Abbildungen der Seite
PDF
EPUB

with their diameters. It may at least enable us the better to appreciate the better lights since shed upon the subject.

LXXXVIII. EXPERIMENTS UPON THE NEGATIVE STRENGTH OF CAST IRON, IN LONG PIECES.

Ends, flat cones or pyramids.

[merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small]

L 9.

19

Form

of

section.

Inches.

Diam.

: : S | Length

[blocks in formation]
[ocr errors]

Remarks.

0 16 990 1002 Broke in. from centre.
978 990 Broke in. from centre.

0.15 803

"

66

854 Deflected cornerwise, and flew out without breaking.

914 938 Broke in half a minute not cornerwise, inch from centre. 7.1 0.126 1417 1437 Broke in 3 seconds, in. from

6

[ocr errors][ocr errors][ocr errors][ocr errors]
[merged small][ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small]
[blocks in formation]

From experiments 7 and 8, in the above table, it appears that cast iron will sustain at the extreme, in cylindrical pieces whose lengths equal about 14 diameters, a negative strain of 41,000 to 51,000lbs to the square inch, say an average of 46,000. Square bars, according to experiment 9, length equal to 18 diameters (or widths of side), will sustain about 45,000lbs to the square inch.

Now, a hollow cylinder of a thickness not exceeding about of the diameter, according to calculation, has a stiffness transversely, about 50 per cent greater to the square inch than a solid square bar whose side equals in width the diameter of the cylinder. Hence, a hollow cylinder of a length equal to 18 times its diameter, should sustain a negative strain of 67,500 lbs. to the square inch. But it should be observed, however, that direct experiments upon the transverse strength of the pieces used in the experiments leading to the results and conclusions above stated, as to negative strength, showed themto possess uncommon strength transversely, even to from 30 to 50 per cent greater than the fair average transverse strength of cast iron; as will be seen hereafter. It is therefore not considered proper to estimate the strength of hollow cylinders of the propor tions above stated at more than 45,000 or 46,000lbs. to the square inch.

The hollow cylinder is undoubtedly the form best adapted to the sustaining of a negative strain, having equal stiffness in all directions. It is therefore highly desirable that the power of that form of pieces to resist compression, with different lengths, should be ascer tained by a careful and extensive series of experiments. But until that shall have been done, and the results made known, I shall assume the above estimate upon the subject, as probably not very far from the truth; subject, however, to correction, whenever the facts and evidences shall be obtained, upon which the correction can be founded.*

In the mean time, since we know not the exact ratio between the greatest safe practical stress, and the ab

* Since the original writing of this paragraph (25 years ago), extentensive experiments and investigations have been made, in the direction

Bolute strength of iron, and therefore should in practice keep considerably within the limits of probable safety, it becomes a matter of less importance to know the exact absolute strength; though this, of course, is desirable.

LXXXIX. Having decided upon a measure of strength for pieces of a given length, we may properly endeavor to ascertain the rate of variation for different lengths as compared with the diameters.

It is seen in the table, [LXXXVIII] that two cylindrical pieces of 9 inches in length, bore the one 990, and the other 978bs., giving a mean of 984 pounds.

d's

729

Now, by the formula. the same cylinders reduced to 4.5 inches, should sustain four times as much, or 3936lbs. But, by experiments 7 and 8, we find that they bore only 2,580, and 3,218, a mean of 2,899 pounds. Whence it appears that, the diameter being the same, the strength diminishes faster than the length increases, but not so fast as the square of the length increases; being about half way between the two. In fact, if we examine the results of these experiments. throughout, we find that the weights borne by pieces of like cross-sections, whether round or square, were very nearly the arithmetical mean between the results obtained by considering them to be inversely as the simple length, and as the square of the length, successively.

For illustration; take experiments 1 and 5. If the piece 9 inches long bore 990 lbs., taking the strength

here indicated, and ingenious and convenient formulæ deduced upon the subject involved, which might perhaps, be profitably substituted for the writer's own crude deductions in this behalf. But, as previously remarked on other occasions, the latter may possess interest as affording a monument upon the line of the march of progress.

[ocr errors]

to be inversely as the length, we have this proportion

1

9

:

1

7.1

: 81

:: 990: 1,255. Then, taking the strength to be inversely as the square of the length, we have: 15041 :: 990: 1,591. Taking the mean of these results, we find (1,255 +1,591), ÷ 2 = 1423. This is the weight which, according to the rule, the piece in experiment 5 should have borne, and it varies only 6lbs. (less than of one per cent), from what it actually did bear.

Again, take experiments 1 and 8; in which the lengths were as 2 to 1. Supposing the weights to be inversely as the lengths, and as the squares of the lengths successively, and taking the mean of the results, we have (1,980+3,960)÷2=2,970, which is 248lbs. less than the weight borne in experiment 8. But it is also 390lbs. greater than that borne in experiment 7, by a piece of similar form and dimensions, but an inferior specimen. It does not seem, therefore, that the rule is widely at fault.

The same rule applied to experiments 4 and 9, lengths being also as 2 to 1, gives 2,784 lbs. as the bearing weight, and 2,814 as breaking weight for No. 9; the former varying 71lbs. and the latter 24lbs. from the weights shown in the table. Now, if we observe that the one broke in a quarter of a minute, and the other endured half a minute, it is no extravagance to assume that if No. 9 had been loaded with 24lbs. less, it would have stood of a minute longer, giving a result in precise accordance with the rule.

From what precedes, it is believed that the following may be adopted as a safe practical rule for determining the power of resistance to compression, for pieces of similar cross-sections, after knowing from experiment, the power of a piece of given dimensions, and similar cross section.

[ocr errors]

and as D

L

[ocr errors]

Rule: Make the power of resistance as cessively, and take the mean of the results thus obtained, as the true result; D representing the diameter (or width of side, in square pieces), and L, the length of the piece.

This rule will be probably apply without material error, to pieces of lengths from 15 to 40 times as great as their diameters, and perhaps for greater lengths; although, in bridge building, greater lengths will seldom be employed.* But, as the length is reduced to 8 or 10 diameters, or less, it is manifest that the power of resistance increases at a less rate than that given in the rule. For, we see by the table of experiments, that a square piece of a length equal to 18 diameters (experiment 9), bore at the rate of 45,000lbs. to the square inch, which is nearly one-half of the average crushing weight of cast iron, and one-third that of the strongest iron. But according to the rule, a piece of half that length, or equal to 9 diameters, should sustain 135,000lbs. which is about the maximum for cast iron; whereas, experiment shows' that the power of resist ance increases with reduction of length, down to about 2 diameters. It may, therefore, be recommended to apply the rule above given, to hollow cylindrical, and square pieces above 15, and to solid cylinders, above 12 diameters. From those lengths down to 2 diameters, it cannot lead to material error to estimate an increase of power proportionate to diminution of length, according to the differences between the weights, or resisting powers determined as above, for square pieces and hollow cylinders of 15, and solid cylinders of 12 diameters in length, and the absolute crushing

*It is probable that for greater lengths than 40 diameters, the formula alone, would be more nearly sustained than in case of smaller lengths.

L2

« ZurückWeiter »