CHAPTER XI.

STRENGTH OF POSTS, STRUTS, AND COLUMNS.

As the strength of a post, strut, or column, depends primarily upon the resistance of the given material to crushing, we must first determine the ultimate crushing-strength of all materials used for this purpose.

The following table gives the strength for all materials used in building, excepting brick, stone, and masonry, which will be found in Chap. VI.

TABLE I.

Average Ultimate Crushing-Loads, in Pounds per Square Inch, for Building-Materials.

The values given for wrought and cast iron are those generally used, although a great deal of iron is stronger than this. The values for white oak, yellow pine, and spruce, are derived from experiments on full-size posts, made with the government testingmachine at Watertown, Mass.; the smaller value representing the strength of such timber as is usually found in the market, and the larger value, the strength of thoroughly seasoned straightgrained timber. For these woods a smaller factor of safety may be

used than for the others, the strength of which was derived from experiments on small pieces.

The values for wood are for dry timber. Wet timber is only about one-half as strong to resist compression as dry timber, and this fact should be taken into account when using green timber.

The strength of a column, post, or strut depends, in a large measure, upon the proportion of the length to the diameter or least thickness. Up to a certain length, they break simply by compression, and above that they break by first bending sideways, and then breaking.

Wooden Columns.

For wooden columns, where the length is not more than twelve times the least thickness, the strength of the column or strut may be computed by the rule,

Safe load =

area of cross-section X C
factor of safety

(1)

where C denotes the strength of the given material as given in Table I.

The factor of safety to be used depends upon the place where the column or strut is used, the load which comes upon it, the quality of the material, and, in a large measure, upon the value taken for C.

Thrus for white oak, yellow pine, and spruce, the value C is the actual crushing-strength of full-size posts of ordinary quality: hence we need not allow a factor of safety for these greater than four. For the other woods, we should use a factor of safety of at least six.

If the load upon the column or post is such as comes upon the floor of a machine-shop, or where heavy machinery is used, or if the strut is for a railway-bridge, a larger factor of safety should be used in all cases.

If the quality of the timber is exceptionally good, we may use the larger values for the constant C, in the case of the last four woods given in the table. For ordinary hard pine or oak posts, multiply the area of cross-section in inches by 1000; for spruce, by 800, and for white pine, by 700 pounds.

EXAMPLE I. - What is the safe load for a hard-pine post 10 by 10 inches, 12 feet long?

Ans. Area of cross-section = 10 x 10 = 100 square inches; 100 × 1000 100,000 pounds.

EXAMPLE II.-What is the safe load for a spruce strut 8 feet long, 6" x 8"?

Ans. Area of cross-section = 48; 48 x 800 = 38,400 pounds.

Strength of Wooden Posts over Twelve Diameters in Length.

When the length of a post exceeds twelve times its least thickness or diameter, the post is liable to bend under the load, and hence to break under a less load than would a shorter column of the same cross-section.

To deduce a formula which would make the proper allowance for the length of a column has been the aim of many engineers, but their formulæ have not been verified by actual results.

Until within two or three years the formulæ of Mr. Lewis Gordon and Mr. C. Shaler Smith have been generally used by engineers, but the extensive series of tests made on the Government testing machine at Watertown, Mass., on full-size columns, show that these formulæ do not agree with the results there obtained.

Mr. James H. Stanwood, Instructor in Civil Engineering, Mass. Institute Technology, in the year 1891 platted the values of all the tests made at the Watertown Arsenal up to that time on fullsize posts From the drawing thus obtained he deduced the following formula for yellow pine posts:

Safe load per square inch

=

1,000 - 10 x

length in ins.
breadth in ins.

The author has carefully compared this formula with the results of actual tests, and with other formulæ, and believes that it meets the actual conditions more nearly than any other formula, and he has therefore discarded the tables of wooden posts given in the previous editions of this work and prepared the following tables for the strength of round and square posts of sizes coming within the range of actual practice.

For other sizes the loads can easily be computed by the formula.

The loads for oak and white pine posts were computed by the following formulæ :

in which the breadth is the least side of a rectangular strut, or the diameter of a round post. The round posts were computed for the half-inch, to allow for being turned out of a square post, of the size next larger.

The formula were only used for posts exceeding 12 diameters for yellow pine, and ten diameters for other woods.

For posts having bad knots, or other defects, or which are known to be eccentrically loaded, a deduction of from 10 to 25 per cent. should be made from the values given in the tables.

SAFE LOAD IN POUNDS FOR YELLOW PINE POSTS (ROUND

6 x 6.

6x8.

6 x 10..

7 Round
8×8.
8 × 10.
8 × 12

9 Round

10x 10.. 10 × 12.

10 × 14.

11 Round 12 x 12....

12 x 14.

12 x 16.

14 × 14. 16 x 16. 18 × 18

20 x 20.

