shearing as for breaking wrought iron by extension, it would be necessary to give the pin a cross section equal to the sectional area of the smallest portion of the link only. The fact of the possibility of links being torn and destroyed by the pin being too small to present the necessary bearing surface, althougth quite large enough to resist the calculated shearing force brought to bear upon it by the links, seems hitherto not to have attracted notice; but as the strength of a chain depends upon the proper extent of surface being offered by the pins of the links to pull against, such a mode as the one described has been proved by experiment to be altogether fallacious. For by this mode

Fig. 1. Link for Kieff Bridge. Depth of head, 161⁄2 inches, of centre, 10 inches diameter of hole, 4 inches.

Fig. 2. Elevation, showing result of proof.

Fig. 3. Section through centre, showing result of proof.

Fig. 4. Experimental link, with wider head. Depth of head, 18 inches, diameter of hole, 4 inches.

Fig. 5. Link with properly proportioned hole for pin. Depth of head, 171⁄2 inches, diameter of hole, 6 inches.

Fig. 6. Plan of chain and section of pin and links.

of estimating, the size of a pin passing through links 10 inches wide and of uniform thickness (that is, not having the head thicker than the body of the link) would be something less than 3 inches in diameter, whereas (as will presently be shown) in order to get the whole benefit from such a link, the pin must be somewhat more in diameter than 6 inches, and for the following reasons:

In wrought iron the initial forces necessary to extend or diminish by compression the length of a bar are practically the same; and hence it arises that unless the surface of the pin on which the semi-cylindrical surface of the hole in the link bears is as great as the smallest cross section of the link itself, the head will be torn by the pin; and since

to provide this necessary surface it is essential to have a pin of much larger size, the question of its ability to resist the operation of shearing never arises, and the whole subject resolves itself into one of bearing surface.

If the pin be too small, the first result on the application of a heavy pull on the chain will be to alter the position of the hole through which it passes, and also to change it from a circular into a pear-shaped form, (vide Fig. 2,) in which operation the portions (AA, Figs. 2 and 3) of the metal in the bearing upon the pin become thickened in the effort to increase its bearing surface to the extent required. But while this is going on, the metal around the other portions (B B, Figs. 2 and 3) of the hole will be thinned by being stretched, until at last, unable to bear the undue strains thus brought upon it, its thin edge begins to tear, and will, by the continuance of the same strain, undoubtedly go on to do so until the head of the link be broken (or, rather, torn) through, no matter how large the head may be; for it has been proved by experiment that by increasing the size of the head, without adding to its thickness (which, from the additional room it would occupy in the width of the bridge, is quite inadmissible) no additional strength is obtained.

Acting upon the principle above described, most engineers have made the pins of their chains far too small, whereby much money has been wasted by making the links of a size, and consequently of a strength, of which it was, through the smallness of the pins, impossible to obtain the full benefit. Indeed, to such an extent has this been carried, that in one of the most noted suspension bridges hitherto constructed, a very large sum has been thrown away upon what is worse than wasted material, inasmuch as that material, remaining as load only, has to be carried by the chains, and correspondingly weakens the structure.

I am also acquainted with a very recently constructed suspension bridge, in which some of the links, which are 10 inches wide, have the holes in their heads but 2 inches, instead of 6 inches, in which case more than two-thirds of the iron in the links is useless.

The first time my attention was seriously called to this important subject was when Mr. Vignoles entrusted my late firm of Fox, Henderson & Co. with the manufacture of the chains of the great suspension bridge for carrying a military road over the Dnieper at Kieff, which was constructed by him for the Russian government.

As the chains for this bridge weighed upwards of 1600 tons, upon which the expense of transport was very heavy, they having to be shipped to Odessa, and thence carted over very bad roads for upwards of 300 miles to Kieff, it was considered of the first importance to ascertain whether or not they were well proportioned; and accordingly a proving machine was specially prepared, of power sufficient to pull into two any link intended to be used on this bridge.

