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If the weight to be sustained be given, and the sectional dimensions of the bar be required, divide the weight given by one third or one-quarter of the cohesive strength, and the square root of the quotient will be the side of the square. If the section b rectangular, the quotient must be divided by the breadth.

TABLE I., OF THE ABSOLUTE COHESIVE POWER (OR BREAKING WEIGHT) OF METAIS: Sectional area, 1 inch square, 1 foot in length.

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Tables I. and II. are derived chiefly from the summary in Rankine's Civil Engineeri p. 511, obtained from the experiments of Clay, Fairbairn, Hodgkinson, Mallet, Mor Napier, Napier and Sons, Rennie, Telford, and Wilmot. Most of the remainder are fr Rennie and other authorities.

1630s. English boiler-plates are stated to be of two classes: Yorkshire, and the mai facture of other districts, classed as Staffordshire.

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R

103,400

33,892 15-08
19,096
30,000

36,000

60,000

17.958

49,000

R 7 to 8,000

4,736 2-11

4,600

3,250

1-45

1,824

0-81

3,300

360

Telford

38 4

in.}

T

600

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TABLE II., OF THE ABSOLUTE COHESIVE POWER (OR BREAKING WEIGHT) OF THE TIMBERS USUALLY EMPLOYED. Sectional area, 1 inch square, I foot in length. (See 1628i.)

TIMBER.

Rennie, 1817, and others.

Turtosa, or African Teak
Teak, or Indian Oak

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15,000
12,915

Oak

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11,500

American Red

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LT BLLLTTAL·LELLA

Ibs. 12,346

Tons.

12,400

11,592

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R

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14,000

Walnut

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11,835

L

8,800

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1630t. The tensile strength of cast iron was long very much overrated when Tredgold estimated it at 20 tons. Captain Brown, however, put it at 7.26 tons; G. Rennie (Phil. Trans. 1818) obtained 8.52 and 8-66 tons; Barlow conjectured at least 10 tons from theoretical principles; Hodgkinson made the following experiments more recently;

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Low Moor, (Yorkshire,) No. 3, bore 6 tons.

A mixture of irons, a mean of four experiments, gave 7 tons 7 cwt.

1630. The mean of several experiments on the ultimate cohesive strength of a wrought

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No. 3 experiments by Brunel, on hammered iron, gave 304, 323, and 30'8 tons

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188 bars, rolled, experimented upon by Kirkaldy, 68,848 44,584

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57,555 54,729 63,715 37,909 62,544 37,474 50,737 | 60,756 32,450 46,171 ( He states that 25 tons for bars and 20 tons for plates, are the amounts generally assumed

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1630v. The detailed experiments by Messrs. Clarke and Fairbairn, on the strength of sron plates, are given in the work by the latter, and in the Engineers' Pocket Book for 1861 and 1865. Clarke assumes the ultimate tensile strength of wrought iron plates at 20 tons per square inch, and of bars at 24 tons, and that within this former limit, its extension may be taken at 10,000 of the length, per ton, per inch square of section. The ultimate strength of plates drawn in direction the fibre

fibre

experiment 1,

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2,

19-66 tons 20. 2

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The ultimate extension was twice as great when the plate was broken in the direction of the fibre. The best scrap rivet iron, made by Messrs. Mare at their London works, broke on an average with 24 tons per square inch; the mean ultimate extension, which was uniform, was of the length. (See 1631r.)

COMPRESSION, &c.

1630w. Compression is the second of the forces under which TRANSVERSE STRAIN is com prised. The following facts appear to be well established as to materials under a crushing force. I. The strength is as the transverse area or section. II. The plane of rupture in a crushed body is inclined at a constant angle to the base of the body.

III. The measure

of compression-strength is constant only within certain proportions of the height and diameter in any specimen. Hodgkinson found that twelve cylinders of teak wood furnished the following results:

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The areas being as the squares of the diameters an exact proportion would have been 1, 4, and 16; but some materials may possibly be found to have an increased apparent strength TABLE I., OF EXPERIMENTS ON TIMBER PILLARS, made by the Committee of the Institute of British Architects, 1863-64.

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Rondelet gives the power of Oak as 6,853 lbs., and of Fir as 8,089 lbs. (See par. 1601.) Rennie (inch cube, crushed) English oak, 3,860 lbs. ; a piece 4 inches high, 5,147 lbs. Elm, 1,284 lbs.; White Deal, 1,928 lbs.; American Pine, 1,606 lbs.

TABLE III. OF COMPRESSION OF TIMBER. (Hodgkinson and others).

