208 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[July, 



The cause of llie fracture we believe to be, that the girder vvas jointed, 

 and that due consideration was not given to that circumstance in assigning 

 their relative proportions to the flanges. As the effect of a joint is one 

 that practical men are apt to overlook, we propose to examine the subject 

 in detail— excluding as much as possible symbolical language, in order 

 that our reasoning may clearly be apprehended. It is well known that 

 there are usually three distinct divisions of a girder, consisting of the 

 upper and lower flanges and the web: the vertical and transverse section 

 of such an arrangement would resemble somewhat an H laid on its back 

 — thus ::: . The reason of this mode of construction will be better under- 

 stood when we have determined the nature and amount of the strains and 

 thrusts experienced by the several parts of a loaded girder. 



•. Q^ 



N 



Let ABdc be a vertical section of a girder, resting on the points A and 



B, and loaded with the weight «c at Q. Let cQ — a; c d = I ; Bd = A; 



<r D, the section of the upper flange ; C i, of the web ; and a B, of the 



lower flange. Let R = reaction at A; R' = reaction at B ; «>' = weight 



nf the girder, which is supposed symmetrical and uniform throughout its 



length. 



Tbeo we shall have these equations, when there is equilibrium^ 



tv'l w'l 



«.a + -^ =R7; w{i — a)+—-ni. 



Let us now suppose a vertical section to be made through some point, 

 M, of the girder. Let c M — h; Cc =: c; A a = d. 

 Consider now the equilibrium of the part c N : c N is kept at rest by 



w'h 

 the reaction R at A, by its own weight — > an<l by vertical and hori- 

 zontal forces arising from its connection with M B : let Y be the vertical 

 force; < and <' acting at in and n, in the directions indicated by the ar. 

 rows, the horizontal forces. LetNni^i-, Nm=j;': 

 Then we have for the equilibrium of cN 



IV 'k 

 R-fY = w + — ; t' = t; 



also, taking moments about A, 



w'h- 



VA + (X = uio + -^ + t'x\ 



Now, t-f; R = w{l — a) + iw -l 

 I 



I'A „ u'a tv' (2 A — I) 

 — R—-r+- 



\ =1 w + 



I " - I ^ 2 1 



Substituting this value of Y, we find 



t (x' — x) = <p (a, h, I, w, ui',) : 

 .•.((a' — i) is known, and depends simply ou the weight of the beam 

 and its load, and not on the shape of the beam — the only condition to that 

 effect being, that the beam shall be longUuiiinally uniform. 



We find, then, that at the upper part of the beam there is a thrust, and 

 at the lower part a tension. Consequently, at the upper part the particles 

 of the beam are in a state of compression, and at the lower in a state of 

 extension. Therefore, between M and N there is some point where the 

 particles are neither extended nor compressed. Let o be this point : o is 

 said to be a point in the neutral axis. If, now, the beam were laminated — 

 that is, composed of parallel laminae, incapable of sliding over each other, 

 and which obeyed Hooke's law — the amount of the forces arising from the 

 extension and compression of the particles in M N, would vary as their 

 distances from 0. This is the law usually assumed for materials of even 

 a crj slalline texture ; at all events, the probabilities are, that even if the 

 tension and compression do not in all cases vary directly as the distance 

 from o — they vary as some higher power of the distance : according to 

 either supposition, it is clear that the particles near o are not so effective 

 in supporting w and «•', as tliose farther from it; and, consequently, we 

 see the reason why the greater part of the substance of the girder is distri- 

 buted at the greatest available distance from o, in the form of flanges. 



In the case of a cast iron girder like that of the Dee Bridge, it is not 

 rn;ce;saiy to make the upper flange as thick as the lower one, because cast 



iron exerts a much greater force for compression than it does for extension 



to the same amount, and bears a much greater crushing than rending 



strain. Suppose now M N to be a joint, and the connection to be effected 



by means of bolts let through projecting lips, as was the case in the girdtr 



that broke ;— the question immediately arises, how would that effect the 



thrust and strain on the upper and lower flanges ; Before we consider 



this question, it w ill be advisable to show that in the molecular connection, 



first noticed, a' — x is either or very nearly a maximum; and, therefore, 



y either or very nearly a minimum— for i/(x' — x) is a constant, as we 



proved. 



