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the reduced breaking weight, as in col. 8, showing an error of 60810 --- 60075 = 1.012, or + 1.2 per cent., as in col. 9, &c.

(224.) The sum of all the + errors in col. 9 is 225.6, and of all the errors, 243.2, giving on the thirty-six experiments an average of (243.2-225.6) = 36 = 0.461, or – 0.461 per cent. only. It will also be observed that the range of the error plus and minus is nearly equalized, the greatest + error being + 30-4, and the greatest

error is

33.0 (959). (225.) “Square Pillars of Wrought Iron." —Admitting that for wrought iron, the ratio of the strength of round and square pillars is 1.0 to 1.7, as shown by theory, we obtain the values of Mp given for square pillars by Table 34. The rules in (196) then require a simple modification, and become :(226.)

F = Me X 988 ; L?. (227.)

S = $(F XL' = Mp). (228.)

L = Y(Mp x 93-6 ; F). (229.)

FXL $96. In which S = the side of the square, and the rest as in (196). Say that we have a pillar 14 inch square, 5 feet long, with both ends pointed; then taking Mp from Table 34 at 72.74 tons, and 1736 from Table 35 = 2.2, the rule becomes 72.74 X 2.2 + 25 = 6.703 tons = F, or the breaking weight by flexure. This result will not require correction for incipient crushing : thus the area is 1.25 X 1.25 = 1.5625 square inches, and the crushing strength being 19 tons per square inch, Cp becomes 1.5625 x 19 29.69 tons, and ] Cp = 7.425 tons, and as F is less than that (169) the correction is not required.

For hollow square pillars of wrought iron the rules become :(230.)

F = Mp X (936 – 936) L. (231.) (93** — 58-6) = F x L : Mp. (232.)

{Mp * (S*** – 896) =- F}. In which S = the side of square externally, and s, internally; the rest being as in (222). Thus for a pillar in which 8 =

Me

L =

TABLE 52.-Of the STRENGTH of CYLINDRICAL PILLARS,

Diameter in Inches.

Number

of Experiment.

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Inside.

6.1064

incbes. • 1298

square inches.

2.547

1 2

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· 0939

101 098

5

6.000 5.973 5.929 3.750 3.790 3.772 3.511 3.505 3.504 3.513

•150 • 136 • 139 .2435 • 250 .2425 .241

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

99

3.504 2.717

2.712 2.693 2.275

.2455 168 .153 - 151 . 1075

feet. 10.00

7.50 10.00 5.00 2.50 9.94 7.50 9.94 7.44 7.44 7.44 5.00 2.36 5.00 7.50 2.354 9.940 9.917 5.000 2.500 2.492 2.425 10.000 5.000 2.492 2.425 10.000 5.000 2.500 2.500 9.917 5.000 2.500 9.917 5.000 2.500

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21 22 23 24 25

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26 27 28 29 30

1.939 1.910 1.925

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31 32 33 34 35

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Outside.

6.366

6.187 6:175 6.125 4.060 4.052 4.050 4.000 4.000 4.000 3.995

1.799 1.799 1.799 1.905 1.613 1.7078 2.879 2.897 2.873 2.848

99

3.995 3.035 3.000 2.995 2.490

2.895 1.414 1.414 1.349 .8045

2.382 2.373 2.350 2.350 2.343 2.343 2.310 2.335

1.651 1.554 1.605 1.4721 1.407 1.3587 1.4353 1.3718 1.4353 1.4353 • 6104

1.964

.

1:495

.4943

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made of THIN WROUGHT-IRON PLATES : both ends Flat.

Calculated Breaking Weight.

Breaking Weight by Experiment.

16,570 18:464

lbs. 91,402 106,122 60,075 69,002 74,411 49,900 53,770 47,212 74,988 76,780 79,916 98,122 137,322 86,922 42,122 52,874 37,356 23,958 28, 244 29,364 54,666 57,354 37,516 43,180 53,770 53,770 31,828 41,164 52,588 50,796 14,158 20,332 22,572

Ultimate Strength per Square Inch by Experi

ment.

Error or
Difference

Reduced,

By Flexure F.

Crushing
Strain.

per Cent.

lbs. 108,400 108,400 76,570 76,570

tons 16.021 18.600 14.908 17:123

11.710 14.880 12.340 11.628 11.832

12.418 15.381 21.530 13.404 13.299

6,514 13,860 15,204

lbs. 86,800 95,090 60,810 72,200 75,370 53,310 53,070 47,880 93,660 94,320 93,760 106,350 117,550 108,100 54,910 56,934 30,850 16,020 26,560 31,930 64,750 61,230 28,940 46,620 55,180 58,950 25,650 31,660 56,040 56,010

9,667 18,200 23,510

5,137 11,235 16,130

5.0 -10.4 + 1.2 + 4.6 + 1:3 + 6.8

- 1.3
+ 1.4
+24.9
+22.8
+20.3
+ 8.4
-14:4
+24:4
+30•4
+ 7.7
-17.4
-33.0

- 6.0
+ 9.0
+18:4
+ 6.8
-22.8
+ 8.0
+ 2.6
+ 9.6
-19.4
-23:1
+ 6.5
+10.3
- 31.8
- 18.4
+ 4:1
-21.2
- 19.0
+ 6.1

lbs.
326, 600
580,500
221,700

950,300 3,610,000

116,750 175,200 105,200 297,900 301,000 301,500

650, 200 2,919,000 660,500

95,230 791,000 50,010 22,575 88,800 355,200 619,500 619,000

37,660 136, 600 525,800 540,000

33, 160 127,150 508,600 508,600 11,530 45,360 181,440

5,295 20,830 83,310

81,075 68,650 72,690 122,500 123,300 122,300 121,200 121,200 123,200 60,180 60,180 57,420 34,240 34,240 34,240 70,270 66,140 68,310 62,650 59,880 64,210 61,090 58,380 61,090 61,090 26,040 26,040 26,040 18,870 18,870 18,870

