JS-tO.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



209 



lull descriptions of those bridges are to be met witli elsewhere, it will 

 not be necessary to notice them farther. 



In ISls, Mr.Telford was consulted by government as to the pra'cti- 

 cability of erecting a suspension liridge over the Menai Strait, and was 

 commissioned to prepare a design, if, upon an examination of the lo- 

 calities, he found the project feasible. Having accordingly surveyed 

 the spot, he was led to propose the construction of a suspension bridge 

 near Bangor Ferrv, and in ISIO an act was obtained anthori/.ing the 

 erection of the bridge, a sum of money having been previously voted 

 by Parliament for that purpose. This structure, which will always be 

 regarded as a monument of the engineering abilities of Telford, was 

 connnenced in August 1S19, and opened to the public on the 30th 

 January, ls:}i5, Iraving occupied six and a half years in its erection. 

 The Union IJridge across the Tweed was designed and executed by 

 Captain Brown, and was the first bar chain bridge of cousiilerable size 

 that was completed in this country. It was commenced in August 

 1810, and finished in the month of July 1S2U. After the com|)letion 

 of the Mcnai Bridge, bridges on the suspen>ion principle began to be 

 universally adopleil throughout Euro])e ; but it was not till /;«« wins 

 had been proved to be more jinn than bars of a gitdkr lliickiicsn that 

 these bridges received their most extensive api)lications.* Since 1S21 

 Messrs Sequin have constructed more than 50 wire briilges in France, 

 with the most complete success.* The wire sui))ension bridge at 

 Freyburg, in Switzerland, the largest in the world, was erecteil by 

 Mons. Challey, and depends across the valley of the Sarine. It was 

 commenced in 1S31, and thrown open to the pubic in 183-1. A sus- 

 pension bridge has also been erected at Montrose, the size of which is 

 scarcely inferior to that of the Menai bridge. At Clifton a very large 

 suspension bridge is now in progress of erection by Jlr. Brunei, and a 

 suspension bridge lUito feet in length is about to be erected over the 

 Danube, between Pest and Often, tlie design for which is the produc- 

 tion of Mr. W. Tierney Clark, and under whose able superintendence 

 its construction will be effected. 



Having completed this sketch of the eaily history and subsequent 

 progress of these interesting structures, I shall now proceed to investi- 

 gate the friiicipkn upon which their stability depends, and by whose 

 aid we are enabled to deduce practical rules for their construction. In 

 this inquiry 1 prefer proceeding entirely upon abstract grounds, as by 

 disencumbering our ideas of iiuUcrial circamsUuiccn, a greater facility 

 of thought is conferred, and the results of the investigation are made 

 to rest upon a broader and more certain basis. When a prinei|)Ie has 

 once been established in a ^'tyft/'u/yu/w, its application will be found 

 with comparative ease, as we have then only to observe tliat in sub- 

 stituting the particular lor the general case, we do not violate any of 

 the fundamental conditions of the problem. 



The theory of suspension bridges is susceptible of division into two 

 parts. I. The statical theory. II. The dynanucal theory. In the 

 first, we consider the forces which are develoi)ed, ami the laws which 

 are brought into operation, when all the parts are at rest ; in the second, 

 we suppose the action of the impressed force is evinced by the pro- 

 duction of motion, and upon that su|iposition proceed to investigate 

 the beh.iviour of each particle, and inter the effect of their cumbinetl 

 motions. In the pres(Mit paper the statical theory alone will be con- 

 sidered. The statical theory of suspension bridges is evidently in- 

 volved in the general problem, to dtkrmitie l/it cotidilw/m oj' aimlibriam 

 of aiii/fvrcis /c/iukrer, acting in space njxin pvinln cuniiiclid by Inns 

 loholly Jtcxibk and vicrlinxibk. In the solution of this problem, tlien, 

 we shall be gradually approaching our subject. 