These links, as shown in the drawing attached to the contract, (see Fig. 1,) were, for convenience of transit, but 12 feet long from centre to centre of pin-holes, 10 inches wide by 1 inch thick in their body

or smallest part, with a head at each end also 1 inch thick, swelled out to 16 inches in width, so as to allow of holes for receiving pins 4 inches in diameter. The cross sectional area of these pins was 15.9 inches, or rather more than 50 per cent. in excess of the cross sectional area of the link at its smallest part.

According to the usual mode of ascertaining the size of these pins, by making them of such dimensions as to resist the force required to shear them, they possessed upwards of a third more section than was thus shown to be necessary. Still, in practice, a pin of this size proved altogether disproportionate to the size of the links, and required to be increased from 4 to 6 inches in diameter before it was possible to break a link in its body or narrowest part-fracture in every previous case taking place at the hole, and through the widest part of the head, as shown in Fig. 2.

The iron in the links for this bridge was of a very high quality, and was manufactured by Messrs. Thorneycroft & Co. from a mixture of Indian and other approved pig iron, and required a tensile strength of about 27 tons per sectional inch to break it, so that taking the narrowest part at, say 10 inches, a strain of 270 tons ought (had the size of the pin been in proper proportion) to have been required to pull it into two; instead of which, so long as the pins were but 4 inches in diameter, the head tore across (as shown at Fig. 2) at its widest part with about 180 tons, or two-thirds only of the strain desired and provided for, as far as the size of the body of the links was concerned.

This unexpected result led to the belief that the size of the heads was insufficient, and accordingly a few experimental links were prepared with their heads 2 inches wider than before (as shown in Fig. 4); but these nevertheless were found to require no additional force to tear asunder; hence it became obvious that fracture arose from some cause not yet ascertained.

As has already been stated, the rupture took place across the widest part of the head (c c, Fig. 2); but on attempting to adjust the piece broken off, to the position it originally occupied in the link, it was observed that while the fractured surfaces came in contact at the outside of the head, they were a considerable distance apart at the edge of the pin-hole. (See Fig. 2.)

This at once proved that during the application of the tension, which at last ended in producing fracture, the various portions of the head had been subject to very unequal strains; and upon careful examination, the rationale of this fracture became apparent from the consideration that the hole which originally was round had become pearshaped, (see Fig. 2,) having altered its position, and that the iron of the link which, during the application of the load, bore upon the pin, and was consequently in a state of compression, had become considerably thickened in consequence, as was now evident, of an effort to obtain a greater bearing surface, (see A, Figs. 2 and 3,) while the other portion of the iron around the pin-hole, being subject to tension, had been so weakened and thinned by being stretched, as to cause a tearing action to take place, which, having once commenced, would obvi

ously, by the continuance of the same strain, rend through the entire head, no matter what its width might be.

From this it was clear that any increase of size of the head (unless by thickening, which, as I have before stated, is inadmissible) was of no avail; and it was now that the principle which forms the subject of this paper became manifest, viz: that there was a certain area of semi-cylindrical surface of the hole having a bearing on the pin proportionate to the transverse section of the body or narrowest part of a link, and quite essential to its having equal strength in all its parts; and that any departure from this proportion could not fail to bring about either waste of iron in the body of the links, if the pin was of insufficient size to offer bearing surface, or waste of metal in the heads of the links and in the pins, if the latter were larger than necessary for obtaining this fixed proportion of areas.

Having arrived at this point, a link, similar in all respects to the previous one, with holes 4 inches in diameter, and which broke across the head with 180 tons, was taken, and its holes enlarged to 6 inches, but without increasing the width of the head, which still remained 161 inches; so that the only difference was the removal of an annular piece -inch in width from the hole, and so making it 6 inches instead of 4 inches in diameter, thereby actually diminishing the quantity of iron in the head to this extent-when it was most interesting to discover that by this slight alteration, by which the semi-cylindrical surface bearing on the pin had been increased from 7.0 to 9.4 sectional inches, the power of the link to resist tension had increased in about the like proportion, having rendered a force of nearly 240 tons necessary to produce fracture.

