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CHAPTER VI.

ON THE CRUSHING STRAIN.

(129.) We are indebted to Mr. Hodgkinson for almost the whole of our exact knowledge of the strength of materials in resisting crushing strains, and from his experimental investigations we obtain the following laws:—

1st. That for specimens whose height is between 1 and 3 times the diameter or side of square, the crushing strain is simply proportional to the area.

2nd. In that case the plane of rupture is inclined at an angle with the base, and therefore with the axis, which angle is constant for the same material, but is different for different materials.

3rd. That for heights less than 1 times the diameter, the crushing strain becomes greater irregularly with the reduction in height (130).

4th. For very great heights, the specimen becoming a pillar of considerable length in proportion to the diameter, failure takes place by lateral flexure, with a load very much less than that necessary to crush the material (306).

5th. For intermediate heights, the pillar fails with an intermediate load, partly by flexure, and partly by incipient crushing (163).

(130.) "Cast Iron."-The effect of height is well illustrated by some experiments by Mr. Hodgkinson on cylinders inch diameter, the heights being

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tons; the equivalent strains per square inch were

69.3 63.5 60.0 55.0 53.3 53.3 49.6 34.4 tons. It appears from this that when the height is equal to the diameter the resistance to crushing is 5553·3 = 1·032, or 3.2 per cent. greater than when the height is between 1 and 2 with diameter 1.0.

(131.) Table 31 gives the general results of Mr. Hodgkinson's experiments on the crushing strength of cast-iron cylinders inch diameter; those in col. 1 were 1 inch in height, or double the diameter; those in col. 4 were inch high, and they show an excess of 5.8 per cent. over those in col. 1.

Most of the old experiments on the resistance of materials to crushing by Rennie, Bramah, and others, were made on cubes, and it has been objected that this fact vitiates their results, but we have seen that in cast iron at least the difference is from 3.2 to 5.8 per cent. only, so that the earlier experiments on cubes may be accepted as correct enough for practice.

TABLE 31.-Of the TENSILE and CRUSHING STRENGTH of CAST IRON, in Tons per Square Inch.

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(132.) Admitting the experiments on specimens whose height is double the diameter, col. 1, as the more correct, the mean resistance of cast iron to crushing may be taken at 43 tons, or 96,320 lbs. per square inch, and the mean tensile strength, in col. 2, being 7.142 tons, or 16,000 lbs., the ratio becomes practically 6 to 1.

It will be observed that there is great variation in the crushing strength of cast iron, as shown by col. 1, Devon being 64.92 and Lowmoor 25 198 tons, giving a ratio of 2.57 to 1.0. The mean crushing strength being 100, the maximum = 156, and the minimum 61; the effect of re-melting is shown by

col. 3 of Table 2.

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With the tensile strength the variation is much less, ranging from 10.477 tons in Clyde iron to 5.667 with Lowmoor, the variation being 1.85 to 1.0: the mean tensile strength being 100, the maximum = 147, and the minimum 79. Table 147.

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(133.) "Wrought Iron and Steel.”—It is shown in (503) that there is great difficulty in determining the ultimate or absolute crushing strength of all malleable metals such as wrought iron, which in short specimens flow or spread out laterally under the pressure rather than crush or break. Wrought iron practically fails entirely with about 12 tons per square inch, the extensions and compressions with greater strains becoming excessive, as shown by the diagram, Fig. 215. Experiments on the transverse strength (520) seem to show 24 tons as the absolute crushing strain, but with pillars of different kinds 19 tons per square inch agrees the best with the results of experiment (201), from which it appears that the resistance of wrought iron is 24 ÷ 19 = 1.26, or 26 per cent. greater in beams than in pillars. The wrinkling strain shows similar differences, namely, 10480 = 1.30, or 30 per cent. greater in beams than in pillars (322).

With steel, the apparent crushing strength under transverse strains seems to be 61.48 tons per square inch (507), but with steel pillars, 52 tons agrees better with experiment (268), the difference being 61.4852 = 1.18, or 18 per cent.

This difference of resistance to crushing in beams and pillars is remarkable, but admits of explanation. In a short pillar

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every part of the cross-section is equally strained or nearly so, but in a beam the strain is a maximum at the edge of the section, and is supposed to diminish in arithmetical ratio toward the neutral axis, where it becomes nil, as shown in (494) and Fig. 164. But when a wrought-iron bar is deflected by the transverse strain, the malleable nature of the metal causes it to yield so much under the maximum pressure at the remote edge that heavier strains are thrown on the rest of the section. For example, Fig. 30 is the section below the neutral axis of a bar of any material whose maximum resistance to crushing at A = 19 tons per square inch, therefore 9 tons at B, 4 at C, &c., the mean of the whole being 9 tons. Let Fig. 31 be a similar beam where the maximum 24 tons, &c., the mean of the whole being 12 tons. Now let Fig. 32 be another beam whose resistance at B 14 tons: if, therefore, the resistance is proportional to the distance from the neutral axis, it should be 29 tons at A, but if we allow that the metal there compresses excessively, as in diagram, Fig. 215, until it is reduced to 19 tons, we then have a double series of strains as in the figure, the mean of the whole being 12, as in Fig. 32. It will now be observed that Fig. 32 gives the same mean crushing strain with 19 tons maximum, as Fig. 31 gave with 24 maximum: the apparent maximum strain in Fig. 32 is 24 tons, although the real maximum 19 tons only: see (504).

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In confirmation of this reasoning it should be observed that with cast iron, which maintains comparative uniformity in its compression under crushing strain, as shown by the diagram, Fig. 215, the crushing strength is the same in pillars as in beams, namely, 43 tons per square inch.

(134.) “ Timber.”—Table 32 gives Mr. Hodgkinson's experiments on the crushing strength of various kinds of timber: the results in col. 2 were a mean of about 3 experiments on cylinders 1 inch diameter and 2 inches high, with flat ends, the woods being moderately dry or in the ordinary state. Col. 1 were specimens turned to the sizes and kept drying in a warm place for two months: the lengths of these specimens were in some cases 1 inch only, being equal to the diameter, which would increase the strength a little (129).

TABLE 32.-Of the STRENGTH of TIMBER to RESIST CRUSHING STRAINS, in Lbs. and Tons per Square Inch.

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* Calculated from the general ratio of the experiments in columns 1 and 2, which is 1.3 to 1.0.

The effect of the drying process on most kinds of wood is to increase the crushing strength, varying from nothing with bay, mahogany, and pitch-pine to 2.11 with willow, col. 5: the mean increase for the 29 kinds of timber is 1.30, or 30 per cent. In several cases indicated by a *the experiments were made with the wood in one of the states only: in those cases the strength in the other state was calculated by the general ratio 1 to 1.3, &c.

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