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1630r. It is now a well ascertained circumstance that the crushing strength of a body varies according to its relative height and breadth. Hodgkinson remarks, "When bodies are crushed they give way by a wedge sliding off in an angle dependent on the nature of the material; and in cast iron the height of this wedge is about 14 of the diameter or thickness of the base of the wedge." Gregory puts the angle of this wedge at 34°. If the body to be crushed is shorter than would be sufficient to admit a wedge of the full length to slide off, then it would require more than its natural degree of force to crush it; because the wedge itself must either be crushed, or slide off in a direction of greater difficulty. If, on the other hand, the height of the body to be crushed be much greater than the length of the wedge, then the body will sustain some degree of flexure, and fracture will be facilitated in consequence. Phil. Trans., 1840, cxxx, page 419. Warr says, "It is highly probable that none of Hodgkinson's values would agree with the most careful trial on any similar woods." See 1502d, et seq.

1630y. The power of resistance to compression of cast-iron was heretofore very much overrated. It has now been well ascertained by experiment that a force of 93,000 lbs. upon an inch square will crush it; and that it will bear 15,300 lbs. upon an inch square without permanent alteration.

TABLE OF THE COMPRESSION OF A CAST IRON BAR (AS & PILLAR), 10 feet long and 1 inch square.

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Rennie's

1630z. Hodgkinson's experiments in 1851 on the ultimate strength of cast iron, the pieces being placed in an iron box or frame, gave a mean in 81 trials of 107,750 lbs. per square inch, or 48 tons 2 cwt.; and the crushing force to the tensile, as 6.507 to 1. calculations gave only 40 tons per square inch for the lowest estimate. TABLE OF THE CRUSHING OF CUBES OF IRON.

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1631. Hodgkinson, "considering the pillar as having two functions, one to support and the other to resist flexure, it follows that when the material is incompressible (supposing suct to exist), or when the pressure necessary to break the pillar is very small on account of the greatness of its length compared with its lateral dimensions, then the strength of the whole ransverse section of the pillar will be employed in resisting flexure; when the breaking pres. sure is one half of what would be required to crush the material, one-half only of the strength may be considered as available for resistance to flexure, whilst the other half is employed to resist crushing; and when, through the shortness of the pillar, the breaking pressure is so great as to be nearly equal to the crushing force, we may consider that no part of the strength of the pillar is applied to resist flexure." Thus he assumed that the real breaking weight would be equal to the breaking weight as obtained for the long columns, multiplied by the force requisite to crush it without flexure; and divided by the same two quantities added together, minus the pressure which it would support as flexible, without being weakened by crushing. The formula thus found for calculating the strength was W+3. Here W breaking weight of long pillars, and e crushing force of the iron. (Warr and Gregory.)

We

1631a. Euler, treating on the strength of pillars purely on theoretical grounds, showed that the strength varied as the fourth power of the diameter, and inversely as the square of the length of the pillar. The strength of similar pillars increases as the square of their diameter; and as the area is as the square of the diameter, the strength increases as the area of the pillar (Warr.)

16316. The strength of a pillar or a column, or the power of resistance to compressive force, is obtained by the law that the resistance to crushing is as the cube of the thickness multiplied by the width, and this divided by the square of the length. Therefore in columns of equal length and thickness, the resistance is as their width; and in equal lengths and widths, it is as the cube of the thickness. If the width and thickness be equal, or if the pillar be square, the resistance is inversely as the square of its length. Ia. The formula for a rectangular pillar of oak, is

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Rd4 4d +1872

Rd4 4d2+1672

=

W lbs. R= 3,960.

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Here length in feet; b breadth in inches; d diameter in inches; R resistance to compressive force; W breaking weight of the pillar or cylinder. (Tredgold, Cast Iron.) 1631c. The relative strengths of long columns of different materials, but of the same dimensions, are as follows:

Cast iron. Cast steel. Wrought iron. 1,000

100

2,518

180

1,745

79

Dantzic oak.
108.8

Red deal.

78.5 (Gregory)

19

English oak. Red Pine. Teak. Larch. Elm. 18 15 12 10 (Hurst. 1631d. Hodgkinson, Cast Iron, 1846, states that there are general properties common t wrought iron, steel and wood. It appeared from experiments that long (solid) pillar break first at, or near to, the middle; this occurred in all cases. Pillars were, therefore tried, having a middle diameter of from 1 to 2 inches, the ends being 1 inch. The strengt was not increased according to the increase of the middle diameter, but appeared to b from to or from one-seventh to one-eighth; they did not, however, fracture i the middle, as did those of uniform diameter. He found thatThe strength, as dependent on the diameter, was on the mean

1 6.62

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I, The formula given by him for long solid cylindrical pillars (when 7 exceeds 30 d) wi flat ends and fixed, is W tons, or (33,379 lbs. =14.901 tons). formula for ditto with rounded ends (or when I is less than 30d and exceedi 15d, is 21-7 W tons, or (98,922 lbs. =44·16 tons). Here d external diamet inches; length feet; of W to be taken for safe weight.

14.9 tons d3 76

=

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