I8-t8.J 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



293 



the latter is the estimation of the statical strain to which a chain is 

 subjected when its weight and all its dimensions are known. This 

 particular branch of the question may be set at rest without much 

 difficulty. The object of the present paper is to do this by methods 

 distinct from those which have been adopted in the previous dis- 

 cussions of the question. 



Sir Howard Douglas, who first publicly moved the subject of the 

 sufficiency of Hung-erford Bridge, has ably calculated the strength 

 of the chains, on the assumption that the form of them is the 

 " common catenary :" this method, the most scientific and exact 

 of any, involves however considerable mathematical skill in its 

 application. The mode about to be employed may be readily used 

 in general practice, as it does not require a knowledge of mathema- 

 tics; and the agreement of its result with that obtained by the 

 process referred to, tends to their mutual confirmation. 



In suspension bridges, the central deflection is always small com- 

 pared with the span between the points of suspension. It follows 

 that tlie curvature of the chain is very small ; and whether it be 

 considered a catenary, a ])arabola, or even the arc of a circle, the 

 deviation from the real form will not be considerable. It is very 

 usual, for the sake of simplicity, to assume the curve to be a para- 

 bola, and that assumption will be here adopted after a few remarks 

 tending to prove its accuracy. 



If the horizontal distribution of the weight of the chain and its 

 load were unifornv, the curve would be exactly a parabola, as may 

 be easily ascertained by reference to any standard treatise on 

 mechanics which refers to the subject. Now, when the bridge is 

 crowded, the load on the platform is uniformly distributed hori- 

 zontally. Tliis is also the case with the weights of the platform 

 and the parapet, which are considerable. The only mass not so 

 distributed is that of the chains themselves, of which the links are 

 liorizontal at the centre, and inclined more and more up to the 

 points of suspension. But practically this inclination is, never 

 large; for instance, in Hungerford Bridge at the points of suspen- 

 sion, as will be presently shown, the tangent of the angle ot in- 

 oliuation is about j\. This gives the cosine of the angle less than 

 ■^ ; or 18 feet measured along the chain there, nearly corresponds 

 with 17 feet measured horizontally. This shows that the hypothesis 

 of horizontal distribution, even for the chain alone, does not involve 

 any considerable error ; and when the additional effect of the mass 

 of the load and platform, which is really so distributed, is taken 

 with it, the deviation from the truth must be inconsiderable. 



On this assumption, then, the vertical line through the centre of 

 gravity of half the chain and its load is situated midway betvveen 

 the centre of tlie chain and the extremity of the platform ; or the 

 horizontal distance of this centre of gravity from the abutment is 

 equal to one-fourth the span. Tlierefore, the moment about the 

 point of suspension of the weight of half the chain and load, is the 

 product of tliat weight and one-fourth the span. 



At the centre of the cliain the tension is horizontal : its vertical 

 distance below the point of suspension is equal to the deflection of 

 the chain. Therefore, the moment of this tension about the point 

 of suspension is the product of the tension and the deflection. 



The moments just determined are equal, the total eff'ect to turn 

 the half-chain about the point of suspension being produced l)y the 

 weight, and this eff'ect being resisted by the efl^ect of the horizontal 

 tension. (The platform not being rigid, contributes nothing to 

 the ultimate support of the load.) Also, in Hungerford Suspension 

 Bridge, the deflection is 50 feet, and the quarter-span 169 feet. 

 Consequently, 



Horizontal tension x 50 ^ weight of Italf-spmi X 169. 

 Hence the weight of the half-span is -j^, or very nearly five-seven- 

 teenths of the tension at the centre of the chain. 



On the authority of Mr. Cowper, who is believed to have ob- 

 tained authentic and accurate information, it is stated, in Part 93 

 of this Journal (June, 1845), that the total sectional area of 

 the chains at their centre is 296 square inches. The Bridge is 

 supported by four chains, two on each side of the platform, and 

 the above is the sum of the sectional area of all four together. 

 The horizontal tension is supposed to be uniformly distributed 

 over these 296 inches. 



Wrought-iron bars become sensibly stretched and impaired 

 when subject to a tension of 17 tons per square inch. They will 

 not bear that strain permanently; and in practice it is not con- 

 sidered safe to subject them to a greater tensile force than 9 tons 

 per square inch. Taking the latter measure, the greatest horizontal 

 tension which the four chains together can safely bear is 296 x 9 = 

 2664 tons; and the greatest weight of the half-span must, by 

 what has already been said, be -j^^jths of this, or very nearly 

 788 tons. Consequently, for the whole-span, 



The greatest total load =. 1576 tons. 