From subsequent experience, it has become evident that had the pins of these chains increased to 6 inches diameters, giving a bearing surface of 10.2 square inches, the proper proportion between them and the body of the links would have been very nearly arrived at, while with those of only 6 inches in diameter about an inch of the body of the links was wasted.

The practical result arrived at by the many experiments made on this very interesting subject, is simply that, with a view to obtaining the full efficiency of a link, the area of its semi-cylindrical surface bearing on the pin must be a little more than equal to the smallest transverse sectional area of its body; and as this cannot, for the reasons stated, be obtained by increased thickness of the head, it can only be secured by giving sufficient diameter to the pins.

That as the rule for arriving at the proper size of a pin proportionate to the body of a link may be as simple and easy to remember as possible, and bearing in mind that from circumstances connected with its manufacture the iron in the head of a link is perhaps never quite so well able to bear strain as that in the body, I think it desirable to have the size of the hole a little in excess; and accordingly for a 10inch link I would make the pin 63 inches in diameter, instead of 61 inches, that dimension being exactly two-thirds the width of the body, which proportion may be taken to apply to every case.

As the strain upon the iron in the heads of a link is less direct than in its body, I think it right to have the sum of the widths of the iron on the two sides of the hole 10 per cent. greater than that of the body itself. (See Fig. 5.)

As the pins, if solid, would be of a much larger section than is necessary to resist the effect of shearing, there would accrue some convenience, and a considerable saving in weight would be effected, by having them made hollow and of steel.

In conclusion, I would remark that my object in writing this paper has been, first, to call attention to the fact that a link is far more likely to be torn by the pin being too small, than a pin to be sheared by a link; and secondly, to try to establish a simple rule by which their proper comparative sizes may always be arrived at; and I have been induced to investigate this very important subject from having generally found in existing suspension bridge chains a wide departure from what is right in this respect, in having the pins far too small.

On the Wear and Tear of Steam Boilers. By FREDERICK ARTHUR PAGET, Esq., C.E.

From the Journal of the Society of Arts, No. 649.

According to the published report of the engineer of the Manchester Boiler Assurance Company, forty-three explosions, attended with a loss of seventy-four lives, occurred in 1864 in this country. The engineer of the Midland Boiler Assurance Company gives the number as forty-eight, causing the deaths of seventy-five and the injury of one hundred and twenty persons. These statistics are confessedly incomplete, being, from obvious causes, numerically understated. The Royal Commissioners on the metallic mines report, that in the districts of Cornwall and Devon, boiler explosions are of very frequent occurrence;* and, in these sparsely populated districts, they easily escape the public attention. Explosions, again, which only injure without killing outright, and therefore do not call for a a coroner's inquest, also happen without attracting much notice. The figures cited thus understate the destruction and injury to life through boiler explosions, while only a guess can be hazarded as to the annual loss of property they cause. Each explosion testifies to the probability that a number of boilers have been prevented from exploding by mere chance, as also to much unchecked decay and deterioration, which might have been prevented by greater care and more knowledge. Besides, apart from the disastrous results of an explosion itself, the undue wear and tear of boilers means the suspension of the workshop or factory and the demurrage of the steam vessel. With respect to the causes of explosions themselves, "there are," to use the words of the late Mr. Robert Stephenson,t "but few cases which do not exhibit undue weakness in some part of the boiler;" and * Report of the Commissioners on the Metallic Mines. Presented to both houses of Parliament by command of Her Majesty, 1864, page 21.

† Proceedings of the Institution of Civil Engineers, 1856, page 281. VOL. XLX.-THIRD SERIES.-No. 1.-JULY, 1865.

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