad es , r oa d-w ay, and pavem ent, are distributed throtlghout thele ng th , w ith ou t se nsib le in eq ua lity , m ak in g 8 79 to ns ;from whic11 the part im mediately above the piersmight be deducted; but it w ill be safer to retain thewhole w eight, especially as som ething m ust be al-lowed for the greater extent of the upper surface of

ocing 60.8, a' 11. !;8, a nd r = ?I t = SQ 9 f eet, th e, Bridgr.a ~radius of curvature of the curve of equilibrium at thevertex, while that of the m iddle of the blocks is 334.In order to determ ine the ordinate !/, w c have my ::::~ axf+ l~ bX4; bu t ~a x for the w hole arch is 728.2,

1 . 50an d 4; b;):~= 50; cons equen tly my = 728,~x + 8 x,the f irst portion varying as X2, and the second as X4 ;and the sum y being QS= 22.49 + . 51 , t he o rd in at e1 . .11at 4. x or 30.4 feet IS 16 X 22.49 + 25 6 X .51=1.41 ; and, in a s im i la r manner , any o th er o rd in at em ay be calculated, so that w e have,

Hence it appears that the curve of eauilibriumnowhere deviates m ore than about two in~hes fromthe middle of the blocks, which is less than onefo rtieth o f the w ho le depth .T he half w eight of. the sm aller arches is probablyabout 1300 tons, and their lateral thrust 3500; and,since the abutm ent w eighs 11;000 tons, the founda~

h bl '" 3500tion ought to ave an 0 Iqulty of -, o r m ore1 2 3 0 0than 1 in 4, if it were intended to stand on the pilesw ithout friction; but in reality it rises only 66 inchesin 624, or nearly I in 9; so that there is an angulardifference of 1 in 7 between the direction of thepiles and 'that of the thrust, which is probably a de-v ia tio n o f n o p ra ctic al im po rta nce .It remains to be in.quired how far the series of .masses ,o f so lid iron , co nstitu ting th e m ost essen tialpart of the arch, is well calculated to withstand theutm ost changes of tem perature that can possibly oc-cur to it in the severest seasons (Prop. K .) Forthispurpose, we may take the mean depth a ; :: ::7 feet ,


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B R I D G E .nridl\e. about 10,000,000 feet, this change w ould produce~ a resistance equivalent to the weight of a columnof the same substance 2258 feet high: that is, toabout three tons for each square inch, dim inishingO 'radually tow ards the' m iddle of the blocks, and~onverted on the other side into :in opposite resist-ance: so that this force wo~ld be added to the ge-neral pressure below in case of contraction, and

above in case of extension. Now , the lateral thrustis . d er iv ed f rom ~ p re ss \lre . e qu iv ale nt to a c olumnab ou t.3 29 f ee t h ig h, o f m ater ia ls w eig hin g 1 52 3 to ns,w 11 iJeth e b lo ck s th eI J;1 selv es w eig h 3 57 ; th at is, to acolumn' equal in section to the blocks, and 1400feet higl1: it, w ill, therefore, am ount to about tw otons on each square inch: consequently such.achange of tem perature, as has been supposed, willcause the extrem e parts of the abutm ents. to bear aJ ;1 re ss ur e o f f iv e. t o ns , whe re , i n t he o rd in ar y c ir cum -stances, they have only to support two. .T he ingenious architect prop oses to d im inish thiscontingent inconvenien ce, b y causing the block s to'bear som ewhat m ore st\'ongly on the abutm ents atthe middle than. at the sides,. so as to anow somelittle-latitude of elevation and depression, in the na-ture of- a joint: and, no doubt, this expedient; willprevent th e great inequ ality of pressure w hich m igbto th erwise a rise fr om th e a lter natio ns o f h ea t a nd co ld .But. it calinot be denied that there must be somewaste of strength in such an arrangementj the ex-tre.m e parts C !f the ~butm el'!ts, and of the, blocks

n ea r t hem ,. c on tr ib uti ng .v er y l it tl e t o. t h e- g en er a~ r e-sistance ;. and .w hen w e consider the. very accurate,adjustm ent o f theequitibrium throughou t the w halestl'u,cture, w e shall b e convinced th at there is no ne-cessity.,for any thing like so great a depth of ,the so-lid blocks, especially near the aputm ents; and thatthe security would be am ply sufficient if, with thesame weight of metal. they were made wider in atr an sv erse d ir ec tio n, p re ser vin g o nly th e fo rm o f:th eexterior ones on each. side, if it were thought m oreagreeable to,the eye. In carpentry, where there' i~often a transverse strain, anu w here stiffness is fre-quelltly required, w e generaJly gain immensely bythrowing m uch. of the substaQ ce of our beam s intothe depth ; but in a bridge perfectly weJl balanced,there is no advantage \\>hateverfrom depth oftjleblocks: we only want enough. to secure us .againstac cid en tal e rr ors o f co nstr uctio n, a nd ag ain st p ar tia lloads from extraneous weights ;. and it is not pro-

519sides a foot paveUl~nt of seven feet 0\1 each side. Br~dg~The arches and piers are built of large b~ocks of~~granite, with short counterarches over each pier.The haunches are filled up, as is usual in the mostmod ern . b rid ge s, b y sp an dr ils, o r lo ng itu din nl w allsof brick, covered w ith flat stones, and extending.over about half the span of the arch; the rem ainderbeing m erely covered w ith earth or grayel, w hich isa ls o c on ti nu ed o ve r t he s to ne s c ov er in g t he s pa nd ri ls ~T he hollow spaces betw een th e w a]]s:are cal"e(ullyc lo se d abo ve , a nd p ro vid ed w ith o utle ts b elow, . inord er to secU re th em from becom ing recepta,cles ofwat er , wh ic h wou ld b e i nj ur io us t o th e.d !! ra bi l,i ty .o f,the. structure. T he m ean sp ecific gravity of the m (t-ter~als . is li'u ch, t ha t a c ubic .. yal'd o f th e g ra nitewCIghs exactly two tons, of the brick work. oneton, and of the earlh a ton'and an eighth: Hence.the weight of the w hole m ay.be obtained from theannexed,statem ent. (Plate X LIV . fig. 1, 2,3;) .

Contents 0/ ' the m aterials in half an arch 0/ ' Wa-terloo i3ridge, from , the m iddle if the pierlo thecro'W n, beginningfrom the springing o/'the arch.Cubic.Ffet.H alfo fthe arch stones, " 2:5311.H alf of the in verted arch, ~5P5Squ ar e s pa nd ri l b etwe en th em" 199,t.Outside spandril walls, ,. 4$74SpilI1drils of brick, - 4 !)76 ( ~ .24~9}.Kii-belaofthe brick spilndri ls , / 1~7.fFIat stone cover~.' . 969 .Earth,. lO~60(=:5771}Foot pavement , . . 6~OFrises, E. and ,Wo 1586 .Cornice, E. and. W . . . " . 11~O.P linth of baluljtrade, , .510Solid in parapet,

Young Bridge

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