16.693 12.362 13.294 15.670 16.290 14.780 16.476

9.600 13:094 17.060 17.665

9.901 13.392 16.357 15.799 10.350 14.866 16.509

6.550 13.920 15.277

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4 inches, 8 = 3.4 inches, L = 11 feet, both ends flat, we have 223 (436 – 3.486) 11°, or 223 (147 – 90.9) = 121 = 103.5 tons = F. Correcting for incipient crushing (164), the area of the section being 4.75 square inches, Cp becomes 4.75 X 19 = 90.25 tons, i Cp = 67.69 tons, hence Po (103.5 x 90 25) = (103.5 + 67.69) = 54:56 tons breaking weight.

With thin plates of wrought iron correction is required for incipient “ Wrinkling" (249) rather than incipient crushing: in our case, however, the wrinkling strain is (V.2514) 80, or (.5 = 2) x 80 = 20 tons per square inch, which being in excess of 19 tons, the crushing strength of wrought iron in pillars (201), the strength is governed by the latter.

(233.) “ Rectangular Pillars of Wrought Iron.”—For rectangular sections, other than square, the rules for square pillars are modified, and we have:

(234.) F = Mp x 26 xb;L?.
(235.) t="${F L'=(Me * b)}.
(236.) b = F x L2 = (Mp X 12°c).
(237.) L = Y(Mp x 428 x b = F).

(238.) Mp = F x L = ( x b). In which the letters have the same signification as in (177), namely F = the breaking weight by flexure in lbs., tons, &c., dependent on the value of Mp as given by Table 34, t = the thickness or least dimension of the rectangular pillar, the 2.6 power of which is given by col. 3 of Table 35; b = the greatest dimension, and L = length in feet, &c.

(239.) Table 53 gives the results of twenty-one experiments on solid rectangular pillars of wrought iron by Mr. Hodgkinson; col. 9 has been calculated by the rule (234), the value of Mp for rectangular pillars with both ends flat being taken at 498,500, or say 500,000 lbs., from Table 34. Thus taking No. 9 as an example, to find t's, the logarithm of .995 or 1.9978 x 2.6 = 1.99428, the natural number due to which, or .9869, is the 2.6 power of t, and 7.5being = 56.25, the rule becomes 500000 x .9869 x 5.86 • 56.25 = 51410 lbs. = F, or the breaking weight by flexure, as in col. 9. We shall find that this does not require correction for incipient crushing; the area of the section is 5.86 x .995 5.8307 square inches, and the crushing strength being 19 tons or 42,560 lbs. per square inch (201), Cp becomes 42560 x 5.8307 = 248100 lbs., as in col. 8, therefore Cp = 62025, and as F is less that, namely 51,410 lbs., the correction is not required (164). The experimental breaking weight was 54,114 lbs., as in col. 5, hence we have 51410 = 54114 • 95, showing a difference or error of 5 per cent., as in col. 7. TABLE 53.-Of the STRENGTH of RECTANGULAR, SOLID PILLARS of

WROUGHT IRON, both ends Flat.

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feet.
tons. lbs. lbs.

lbs.

lbs. 1 10 2.98 x 497.364 ? 1,222 2,418

63,030 2,418 210 3.01

X 766 1.508 7,793 7,526 3.4 98,140 7,526 310 2.99

X .995

1.911 12,735 14,760 + 15.0 126,600 14,760 410 3.00 x1.51 4.538 46,050 43,800 4.9 192,800 43,800 5 7.5 1.024 x1.025 4.354 10,236 9,691 5.344,670 9,691 6 7.5 2.983 x 5023 1.076 3,614 4,424 + 22:4 63,770 4,424 7 7.5 3.005 x .9955 4.425 29,616 26,400 10.9 127,300 26,400 8 7.5 3.00 x1.53 8.923 91,746 59,600 - 34.8 195,300 64,310 9 7.5 5.86 x 995 4.143 54,114 51,410 5.0 248, 100 51,410 10 5 1.024 1.024 7.709 18,106 17,590 2.8 44,600

21,780 11 5 2.98 X 507

2.502 8,469 10,190 + 20.4 64,310 10,190 12 5 3:01 x 767 5.790 29,955 28,400 5.2 98,270 30,060 13 5 3:01

X +995

8.066 54,114 48,860 9.7 127,400 59,420 14 5 5.84 x •996 7.901102,946 94,980 7.7 247,600 115,600 15 2.5 1.0235 x1.0235 11.307 26,530 32,200 + 21:4) 44,580 86,980 16 2.5 2.9867 x 5026 7.524 25,299 29,080 + 15.063,890 40,030 17 2.5 3:01 x 763 12.396 63,786 60,530 5:1 97,760 119,200 18 2.5 3.00 x 996 13.239 88,610,90, 730 + 2.4 127,200 237,500 19 1.25 1.023 x1.023 15.426 36,162 40,630 + 12 3 44,540 347,400 20 0.625 1.023 x 1.023 21.733 50,946 43,500 - 14.6 44,5101,389,000 21 0.3125 1.023 *1.023 23.549 52,749 44,284 44,540 5,558,400 (2) (3)

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