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EXPERIMENTS ON THE STRENGTH OF IRON BEAMS.

THE experiments of Mr. Eaton Hodgkinson, of Manchester, are said to have led to a practical economy of material in the construction of the great iron girders or beams, so generally used, there and in other manufacturing districts, in the building of factories, amounting to not less than 20 per cent. of their weight.

It is very rarely that the application of principles of exact science to the uses of society is attended with success like this. And we feel that the pages of this magazine cannot be occupied more in accordance with the purposes for which it was established, than by giving publicity to these experiments.

If a beam of iron, or any other elastic or flexible material, be bent by a weight which it supports, it is manifest that the part of it lying near that side which supports the weight, will in the act of flexure be compressed, whilst that on the opposite side will be extended*. It is at that part of the beam which is nearest to its extended side that the extension is greatest, and at the part nearest to the compressed side that the compression is greatest. Between the point of greatest extension, and the point of greatest compression, the extension diminishes continually up to a certain point, where it is nothing; and beyond that point the compression commences, and continues to increase up to the other side of the beam where it is greatest. The point of the beam where the extension of its material terminates, and the compression of it begins, and where there is, therefore, neither extension nor compression, is called its neutral point. It is not at one point only, however, of the beam, that this neutral state of its compression and extension exists, but manifestly throughout all the points of a line crossing the whole width of the beam, and passing through the neutral point. This line is called its neutral axis.

The forces which oppose themselves to the rupture of the beam are the resistance of its material to extension on one side of its neutral axis, and to expansion on the other. Its power of resistance to either of these yielding, it will be broken. Thus, if the one side be so far extended that its material separates, the beam will fail, although the other side may still retain its power of resistance to compression. Or if the one side be so far compressed

* This may be seen in a very simple experiment. Let a piece of deal be gradually bent, and the part where the principal flexure takes place observed. It will be plainly seen that, on the side from which the flexure is made, the fibres elongate, and that on the other side they compress; and when a complete fracture

that it crushes, the beam will fail,

has been made, this process will be further indicated by the appearance of the broken ends which will on one side be jagged, indicating there a rupture of the fibre by tension or tearing asunder,-and on the other side, comparatively smooth, as they would be if compressed.

although the other side is still able to resist the extension to which it is subjected.

In the first case, the beam opening on the extended side, the compressed side would form a fulcrum, about which the separated part of the extended side would turn.

In the second case, the compressed side of the beam immediately beneath the weight, being no longer capable of resisting the compression to which it was subjected, would be crushed in pieces, or otherwise displaced, and the beam entirely broken; although, perhaps, the tensile resistance of the opposite side of it had never yielded.

This power of resistance to compression, and the power of resistance to extension, constituting the strength of the beam; and the yielding of either of these being of necessity followed by its entire rupture, it is manifest that the material of which the beam is composed will be distributed so as to make it the strongest when it is so distributed, that the one side shall be about to yield by compression, when the other is about to yield by extension. For, if either rupture is about to take place when the other is not about to take place, a portion of the beam might be removed from the stronger side, without causing that side to be in a state bordering on rupture, and added to the other side, so as to take that out of the state bordering on rupture. And thus if the powers of resisting compression and extension be unequal, the strength of the beam may be increased by a new distribution of the material.

This being admitted, the question of the best form of the beam resolves itself into this:-How can the material be distributed on the two sides of it so that the resistance to the compression to which the one side is subjected, and the resistance to the extension of the other may be equal? A principal element in this inquiry is manifestly this:Is the power of a given quantity of material to resist compression the same as its power to resist extension?-if it be the same, it seems probable that the object would be gained by any arrangement by which the part which is subject to compression should be made exactly equal and similar to that which is subject to extension. It appears, however, from the experiments of Mr. Rennie, that at any rate in respect to castiron, this law does not obtain. These experiments, and others of the same kind, which had before, and have been subsequently made, show very clearly that the cast-iron will resist a much greater force tending to compress it, than it is able to resist when the force tends to extend it. And that thus to produce an equal power of resistance on the two sides of the beam, a larger quantity of material should be collected on the extended than the compressed side. This idea suggested itself first, it appears, to Mr. Hodgkinson; and he contrived the following ingenious experiment to serve as a verification of it.

G

B

C

He caused two castings to be made, 5 feet in length, and whose cross-section was of the form re- A presented in the figure; the width, AB, being 4 inches, the depth of the rib, DE, 1 inches, and the thickness, BC, of the metal throughout inch. Now, it is manifest VOL. II.