19,590 18,760 17,550 16,500

30,200 28.800 27.400 25.900 25,200 24,500
40,300 38,400 36,500 34,600 33,600 32.600||
50,400 48.000 45,600 43.200 42.000 40,800
38,540 37,130 35,710 34.300 33,590 82.890
64,000 54,400 52,500 50,600 49,600 48.600 46,700
80,000 68,000 65,600| 63,200 62,000 60,800 53,400)
96,000 81,600 78,700 76,800 74,400 73,000| 70,100
70.900 61,970 60.190 58.350 57,429| 56,580 54,800]
100,000 100,000 85,600 83,200 82.000 80,800 78,400) 76,000
120,000 120,000 102.700 99,800 98,400 97,000 94,100 91.200
140.000 140,000 119.800 116,500 114,800 113,100 109,800 106,400
103,900 103,900 90,912 88,730 87.090 86,530 84,160 82,290
144,000 144,000 144,000 123,800 122.400 121,000 118.100 115,200 109,440
168,000 168,000 168,000 144,500 142,800 141,100 137,800 134.400 127.680
192.000 192,000 192,000 165,100 163,200 161,300 157,400 153,600145,920
196,000 196,000 196,000 196,000 170,500 169,100 165,800 162,400 155,800
256,000 256,000 256,000 256,000 229,100 225,300,221,400 217,600 209.900
324,000:324,000 324,000:324,000 324,000 289,400 285,100 280,800272,160
400,000 400,000 400,000 400,000 400,000 400,000 356,800 352,000 342,400

SAFE LOAD IN POUNDS FOR OAK AND NORWAY PINE POSTS (ROUND AND SQUARE).

6×6..

6x8..

6 x 10.

7 Round

8×8
8 x 10.

8 x 12.

94 Round
10 × 10..
10 × 12..
10 x 14..

11 Round
12 x 12..
12 x 14.

12 x 16.
14 x 14.
16 x 16.
18 × 18

20 x 20.

13,680 12,600 11,520

14,700 13,900 13,160 12,370

22,680 21,600 20,520 19,440 18,900 18,360
30,240 28,800 27,360 25,920 25,200 24,480
37,800 26,000 34,200 32,400 31,500 30,600
28,900 27,850 26,780 25,720 25,190 24,660
42,240 40,768 39,360 37,880 37,120 36,480 35,000
52,800 50,960 49,200 47,360 45,400 44,600 43,760
63,360 61,152 59,040 56,830 55,680 54,720 52,500
47,960 46,440 45,160 43,740 43,100 42,400 41,120
75,000 66,000 64,200 62,400 61,500 60,600 58,800 57,000
90,000 79,200 77,040 74,880 73,800 72,720 70,560 68,400
105,000 92,400 83,880 87,360 86,100 84,840 82,320 79,800
77,925 69,820 68,160 66,490 65,770 64,833 63,170 61,600
108,000 108,000 95,040 92,880 91,700 90,700 88,560 86,400 82,080
126,000 126,000 110,800 108,300 107,000 105,840 103,300 100.802 95,760
144,000 141,000 126,700 123,800 122,300 120,900 118,000 115,200 109,400
147,000 147,000 147,000 129,300 128,100 127,000 124,400 121,900 116.800
192,000 192,000 192,000 192,000 170,500 168,900 166,100 163,000 157,400
243,000 243,000 243,000 243,000 243,000 217,000 213,800 210,600 204,100
300,000 300,000 300,000 300,000 300,000 300,000 267,600 264,000 256,000

SAFE LOAD IN POUNDS FOR WHITE PINE AND SPRUCE POSTS (ROUND AND SQUARE).

6×6..

6×8.

6 × 10.

Round

8x8.
3 × 10.
8 × 12..

94 Round

19 × 10.. 10 × 12. 10 × 14.

114 Round
12 x 12..
12 x 14.
12-16.

14 x 14...
16 x 16.

18 × 18. 20 x 20.

11,520 10,550 9,800 8,700
12,350 11,730 11,180 10,490

19,080 18,216 17,352 16,490 16,050 15,620
25.440 24,290 23,140 21,980 21,400 20,830
31,800 30,360 28,920 27,480 26,760 26,040
24,220 23,380 22,540 21,660 21,260 20,820
35,450 34,300 33,150 32,000 31,420 30,850 29,700
44,320 42,480, 41,140 40,000 39,280 38.560 37,120
53,180 51,450 49.730 48,000 47,140] 46,270 44,544
40,000 39,000 37,860 36,800 36,230 35.730 34,670
62,500 55,400 53,960 52,520 51,800 51,080 49,640 48,200
75,000 66,480 64,800 63,000 62,160 61,300 59,570 57,810
87,500 77,550 75,600 73,500 72,520 71,510 69,500 67,480
64,930 58,390 57,140 55,800 55,170 54,550 53,100 51,950

90,000 90,000 79,780 78.000 77.180 76,320 74,590 72,860 69,400
105,000 105,000 93,170 91,050 90,050 89,000 87,020 85,000 80,900
120,000 120,000 106,300 104,000 102,900 101,700 99,400 97,150 92,500
122,500 122,500 110,350 108,350 107,400 106,400 104,460 102,300 98,400
160.000 160.000 160,000 143,870 142,590 141,570 139,260 136,960 132,360
202,500 202,500 202.500 202,500 183,060 181,760 179,170 176,580 171,400
250,000 250,000 250,000 250,000 250,000 250,000 224,500 221,200 215,200