This is, in fact, nearly the load to which the bridge is actually 

 liable to be subjected. The weight of the chains (715 tons) added 

 to that of the platform, parapet, rods, &c., and a crowd covering 

 the platform with a weight of 100 lb. to the square foot, gives, 

 according to Mr. Cowper, the maximum load at about fifteen 

 hundred tons. We come to the conclusion, then, that when the 

 bridge has its full load, the statical tension at its centre is nine 

 tons to the square inch. 



The following method was adopted to test the accuracy of the 

 hypothesis on which this conclusion is founded. By a known 

 principle which applies to catenaries of every form, the tangents 

 at any two points of the curve meet in the vertical line through 

 the centre of gravity of the intervening portion of the chain. 

 Consequently, if the assumption be true that the vertical through 

 the centre of gravity of the half-chain bisects the half-span, the 

 tangent at the point of suspension ought, if produced, to meet the 

 platform midway between its centre and extremity. The observa- 

 tion of this fact would be a crucial test of the above conclusions. 

 This test was satisfactorily performed in the following manner. 

 The inclination of the chain at its summit was observed with a 

 telescope from various positions on the Bridge, and that position 

 was noted in which the inclination of the chain at its highest point 

 coincided with the axis of the telescope. That position of the ob- 

 server's eye for which one end of the highest link covered the link, 

 was of course in the line of that link produced. By these means 

 (applied for the sake of mutual confirmation to the points of sus- 

 pension at both towers), it was ascertained that the centre of 

 gravity of each half-chain was about six feet nearer the end, than 

 the centre, of the platform. The advantage of this method of 

 observation was, that it did not require particular accuracy : an 

 error of 10 or even 20 feet would not ha\e made a considerable 

 difference in the result, while the errors of observation were cer- 

 tainly far within those limits. 



It is important to observe, that if the Bridge were loaded with 

 its full weight, the actual position of the centre of gravity would 

 coincide with that above assumed, even more closely than it did at 

 the time of the observation. 



To ascertain the tension at the points of suspension, we have 

 the following rule, applicable to catenaries of every form. Add 

 the squares of the horizontal tension and of the weight on the 

 half-span: the square root of this sum is the tension at the 

 summits of the chain — which, therefore, in the case before us, is 



= V { (2664)= -I- (778)= } tons. 

 After obtaining this square root, divide it by 9, and the result is 

 308, for the number of square inches over which the tension at the 

 summit must be distributed if the tension be 9 tons per square 

 inch. The actual sectional area of the chain at the points in 

 question is very near this — namely, 312 square inches. 



In the above caculations, the structure has heen supposed to be 

 in a state of equilibrium. The vibrations of the several parts of 

 the chain, arising from the rapid motion of traffic, or the action of 

 the wind, would certainly increase the strains greatly, though no 

 means of calculating that increase have been yet ascertained. The 

 foregoing method shows, with all the precision requisite for practi- 

 cal purposes, that both at the centre and extremities of the chain 

 the tension of the metal is 9 tons per square inch, when the bridge 

 is fully loaded. The fairest way of stating the conclusion from 

 these investigations appears to be this: — If the permanent tenacity 

 of the metal be so great that it maybe safely subjected to a greater 

 strain than 9 tons per square incli, then the excess is a provision 

 against accidental disturbances. If, however, 9 tons per square 

 inch be the utmost strain which the metal will safely bear, no 

 margin is left for security against the eff'ects of rapid motion. 



THE WATER-GAS. 



Some time has elapsed since a patent was obtained for a 

 process of making illuminating gas from water ; but the plan 

 was not carried into practical effect, and dropped out of public 

 notice. The invention has once more been brought before the 

 public, and in a manner calculated to attract attention, by being 

 made the subject of lectures delivered by Air. Ryan at the Poly- 

 technic Institution. The process itself is a very curious one ; and 

 though the expense may probably render it a less economical mode 

 of supplying gas than coals, where they are to be purchased at a 

 cheap rate, yet, in many parts of the country, it is probable that 

 the water-gas may be the cheaper of the two ; and as its purity 

 and iUuminatiug power exceed those of the carburetted hydrogen 



