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Chap. I.
BEAMS AND PILLARS.

439 Table II., OF THE ABSOLUTE COHESIVE Power (or BREAKING WEIGHT) OF THE TIMBERS

USEALLY EMPLOYED. Sectional area, 1 inch square, 1 fuot in length. (See 1628i.)

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Tons

Saul.

lbs

Ton.. Turtosa, or African Teak L 17,200 7.58 Deal, Christiania

12,346 Teak, or Indian Oak

14,500 647
middle

T 12,400
B 15.000
Oak

11,542
12,915

B 1.00
15 780 7.04

L 11,30
L 14.130

Dantzie

L 12,740
T and B 17,207

L
· Riga.

12,8
Beerb
12.000 5.35

T 12,57 5 17
T 17.850

English

T 10,53
B 11,00

American Red

R 10,250
L 12,225
Cedar

L 7.4.0
Poona or Peon
L 12,350 5:51

11,400 Corrie

L 10.960
eľm

11,500 5:13
R 10,000

9,720 Fir or Pine, American 11,800 5.26 Chesnut, Spanish

10,800) 4.82 New England T 13,489

R 13,00
1040
Larch

9.500 4.24
12,000

L 12,240
Spruce
R 12,400

Mahogany, Honduras L 11,475 5 12
American, white
L 10,296

Spanish

L

7,560 3 37 Red Pine.

Р
12,000

B

8,000
14,000
Walnut

7,740 3.45 Weymouth or Yellow L 11.8.35

8,800 Pitch L 9.796

Hempen Rope, 1 sq. in., sec-
Mar Forest

L
7,323
tion, I foot=:578 Îns.

6,400 Scotch

L
7,110
I in.circumf.= 046 lbs.

T
Memel
L 9,540
Ditto, Cables -

R 5,600 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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99

Mean

Mean 7 14 Low Moor, (Yorkshire,) No. 3, bore 6 tons. A mixture of irons, a mean of four experiments, gave 7 tons 7 «wt.

16304. The mean of several experiments on the ultimate cohesive strength of a wrought iron bar, 1 inch square section, was :No. 11 experiments by Captain Brown, gave

56,000 lbs. = 25.00 tons. No. 9 by Telford,

65,520 = 29 25 No. 10 by Brunel,

68,992 No. 4 by Barlow,

56,560 = 25.25

Mean 61.768 lbs. = 27.575 tona. No. 3 experiments by Brunel, on hammered iron, gave 30-4, 32-3, and 30·8 tons

respectively.
Several experiments by Cubitt, gave

58,952 lbs.
= 26 tons 6.3 cwt.

Breaking
Highest

Mean Weight.

Tons, 188 bars, rolled, experimented upon by Kirkaldy, 68,848 44,584 57,555 = 253 72 angle irons

63,715

37,909 54,729 =24 167 plates, lengthways

62,544 37,474 50,737 160 plates, crossways

} -213

60,756 32,450 46,171) He states that 25 tons for bars and 20 tons for "plates, are the amounts generally assumed

Lowest

lbs.

Ibs.

lbs.

1630v. The detailed experiments by Messrs. Clarke and Fairbairn, on the strength of Iron 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 150.800 of the length, per ton, per inch square of section. The ultimate strength of plates drawn in direction of experiment 1, 19-66 tons the fibre

2, 20:2 broken across the l

1, 1693

2, 16:7 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 16311.)

"fibre

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 :

| inch diam. Crushing weight

2439 lbs. 10,171 lbs. 40,304 lbs. Proportion of weights

4:17 , 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 hy the Committee of the

Institute of British Architects, 1863-64.

inch diam.

2 inch diam,

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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.

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Tabli III. or CosiPRESSION OF TIMBER. (Hodgkinson and others).
Damp,

Damp,
Dry,

Dry,
2 ins. high
Woon.

2 ins. high
Inch high
Woon.

