IS-iO.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



299 



metal composing the upper and lower sides of (he tube, and to suppose the 

 strain equally divided over the whole area. In order however that the 

 latter assumption may obtain, it is necessary that the lop and bottom of the 

 tube should be of a particular form. We shall proceed to show that where 

 the lop aud'bottum consist of continuous plates, esteodin;;; from one side of 

 the bridge to the oilier, or where they are formed of cellular comparlnients 

 such as those described in another part of this Journal, the above requisite 

 is not answered, but that on the contrary, a large proportion of the metal 

 is placed where it is almost entirely inoperative, and that consequently any 

 calculation founded on the supposition that this metal contributes to the 

 strength of the tube must lead to dangerous results. 



It the reader will take hold of the page which he is now perusing, at 

 the tup and bottom, and pull it, he will see that if the paper were torn the 

 rent would commence somewhere in the neighbourhood of the straight line 

 joining his two thumbs. If, for example, he held the paper by the two 

 right-hand corners the rent would commence on the right side of the page, 

 and the material on the left side would contribute nothing to resist the tear- 

 ing. Again, if he took the page near the two ends of the black line, sepa- 

 rating the two columns of letter-press, the rent would in this case com- 

 mence in the middle, and the material to the right and left would not under 

 these circumstances contribute anything to the strength of the paper to re- 

 sist tearing. 



These experiments may appear very simple, and perhaps very puerile. 

 But it is precisely these simple illustrations which give us accurate notions 

 of the action of forces. The case of tearing the paper is exactly analogous 

 to that of tearing the lower plale of the Menai Bridge. It has been shown 

 that owing to the connection of the lower plale with the two side plates, 

 the latter communicate to Ihe former a longitudinal tension which acts all 

 along its two sides. Now this tension is most effective in the immediate 

 neighbourhood of the line in which it acts. If the bridge were overloaded 

 and the bottom plate torn, we are sure that tUe rent would cummence at the 

 edges, and not in the middle of the plate. 



If a piece of India rubber, originally square, be stretched by four forces 

 acting in the directions represented by the arrows, it will be found to as- 

 sume the form here represented; that is, the extension will be greatest in 

 the neighbourhood of the lines joining each pair of opposite forces, and 

 least midway between those lines. In fact if the forces be not loo great it 

 is possible to extend the sides of the india-rubber without extending the 

 middle portion at all ; so that a small slit made near the centre will 

 remain closed. There is probably some law for the decrease of tension 

 from the sides towards the centre, but there seems no way of ascertain- 

 ing it except by experiment. 



In the recent discussion respecting the Tubular Bridge, in the Mechani- 

 cal Section of the British Association, it was asserted by Mr. Lamb that 

 provided the lop and bottom plates of the lube were of a given sectional 

 area, it was immaterial what proportion Ihe thickness of the plates bore to 

 their width. If this theory be true, it must be true in the limit; and con- 

 sequently if the top and bottom plates were rolled out till they were no 

 thicker than the finest gold leaf, or the film of a soap-bubble, they should 

 retain their original strength. The mere statement of this notion might be 

 considered a sufficient proof of its absurdity, had not something very 

 similar been sanctioned by high authority. Professor Moseley states in a 

 passage already quoted, that the strongest form of a beam would theoreti- 

 cally be that in which the material of the extended and compressed sides 

 is " collected into two geometrical lines parallel to Ihe neutral axis." Now 

 this would be perfectly true were we dealing with mathematically rigid 

 bodies, but with extensible and compressible substances it seems obvious 

 that the extension or compression could not be uniformly distributed over 



two indefinitely thin flanges, but would be greatest in Ihe neighbonrhnod 

 of Ihe vertical rib. Professor Moseley has throughout his investigation 

 assumed that in the vertical section of a deflected beam the extension or 

 compression is proportional to the distance from the neutral axis, and i' 

 seems curious that he should have overlooked the fact that in a girder with 

 wide flanges Ihe extension and compression of the flanges also would be, 

 not uniform, but greatest in the neighbourhood of the rib. 



M'ecomethen with the utmost security to this conclusion, that the strongest 

 form of a beam is one in which Ihe material of Ihe flanges is collected as 

 closely as possible to the upper and lower edges of the vertical rib. This 

 form is very nearly approached in (he rails in most general use on our rail- 

 ways, and may be easily imitated in the case of the Tubular Bridge. The 

 accompanying diagram shows a section of the 

 bridge with the principal portion of the material 

 collected at the four angles. If we suppose these 

 four masses to have circular sections, it is easy to 

 calculate what diameter they must have in order to 

 satisfy the conditions of the preceding investigation. 

 It will be remembered that the sectional areas of 

 the upper and lower plates were each taken at 18iJ 

 square inches, and if the half of this area be as. 

 signed to each side of the lube, the area of each of 

 the circles represented in the diagram must be 90 

 square inches, and the diameter will consequently be about 10| inches. 

 Let us take the diameter at one foot. Then the thickness of the solid 

 masses at the angles will be equal to one-lhirlieth of the height of the 

 bridge. These masses should not be united by continuous plates but 

 braced together by a laltice of iron rods. There are many reasons for pre- 

 ferring open lattice — they are chiefly these— superior sirength for equal 

 weight of material, diminished resistiince to the wind, admission of light 

 and air to the interior of the bridge, equalisation of Icmperalure by which 

 the danger of distortion by unequal expansion is avoided, and lastly faci- 

 lity of construction. 



The bridge is to consist of two parts, containing two parallel roadways. 

 These two parts should be united so as to afford mutual support ; the sec- 

 tion of the bridge would then appear as in Ihe accompanying illuslralion. 



The upper and lower sides of the 

 bridge would be braced together by lat. 

 lice work similarly to the vertical sides. 

 By these means it will be seen from a 

 mere inspection of the section that the 

 lateral strength would even exceed the 

 vertical. This may be considered 

 another most important advantage aris- 

 og from the disposition of the material 

 in masses at the angles. If the bridge be covered above and below by 

 cellular compartments extending across it, the same apparatus ought to be 

 applied to the vertical sides, as has been clearly proved ; whereas by dis- 

 posing the material in compact masses it is made to answer both purposes 

 al once — it resists the lateral pressure of wind and the vertical pressure of 

 a train with equal efficiency. 



There is one reason more to be assigned for the employment of the upper 

 and lower lattice work. It was observed during one of Ihe recent experi- 

 ments that the top or compressed side of Ihe tube bulged out transversely; 

 and it may be seen that with a bridge of the construction here suggested, the 

 masses at the upper angles would, when in a stale of compression, tend to be 

 similarly bent. They would be likely to be bowed outwards or inwards^ 

 and this tendency is restrained by the horizontal bracing. These con. 

 siderations confirm, to a certain extent, the views of Mr. Byrne, recently 

 propounded in this Journal. The particular mode of calculation adopted by 

 him may fairly be subjected to discussion ; but it cannot be doubled tliat 

 his general views respecting Ihe horizontal transversal strains to which de- 

 flected beams are subject, when they tend to break rather by the distortion 

 of the material than the disruption of it, form a valuable addition to the 

 theory of the strength of beams. 



10. The employment of Suspension Rods. 

 The reader who has followed the course of the present argument will 

 have no difliculty in understanding that the strength of Ihe bridge depends 

 on the moments of the molecular forces about the abutment — that is, the 

 molecular forces multiplied into their perpendicular distance from the abut- 

 ment. And it will foUovf as a necessary coasequeace of this consideratioa- 



