1847.] 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



73 



STABILITY AND STRENGTH OF HUNGERFORD BRIDGE. 



[Reply to the Objections raised in the " Civil Engineer and Architect's Joiirn;il" of 

 Dccemljer, 1641), to the Analytical Investigations and Dynamical Observations, conlaiued 

 in the Pamphlet entitled " Metropolitan Bridges," showing the Defects and Insufflcieucy 

 of Hungerford Bridce, by Sir Howard Douglas.] 



'' lu llie pamplilet eutitled ' Metropolilan Britlges,' &c., it is intimated 

 that, at tlie tops of the piers of Hungerford Bridge, tliere exist horizontal 

 forces, represented by a — «', by which those piers are continually strained ; 

 and which, in consequence of the concussions produced by the Tibrations 

 of the Bridge, may ultimately destroy them. 



Concerning these forces some explanations will presently be given ; but 

 as, in a well written paper which appears in the Vuil Engineer and ^ii-- 

 <;/ii(«i's J»!iv«ai for December, 1810, an attempt has been made to show 

 that the danger which might arise from these forces is obviated by the 

 friction rollers under the saddles to which the chains of the bridge are 

 attached at the tops of the piers, and believing that there is ground for 

 considering the effect of the saddles in diminishing the strain to be very 

 small or nothing, we feel it incumbent on us, iirst, to say a few words on 

 this subject. 



It is much to be regretted that experiments on the friction of cylindrical 

 rollers are as yet too few to allow any precise determination of its value 

 to be founded on them, yet such experiments ai'e not wanting ; and from 

 those of Coulomb principally may be obtained approximations which will 

 suffice for the present purpose ; it may be admitted, in fact, agreeably to 

 many of the experiments made by that distinguished philosopher, that the 

 friction of rollers varies inversely as their diameters, and directly as the 

 pressures which they support. Now, suspending equal weights on oppo- 

 site sides of a cylinder by means of a string passing over a pulley lo which 

 the cylinder served as an axle, and then applying on one side additional 

 weights sufficient lo overcome the friction. Coulomb found the values of 

 that element for wooden cylinders of different kinds and sizes ; reducing 

 these, by the first part of the rule above mentioned, to cylinders four inches 

 diameter, which is the size of the rollers under the saddles of Hungerford 

 Bridge, the friction of wooden rollers is nearly one-hundredth part of tiie 

 weight. This agrees with Ihe experiments made by Mr. Babbage on 

 wooden ntllers, if as usual we estimate the power requisite to draw a body 

 horizontally on a sledge to be one-quarter of the weight of the body. But 

 all these experiments having been made with cylinders compressed by 

 weights w hich are comparatively small, the above estimate is far less than 

 it would be under the enormous pressure to which the rollers supporting 

 the weight of a suspension-bridge chain are subject. 



The experiments of Coulomb on iron axles turning between cheeks of 

 copper give for the friction of metallic rollers a value bearing a much 

 higher ratio to the pressures than that of wooden rollers : the diameter of 

 his axles was 1'48 in. (English), and the friction, without grease, was one- 

 sixth of the weight ; this value, increased in the ratio of 1'4G to 4, gives, 

 for the friction of iron four-inch rollers, one-fifteenth of the weight or pres- 

 sure. It would seem, therefore, that the friction of such rollers, even in 

 circumstances far more favourable to the freedom of their motion than 

 those of the rollers under the saddles on Ihe piers of Hungerford Bridge, 

 cannot be estimated at less than Ihe quantity last named. Now the pres- 

 sure in the vertical direction, arising from the weight of the suspending 

 chains on the tops of the piers on each side of the centre of Hungerford 

 Bridge, being estimated at 850 Ions, it must follow that the friction and 

 inertia of the rollers are together equivalent lo nearly 57 tons ; or strains 

 at the tops of the piers, to that amount, may take place before Ihe saddles 

 will move. What has been said must be considered as indepenilent of the 

 increase of resisting power in the rollers, arising from the probable altera- 

 tion of their figures and the indentation of the planes on which ihey rest, 

 in consequence of Ihe great pressure to which they are subject, each of 

 the twenty-five rollers* under the saddle bearing one-twenly-fifth of the 

 weight on that saddle, or above 17 Ions. The resistance arising from the 

 force of cohesion may also, in time, become sensible under such pressure. 

 The estimate of the friction of rollers on Ihe pier of a suspeusion-bridge 

 which, in the paper referred lo, is derived from that of a railway carriage, 

 is by no means admissible : as well might it be assumed that the body of a 

 railway carriage, if moving on rollers four inches diameter, would ha>e 



• These observations are all made with reference to an accurate plan, showing, in 

 detail, the principle and construction, elevation, plan, and end view ot tlie saddks on the 

 tops of the piers ; the girders, the coupling bolts, and suspension rods, the holding down 

 girders, &c. ; and very accurate observations have been made, by which it i.pp»ars that 

 there is very little, if any, skifting of the saddles, since the bridge was constructed, as 

 stated at page f. 



only half the friction which it has on its wheels. A railway carriage may 

 be considered as moving on rollers whose diamelers are ten or twelve times 

 as great as those of the bridge rollers; and, if any comparison could be 

 made between cases which are so much unltke, it should be inferred ihat 

 the friction of the Bridge rollers, instead of being half that of a railway 

 carriage, should be ten or twelve times as great. 



