318 



THE CIVIL EKGIXEER AND ARCHITECT'S JOURNAL 



[October, 



COMPETITION FOR THE BUILDING OF THE RHINE 

 BRIDGE, NEAR COLOGNE. 



The above certainly is a work which, when com)iletecl, will 

 reflect credit on our ajre, as since the times of Drusus no 

 bridfre ever existed on this part of the Rhine. TIic competition 

 drav.in<rs sent in amount to the large number of IC:?; amonjrst 

 them 2J are from Eni,'land. It cannot, however, be denied, that 

 many of tliem are quite without any practical value. Tliere are 

 compttent^ persons who also think that the small prize of 2.50 

 Frederic d'ors (of about 15.9. each), may not ha\e been sufficient 

 for men of real ability to come forward in the competition. Still, 

 amonfrst the plans from Engrland, there may be several whose 

 authors were rather prompted by ambitious motives tlian those 

 of mere lucre. Some of the drawinjjs attract notice by the splendid 

 way in which they are ornamented. In a few cases there are 

 special landscapes and views added to the plans, which could not 

 have been drawn but by some professional painter of views. Some 

 tew are also framed and gl.ized, but the large size of the panes has 

 occasi(med tlieir breaking during the transport. One of the com- 

 petitors has specially come over to Germany, and lias been pre- 

 senteil to, and has dined with, the King of Prussia. It is, lujw- 

 cver, impossible to form now even an approximate idea, in how far 

 this competition might have been the means to prepare tiie execu- 

 tion of a work whose estimated cost of one and a half million of 

 tlialers proves that even the mechanical means and contrivances of 

 Germany will have to be strained for its ultimate completion. 



REVIEWS. 



On the Strength nf Materials, containing various original and use- 

 ful forinulrc, specially applied to Tubular Bridges, U'rouyht-iron and 

 Cast-iron Beams, S^c. By Tho.mas Tatk, Author of the ' Principles 

 of the Differential and Integral Calculus, Factorial Analysis,' &c. 

 London: printed for Longman, 1850. 8vo., pp. 96. 



AVhe.v doctors disagree, who shall decide? Here is Mr. Tate 

 asserting that the total breaking weight of the Conway Tubular 

 Bridge is 201,3 tons; while Mr. Hodgkinson computes the same 

 quantity as low as lost tons — just about half! 



Before inquiring which computation is nearest to the truth, let 

 lis explain that the difference of the methods by wliich such very 

 different results have been arrived at is mainly this: Mr. Hodg- 

 kinson makes deductions from his own experiments, Mr. 'fate 

 from tliose of Mr. Fairbairn. The former found, from experiments 

 on the direct longitudinal compression of « rought-iron tubes such 

 as were to compose the cells of the top of the Conway Bridge, that 

 eight tons per square inch was the utmost force which they could 

 he relied upon to securely resist, and 12 tons per square inch to be 

 tlieir crushing force. He then assumes (Re])ort of Iron Commis- 

 sion, p. 1()5) the material of which the bridge is made to be perfectly 

 elastic; and wlien that is the case, the neutral line may be shown 

 to be in the centre of gravity of the sections, the areas of the 

 sections of tension and compression being inversely as the distances 

 of the centres of gravity of those sections from the neutral line. 

 He takes into account also the strength of the vertical sides 

 of the bridge, of the angle-irons, &c. He finds the numerical 

 lalues determining the position of the neutral line passing through 

 the centre of gravity, and then shows that eight tons per square 

 inch at the top of the tube (which he deems the limit of safety) 

 corresponds to a load at the centre of the lieam, which amounts, 

 including its own weight, to 10H4. tons, as above stated. 



This is one method. 'Fhe other likewise assumes that the elastic 

 forces are proportional to the extension and compression respec- 

 ti\ely, and that the neutral axis coincides with a line passing 

 through the centre of gravity of the section. Certain rules are 

 laid down respecting the relative strength of beams siinilarli/ pro- 

 portioned. (By the by, though Mr. Tate seems to imagine this 

 method of treating the subject new, it has been employed in the 

 pages of this Journal, and is also constantly referred to by Mr. 

 Hodgkinsim). Then an ex|)eriment on the "model tube," of 80 feet 

 long, in which the breaking weight was stated at 89-15 tons, is 

 taken as the basis of calculation; and assuming the Conway Bridge 

 to be similarly proportioned to the model, its strength is deduced 

 to be 2013 tons. 