Ioch high

and inch diam.

generally

and

inch diam. generally.

lbs.

lbs.
lbs.

lbs.
Alder
6,831 6,960 Oak, Dantzic

7,731 Bech 7,733 9,363

English 6,484 10,058 American Birch

11,669
Quebec

4,231 5,982 English Birch 3,297 6,402 Pine, Pitch

6,790 6,790 Cedar 5,674 5,863

Yellow,full Red Deal

5,375 5,445 5,748 6,586 of turpentine White Deal 6,781 7,293

Red

5,395 7,518 Elm 10,331 Teak

12,101 Spruce Fir 6,499 6,819 Larch

3,201 5,568 Mahogany

8,198
8,198
Walnut

6,063 7,227 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 lf of the diameter or thickness of the base of the wedge.” Gregory puts the angle of this wedge at 34o. 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 A PILLAR), 10 feet long

and 1 inch square.
Compression Total

Compression Total
per Tone
Compression.

Compression.

Total Permanent Set.

Total Permanent Set.

per Ton.

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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. Rennie's calculations gave only 40 tons per square inch for the lowest estimate.

TABLE OF THE Crushing or CUBES OF IRON.
Crushing Weight.

Crushing weight.
Materials.

Materials.
Square inch.

Square inch, A cube of 1 inch side lbs.

lbs.

lbs. Soft cast iron

1,439 92,138 Cubes of | inch side 9,773 156,368 ditto, 2 beights 2,116 135,424 Horizontal casting

10,114 161.824 ditto, 3 or more

1,758

112,524 Vertical casting . 11,110 177,760 (Overman)

Directly cast, not cut from a

219,490 Cubes of 4 inch side :

larger piece Cast copper.

7,318

Same iron, but twice melted,
Cast tin

966
once in the cupola, and

262,675 Cast lead

489

(Rennie) furnace, and cast in cube (Rennie)

lbs.

Wc

4

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1631. Hodgkin son, “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 such 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 pressure 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 Alexure.” 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 +36. Here W breaking weight of long pillars, and c crushing force of the iron. (Warr and Gregory.)

163la. 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. la The formula for a rectangular pillar of oak, is

W lbs. R= 3,960. 4+:57

Ꭱb
Ib.

cast iron, is

= W lbs. R=15,300. 4d? +1872

Rbd3
Ic,

wrought iron, is

4d2+1612=W lbs. R=17,800. Ila. solid cylinder of oak, is

W lbs. R= 2,470.

4d?+-512 IIb.

cast iron, is

W lbs. R= 4d2+.1812

9,562. Ilc

wrought iron, is

4^2 +1672

W lbs. R=11,125. Here I 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 2,518 1,745

108.8 78.5 (Gregory)
English oak. Red Pine.

Larch. Elm.
100
180
79

19 12 10 (Hurst. ) 1631d. Hodgkinson, Cast Iron, 1846, states that there are general properties common to wrought iron, steel and wood. It appeared from experiments that long (solid) pillars break first at, or near to, the middle; this occurred in all cases. Pillars were, therefore, tried, having a middle diameter of from 11 to 2 inches, the ends being 1 inch. The strengtb was not increased according to the increase of the middle diameter, but appeared to be from

or from one-seventh to one-eighth ; they did not, however, fracture in the middle, as did those of uniform diameter. He found thatThe strength, as dependent on the diameter, was on the mean

3:736 length,

1.7 I, Tho formula given by him for long solid cylindrical pillars (when I exceeds 30 d) with

44.16 tons (3.35 Alat ends and fixed, is

W tons, or (33,379 lbs. = 14.901 tons). The formula for ditto with rounded ends (or when 1 is less than 30d and exceeding 15d, is

W tons, or (98,922 lbs. = 44:16 tons). Here d external diameter inches; l length feet; i of W to be taken for safe weight.

Rd

Rd"

Rd4

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Dantzie oak.

Red deal.

Trak.

18

15

1

to 6.62

1
8 05

99

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14.9 tons d3 76

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