By an oversight, it was slated in Ihe pamphlet on ' Melropolilan Bridges 

 &c.,' Ihat Ihe side chains of Hungerford Bridge have the same droop or 

 deflexion as those in the centre ; whereas, Ihe side chains, being carried 

 below the level of ihe road, the droop is greater, while the horizontal 

 length or span is nearly equal to that of half the centre chain: the infe- 

 rence drawn from the difference between the parts of Ihe chain, is, how- 

 ever, correct ; the value of a' being still less thau than that of a. This is 

 manifest from the approximative formula which is given in the pamphlet ; 

 since .>- is small when cotnpared with 3y-, and the whole numerator is 

 di\ided by an increased value of C.r. Bui if the weights suspended from 

 the central and side chains be taken into consideration, the value of a' 

 relatively lo a will be much less thau Ihat which would result from merely 

 subslituliug the augmented value of .r in the formula above alluded to. 

 For the weight of half the chains and roadway between Ihe piers being 

 estimated at 500 tons, while, between either of Ihe piers and the abutment 

 on the laud side, Ihe weight of the chains with Ihe portion of roadway 

 which they in part suspend, and in part support, is about 350 tons :* then, 

 still, for simplicity, considering the curves as common catenaries, and 



»' — .v= 

 using the correct formula for horizontal tension, viz., a— — — — in which 



s, the length of the chain between the points of allachmeni (in this case, 

 Ihe length between Ihe highest and lowest points of the curve,) may be 

 taken to express Ihe weight of the chain and loading between such points, 

 it is evident that u' will be less than a, both ou account of the smaller 

 value of s and the greater value of .r. 



It is, therefore, very correct to say that there exists a force of consider- 

 able intensity, expressed by a — «', which is constantly acting towards the 

 river at the tup of each pier, and which may ultimately be the cause of 

 its destruction. And though it should be admitted that motion may take 

 place in the saddles so as to produce some compensation to the excess of 

 strain tow'ards the middle of the river, yet the effect of such motion would 

 be far from equalising the contrary strains. In the actual state of the 

 Biidge, the horizontal tension of Ihe side chains at each abutment is about 

 eleven-twenty-fifths of the like tension of Ihe centre chains ; and a move- 

 ment of the saddle to the extent of eighteen inches towards Ihe river, 

 while it would diminish the horizontal tension of the centre chains by about 

 one eight part of its value, would increase that of the side cbaius by one- 

 hundredth part only; and this is Ihe whole extent to which Ihe compensa- 

 tion alluded to in the Civil Enginesr and Architect's Journal for Decent. 

 ber (p. 305, col. 1.) would amount. It may be observed, that a siraiu 

 which should cause a movement of a saddle towards the river to the ex- 

 tent of eighteen inches, must be accompanied by a descent of the lowest 

 part of the centre chain as much as six feet vertically. 



The effects of the strains at Ihe pier heads may, obviously, with propri- 

 ety, be determined by the parallelogram of forces as explained in Ihe fifth 

 page of Ihe ' Reply' addressed lo Ihe Editor of Ihe Civil Engineer and 

 ArckitecVs Journal ; and of such resolution of forces an instance occurs in 

 the description of a Jib-Crane, which appears in that journal for Decem- 

 ber, 1840, p. 3G7. It is not, however, to be supposed that a pier of brick 

 or stone is overturned as if it were a vertical rod, capable of turning on a 

 joint at its lower extremity only ; this is an effect which can scarcely take 

 place in such structures ; but continual pressures and accidental straius at 

 lite head of a pier have tendencies to destroy the adhesion of the male- 

 rials, and cause the pier to fall in ruins iu consequence of a fracture taking 

 place at the point where the fulcrum of the lever may be situated. The 

 position of such point will depeud upon the construction of the piers, and 

 those of Hungerford Bridge are not solid in all their height, but each is 

 perforated at a certain distance above the roadway by arched openings at 

 right angles lo one another, so that the top of the tower with the saddle is 

 supported only ou the four portions of Ihe side-walls at the angles. 



This construction renders the towers far less strong thau they would have 

 been if solid, and makes it very probable, that, in the event of undulations 

 of the bridge producing a pressure even less than that value of a — a' which 

 has been above found, fractures will lake place in those portions of the side 



* It must be observed, that this pnrtlon of the roadway, which is equal in length to. 

 half the disi;uico tjetvveeu the piers iu the river, is sappoited at both its extremities. 



U 



