MODULI OF CIRCULAR SECTIONS

INERTIA OF CIRCULAR SECTIONS.

I MOM. OF INERTIA. Z SECTION MODulus.

12.27

63.62

21.21

117.9

33.67

201.1

50.27

322.1

71.57

98.17

130.7

12 1,018

169.6

0.7854 35 73,662 4,209 68 1,049,556 30,869

2.651 36 82,448 4,580
6.283 37 91,998 4,973
38 102,354 5,387
39 113,561 5,824
40 125,664 6,283
41 138,709 6,766
42 152,745 7,274
43 167,820 7,806
44 183,984 8,363
45 201,289 8,946
46 219,787 9,556
47 239,531 10,193
48 260,576 10,857
49 282,979 11,550
50 306,796 12,272
51 332,086 13,023
52 358,908 13,804
53 387,323 14,616
54 417,393 15,459
55 449, 180 16,334
56 482,750 17,241
57 518,166 18,181
58 555,497 19,155
59 594,810 20,163
60 636,172 21,206
61 679,651 22,284
62 725,332 23,398
63 773,272 24,548
64 823,550 25,736
65 876,240 26,961
66 931,420 28,225

69 1,112,660 32,251 70 1,178,588 33,674 71 1,247,393 35,138 72 1,319,167 36,644 73 1,393,995 38, 192 74 1,471,963 39,783 75 1,553,156 41,417 76 1,637,662 43,096 77 1,725,571 44,820 78 1,816,972 46,589 79 1,911,967 48,404 80 2,010,619 50,265 81 2,113,051 52,174 82 2,219,347 54,130 83 2,329,605 56,135 84 2,443,920 58,189 85 2,562,392 60,292 86 2,685,120 62,445 87 2,812,205 64,648 88 2,943,748 66,903 89 3,079,853 69,210 90 3,220,623 71,569 91 3,366,165 73,982 92 3,516,586 76,448 93 3,671,992 78,968 94 3,832,492 81,542 95 3,998,198 84,173 96 4,169,220 86,859 97 4,345,671 89,601 98 4,527,664 92,401 99 4,715,315 95,259 |100 4,908,738 98,175

CHAPTER II.

STRENGTH OF COLUMNS.

JOHNSON'S FORMULA.

The accompanying table of strengths of wrought iron columns is based on the "straight line" formula proposed by Johnson and generally used in America. The value of the constant K is deduced by making the straight line tangent to the curve of Euler's formula.

L

PS-k

Where, P Ultimate compressive unit stress.

S

=

Maximum tensile unit stress.

kA constant whose value depends on the condition of the ends, viz., fixed, flat, hinged or round. Length of column in feet.

L=

r Least radius of gyration.

This formula may be readily memorized for wrought iron columns, thus:

-

on which basis the

r

EXAMPLE.

It is required to find the safe load with a factor of safety of 5 for a hollow wrought-steel strut or column with a length of 46 feet, mean diameter 20 inches and one-half inch thick. r = 20 ×.35 = 7.

P (from table) = 6,900 lbs.

Area of column circ. xt=62,8 × .5 31.4 "
Safe Load W=6,900 lbs. × 31.40 □=216,660 lbs.

Or, if it be required to find the thickness t of the column in the foregoing example, the load being 216,660 lbs.

(See Table of Elements of Circular Sections.)