I E

that this casting being placed in the position shown in the first of

the accompanying figures, with the rib downwards, and being loaded, the portion, ABCG, of the section of fracture would be subjected to compression, and the whole, or the lower part, of the rib DEF would be subjected to extension. Moreover,

the surface, AGCB, resisting the force of compression, being so much greater than the rib DEF, which opposes itself to the force of extension, it is clear that when the casting yielded, it would, under these circumstances,

yield by the extension of DEF. Again, if it were placed as in the second figure, with the rib upwards, and loaded in the middle, the compressed portion of the section of rupture would be the rib, FED, or the upper portion of it, and the extended portion ABCG. The surface sustaining the forces of compression would, therefore, in this case, be less than that sustaining the forces of extension; nearly, perhaps, in the proportion in which the area, EFD, is less than ABCG: and if FED were sufficiently small as compared with ABCG, the rib would of necessity yield to the forces which compress it, before the part ABCG yielded to the forces which extend it. Thus, in both cases, the casting would break by the yielding of the rib, EFD. But, in the first case, it would yield by the extension of that rib; and, in the second, by the compression of it. Now, it was found that the disproportion between ABCD and FED was in these castings sufficiently great to produce these results, i. e. to cause the bar used in the second experiment to yield to the compression of the rib, whilst that in the first yielded by its extension.

If, then, it be true that the same material in a beam yields more easily when it is subjected to extension than when subjected to compression, the casting ought, in the second case, when the rib was compressed until it broke, to have borne a greater weight than in the first, when it was extended until it broke.

In each experiment the supports were placed 4 ft. 3 in. asunder, and the load exactly over the middle point. In the first case, when the rib was broken by extension, the beam just bore 24 cwt., and the breaking load was 2 cwt. In the second case, where the rib was broken by compression, the beam bore 83 cwt., and was broken by 9 cwt.

Thus, then, a beam of this form and these dimensions, when turned with the rib upwards, will bear nearly four times as much as when placed

with the rib downwards, and its rib requires four times as great a power to break it by compression as by extension.

A

D

B

The weights in the last experiment were very gradually laid on, and no rupture of the material could be perceived until the instant of fracture. A wedge then flew out of. the compressed side, of which the form is accurately represented in the figure. Its length, AB, which was in the direction of the length of the casting, was 4 inches, and its depth, CD, 98 inches. This depth, probably, indicated the whole depth of the compressed portion of the section of rupture, which was, therefore, very nearly that of the rib*.

These experiments sufficiently indicate the strength gained by accumulating the material of the beam on that side of it which is subjected to extension; and they at once suggest the inquiry, what should be the amount of this accumulation? It has been shown, that the strongest form will be obtained when the material is so distributed, that it may offer the same resistance to the forces which, on the one side tend to compress it, as to those which, on the other, act to extend it. And moreover, it is now shown that less material is requisite to effect the first object than the second. The aim of the remainder of Mr. Hodgkinson's experiments, was to determine in what proportion it should be less.

Before, however, entering upon this investigation, a very simple improvement in the form of the casting suggested itself to him. Whether the beam was about to break by the separation of the extended part, and the turning of the fractured portions about the compressed part as a fulcrum, or by the yielding of the compressed parts, and the turning of the two ends about the extended part as a fulcrum. It was manifest that the forces which opposed themselves to the fracture would in either case be most effective when they acted at the greatest distance from what would in that case be the fulcrum.

Thus, then, that form of the beam would be best which placed the material which was to resist compression at the greatest distance from that which was to resist extension, or which collected the material on the upper and under sides of the beam.

This principle characterizes the forms of the sections of all the castings used in the following experiments. They were each 51 inches in depth in the middle, and broken between props 4 feet 6 inches apart. The general form or elevation of each, was that represented in the first of the following figures; and the forms of their middle sections were in the order of those shown by the diagrams below, which are each one-fourth of the real size of the section.

* The form of the wedge was remarkably regular, and it preserved its regularity of form, and the same dimensions, in a variety of other similar experiments subsequently made. We know, as yet, too little of the mechanical construction of bodies to be able to give any explanation

of the form of this wedge. The subject will, however, possibly not be found without the reach of analysis, whenever the highest resources of that master-science shall be applied to the theory of the strength of materials.

II

3

4

6

It will be observed that in the first of these the portions of the section subjected to extension and compression were of the same dimensions; and that in the second, the portion subjected to extension was greater than the other; and in the third greater still, and so on, until in the last, the portion resisting compression was exceedingly small, as compared with that opposing itself to extension.

Now, from what has been said before, it is manifest that in the first the material opposing itself to compression is in excess, and that a portion of it might be removed with advantage, and added to the lower portion of the section. This is done in the second experiment, and in a yet greater degree in the third and the fourth, &c. We may therefore expect that the beam would thus be continually strengthened up to a certain point, when the compressed portion would have become so small as to yield before the extended portion; and thus, if the gradations be sufficiently slow, the precise form under which the compressed and extended portions equally resisted the forces to which they were subjected, that is, the best form of the section, would be ascertained.

Now, the best and simplest method of comparing the strengths of beams of different sections, is probably to ascertain the weights in pounds necessary to break them, and to divide this by the number of square inches in the section of fracture of each; the quotient may be understood to be the number of pounds of strength supplied by each square inch of section; and that form of section which thus supplies the greatest