It is a principle in statical science, that when a body, acted on by 

 any number of forces, is supposed to be at rest, all these forces must 

 admit of being compounded into two, which are e()ual and opposite to 

 each other. The same condition, it is evident, nnist exist with regard 

 to each point, out of any number connected by Hexible lines, provided 

 the initial position of these lines be not a straight line, for then, it is 

 clear, no medium exists through which the lorces can be transmitted, 

 and be made to act and re-act upon each other. This case may then 

 be neglected in the present investigation, as it <loes not involve tha 

 principle of cotmecting lines, which here exert, in reality, no mechani- 

 cal influence whatever. The same remark replies .dso when the con- 

 necting lines are right lines, if we still suppose that each point is in 

 equilibrium by virtue of Ihose/orcts alone which act upon itself. But 

 since we easily conceive tht transmission of force from one point to the 

 adjacent one through the intervention of a connecting line, if that line 

 be inextensible and a right line, it is perfectly clear that equilibrium 

 may exist with regard to any number of points thus united, though 

 each point should not, considered by itself, be in equilibrium by virtue 

 of the forces applied to it, provided only we suppose tliat the inter- 



* .See the Alijenicine Baiizeitung. 



change of force between two consecutive point be (««/««/, i(j«ii.' and 

 ojiposih. Moreover, we shall suppose the forces to be receding forces, 

 or such as tend to cause two bodies to proceed from each other. In 

 general, then, it appears that in order that cipiilibrium may exist with 

 regard to a system of points, which we suppose not to be in a state of 

 inde[)eudent ecpulibrium, it is only recpiisite that two simple conditions 

 be observed. I. The line of connection must be a right line. II. The 

 transmission of t'orce between two points must be nialiial, equal and 

 oppusiti. It follows also, from the last condition, that the interchange 

 of force will take place in the direction of the connecting line. We 

 shall now proceed to show that these self-evident conditions being ad- 

 mitted, they may be resolved into others which have a more in-actical 

 bearing, if, to begin with the sim|ilest case, we take two points, A 

 and B, fig. 1, we see at once, that ecpiilibrium being s\ipposed, each 

 must bo acted on by ecpud forces, whose direction are denoted by the 

 arrows. If we now proceed to the case of three points, A, B, C, fig. '2, 

 it is eviileut, that cipiilibrium subsisting, each two will be iu equili- 

 brium with respect to one another, and therefore, as we have seen, will 

 be subject to equal and opposite forces. The directions of these are 

 denoted by the arrows. Now, let the forces acting in the directions 

 A B, C D, at the same point B, be compounded into BB' which re- 

 presents their resultant, and we have, conso([uently, a system of three 

 jioints kept in e(|uilibrium by three forces, of which one is applied to 

 each point. But as the forces acting at A and C, are transmitted 

 through the connecting lines to the point H, and may be regarded as 

 acting there, it is obvious the case differs in no respect frcuu that of 

 three forces in equilibrium around a single point. Consequently, call- 

 ing the forces B A, B B' BC, I', Q, K, we have : — 



P : Q : : sin. B' BC : sin. ABC 

 R : g : : sin. AB B : sin. ABC 



p : R : : sin. B' bc : sin. abR'. 



Hence also, from these propositions ni.iy be found the values of P, 

 Q, and U, in terms of two of the angles and one of the other forces. 



• .1 , ,, sin. B" B C ,^sin. ABB' ,„ 



By comparing the values, ci__^^, Q _-_--^, of P and R, 



we observe that when / AB B' = Z B' B C, P = 

 duced bisects the /ABC. Let / A B C = 2 (8, 



sin. S 

 sin. 2 /3 



sin. $ 



1 



2 sin 3 COS. |8 2 cos. 3 

 1 



Hence P = R : 



R, and B ■ B pro- 

 . sill. B'BC _ 

 ■ ■ Tsin. A B C ~ 



Q 



2 COS. js' 



If Q remain constant, P a » ami if fl remain constant, P a Q 



COS. e 



If Z A B C be increased 



evident from the equationP ^ _^ 



COS. /3 is diminished, and it is therefore 



-, tliat by increasing the Z AB C 



2 COS. /3 



we increase the value of P; consequently, when A B C becomes a 



Q 



right line or S =; '.'0"', the equation becomes P ^-- = a. 



It follows, as Poinsot remarks (Traitc de Statique) that a cord or 

 thread stretched in a right line between two fixed points, will be ne- 

 cessarily broken by the smallest possible force that can be applied to 

 it transversely, sup;)03iiig the cord to bc inextensible and not to have 

 an infinite longitudinal resistance. It may be further remarked, that 

 every material cord being composed of particles having weight, would, 

 if extended between two fixed points lying in a horizontal line, be acted 

 on by transverse forces of a definite magnitude ; consequently no force, 

 however large, would bc sullicient to bring the cord into a horizoiita 

 position. 



It is not difficult to extend the reasoning which has been used in re- 



2 