Something is necessary to be said respecting the accuracy of this 

 celebrated experiment on the ''model tube." Tliis tube was broken 

 several times in succession by the rending of the bottom plates, 



wliich were each time repaired, and increased in strength until at 

 last the tube broke by crushing of its top. In the -'Iron C ommis- 

 sion" Report, p. 159, Mr. Hodgkinson gives the experiments in 

 which the breaking weight was successively increased up to 66 tons, 

 and there stops short, adding significantly, "There was a subse- 

 quent experiment on the same tube, which is not here given, as I 

 conceive there must be some error in it." What error? Did Mr. 

 Hodgkinson imagine that the breaking weight was erroneously 

 set down? or that undue precaution was taken in selecting the 

 very best iron, and so preparing the experiment, that its success 

 was rather apparent than real? ^Ve are not informed for what 

 reason this experiment is rejected; we are simply told that it is 

 not trustworthy; and, considering what an important bearing this 

 very experiment has on the whole question, and on the public 

 safety, it is reasonable to complain that so grave a charge is not 

 circumstantially supported. 



It will be seen from the above account of Mr. Tate's method, 

 that the accuracy of his calculation of the strength of the Conway 

 Bridge depends ultimately on the accuracy of his results deduced 

 from the data of the "model tube." On this subject he makes the 

 following observations (p. 59): — 



"In this model beam the principle of crumpling seems to be 

 eliminated by the thickness given to the plates, by the combination 

 of the cells, and by strong angle-iron used in connecting the plates. 

 This is rendered apparent from the fact that the top area is nearly 

 equal to the bottom one, when the equality to resistance is attained. 

 Hence the model tubular beam may be regarded as a common 

 beam, obeying the ordinary laws of compression and extension 

 when subjected to transverse strain. The assumption, therefore, 

 that the Conway Tube will have the same resistance to compression 

 as the thin rectangular cells ex]ierimented upon by Mr. Hodgkinson 

 is erroneous in principle; and this is rendered still more apparent 

 from the calculations on the model tube given in Art. 6.5, where 

 the resistance per square inch to compression is found to be about 

 18 tons, in the place of 8 tons, which j\lr. Hodgkinson assigns to it." 

 The above method of establishing the original hypotheses re- 

 specting the law of elasticity is altogether inconclusive. Those 

 hypotheses lead to a result which nearly accords with fact — namely, 

 the approximate equality of the areas of the bottom and top of 

 the tube when they are equally strong to resist tension and com- 

 pression respectively. From this fact, Mr. Tate argues back that 

 the hypothesis — not may — but must be true. The fact in question 

 is,however, consistent with a thousand other hypotheseswhich might 

 be contrived and combined so as to lead up to it. This mode of 

 discussing the question is, in fact, the old illogical error of con- 

 founding a direct proposition with its converse— the inferring 

 from "all mutton is meat," that all meat is mutton. T asks T', Do 

 you admit so and so to be fact? Yes. Then my propositions are 

 true, for tbev lead to it. This mode of discussion may be termed 

 a Tate-a-Tate. 



In order that the propositions may be certainly correct, every 

 legitimate consequence of them must be consistent with correctly 

 observed results. But, in trutl\ they lead to a result which, to 

 any one moderately well acquainted with the laws of elasticity of 

 iron, would instantly condemn them. In Art. 65, referred to in 

 the above quotation, the tension per square inch of the bottom of 

 the model tube is found to be 21 tons. Now, it is known, from 

 frequent and indisputable experiment, that the elasticity of 

 wr(jught-iron is almost entirely destroyed by a far less force. In 

 the Report on Iron Structures, page 178, Mr. Hodgkinson states, 

 that it appears "from the results of several experiments that 

 wrought-iron strained by tensionheyowA 15 tons per square inch, or 

 l)y coinpressiim beyond 12 tons per square inch, would be destroyed 

 for all practical purposes." 



It is difficult to ascertain the utmost extent to which wrought- 

 iron can be stretched before breaking, because its ductility permits 

 it to be drawn out almost to any degree — into a wire, in fact. Up 

 to a strain of about 12 tons per square inch the extension increases 

 almost precisely in proportion to the extending force. Beyond that 

 strain the iron begins to be drawn out very rapidly. Consequently, 

 the ratio of the weight to the extension is at first constant, but de- 

 creases very greatly after the strain exceeds the limit just indicated. 

 For instance, in the Report of the Iron Commission,p. +7, the stretch- 

 ing weight (in pounds per square inch) of a wrought-iron bar 10 

 feet long, is found to be to the extension (in inches) in the mean 

 ratio 232223 : 1, which ratio preserves nearly exact uniformity for 

 the first 12 or 13 tons. For a single additional ton per square inch 

 the ratio is reduced to less than one-half — namely, 113228 : 1, and 

 one ton more reduces the ratio to 67363 : 1, which is between one- 

 third and one-fourth the original value. AVhen the strain is about 