In the first place, taking the usual law — and supposing the girder 



2 

 not flanged, but uniform, x' — x would = -. Ac; but when we consider 



the flanges, the resultants of the strains and thrusts will be thrown much 

 nearer to N and M respectively ; and with the ordinary proportions observed 



4 4 



for the flanges and web, x' — x would not be less than -. A c, or - M N 



5 5 



— and it is diflicult to conceive any mode of connection at M N which 

 could make it greater. We cannot, then, suppose that y can be increased ; 

 let us, therefore, suppose that y is the same for all modes of connection. 



If, instead of the ordinary law, we had assumed any other law for the 

 amount and variation of the thrusts and strains, involving a higher power 

 of the distance from o than the first, (for instance that adopted by Mr. 

 Hodgkinson) x' — x would on such a supposition be still more increased. 

 On the whole, we may fairly suppose y to be constant — certainly not 

 capable of being diminished by any mode of connection. 



But although y remains constant, its distribution, both above and below 

 0, will materially depend on the nature of the joint. Suppose, for instance, 

 a single bolt at N ; then this bolt will sustain all the tension — and all the 

 particles about N will be exposed to an enormous rending strain. Again, 

 if, as in practice, when the joint is bolted from M to N, the lip gives and 

 is slightly deflected, and the bolts work loose, then, in order to make np 

 the value of y, more bolts than those between o and N may be in a state of 

 tension, and less of the girder than from o to jM in a state of compression ; 

 consequently, since the area which sustains the thrust is diminished, the 

 thrust per square inch will be increased. Also, if some of the bolts work 

 looser than others, the bolls which work tightest will be in the highest 

 state of tension. Some of these causes of imperfect action may be pr< - 

 sumed always to exist ; and the only way we know of compensating for 

 their effect, is very much to increase the vertical breadth of the girder at 

 the joint. This, however, was not done in the girders of the Dee Bridge. 



To all this reasoning, it may be objected that the girder did not break at 

 the joint. Our reply is, that the strains arising from a bad joint are tran.- 

 mitted to a great distance through the substance of the girder — and where 

 the metal is weakest, there we may expect fracture to ensue. It is not 

 enough to build bridges calculated to endure two or three times the great- 

 est statical strains they can be subjected to — especially when those strains 

 are to be supported by cast iron girders. The continual vibration to which 

 iron is liable, tends to weaken the cohesion of its particles : the alternate 

 expansion occasioned by heat and cold has the same effect. 



Lastly, it must never be forgotten that the vibration of a train increases 

 enormously the tendency to fracture, by bringing into play dynamical 

 strains, the amount of which is beyond calculation ; and that iron bridges 

 are especially adapted to transmit such vibrations. 



Artesian Wells in Volcanic Formalions. — The first attempts of this 

 kind in Naples were made, some years ago, near the Campo Santo, by the 

 Societa Industriitle ; they, however, yielded but a small quantity of water, 

 at a depth of 80 or 90 feet. This led to the great undertaking in the 

 Royal Gardens, which, however, is not likely to yield any favourable re- 

 sult. The deeper the boring proceeds, the harder is the appearance of the 

 strata of volcanic tuffa — and the only advantage derived is the perfect 

 knowledge of the geological stratification of the terrain of Naples, on 

 which the architect, M. Cangiano (who superintends the work) read a 

 paper at the meeting of Italian scienziatc, in 1845, As the supply of 

 water for the metropolis (especially near the Posdippo and Vomero) is 

 constantly on the decrease, government will be obliged to erect new aque- 

 ducts at an enormous expense, and to convey fresh water from Monte 

 I'aburno, or the sources of the Sarno — or even so far as the Tifetini and 

 Trebulini mountains, near Capua. It may be said with certainty, that the 

 volcanic terrain near Naples does not contain a sufficient quantity of 

 drmkable water for its increasing population — even if it be not the cast-, 

 that the quantity of water is yearly decreasing, for reasons not yet 

 properly ascertained. 



