EXAMPLE II.-What is the safe load for a spruce strut 8 feet long, 6" x 8" ? Ans. Area of cross-section = 48; 48 × 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. 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 formulæ 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 AND SQUARE). 6×6.. 6x8.. 6 × 10. 7 Round 9 Round 11 Round 12 × 16. 14 x 14. 16 x 16. 18 x 18. 20 x 20. 18,200 16,800 15,360 19,590 18,760 17,550 16,500 30,200 28,800 27,400 25.900 25,200 24,500 SAFE LOAD IN POUNDS FOR OAK AND NORWAY PINE POSTS (ROUND AND SQUARE). 6x6.. 6x8... 6 x 10.. 8 x 10.. 9 Round 10 x 10. 10 × 12. 10 x 14. 114 Round 12 x 12.. 12 x 14. 12 × 16. 14 x 14. 16 x 16. 18 × 18 20 × 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] SAFE LOAD IN POUNDS FOR WHITE PINE AND SPRUCE POSTS 6×6.. 6×8. 6 x 10.. Round 8×8. 3 x 10.. 8 × 12. 94 Round 10 x 10.. 10 × 12.. 10 x 14.. 114 Round 12 x 12.. 12 x 14. 12 16. 14 x 14... 16 x 16. 18 x 18. 20 x 20 9,800 8,700 11,520 10,550 19,080 18,216 17,352 16,490 16,050 15,620 Eccentric Loading. When the load on a post is applied in such a way that it is not distributed uniformly over the end of the post, the loading is called eccentric and the effect on the post is much more injurious than if the load were uniformly distributed. When a post supports a girder on one side only, or when the weight from one girder is much more than from the other, the load becomes eccentric, and an allowance must be made in the safe load varying from 10 to 25 per cent., according to the amount of eccentricity. The exact allowance cannot be calculated, so that one must necessarily use his judgment in the matter, remembering that it is best to be on the safe side. Fig. 1. Iron caps for timber pillars are often used in important constructions, and are an excellent invention, as they serve to distribute the thrust evenly through the pillar, and also form a bracket, which is often desirable, for supporting the ends of girders where a second post rests on top of the first. Fig. 1 shows the section of one of the simplest forms of caps. The Goetz and Duvinage caps, described at the end of Chapter XXIV., are the best shape for mill construction. Cast-Iron Columns. For cast-iron columns, where the length is not more than six or eight times the diameter or breadth of column, the safe load may be obtained by simply multiplying the metal area of cross-section by 63 tons, which will give tons for the answer. Above this proportion, that is, where the length is more than eight times the breadth or diameter, the following formulas should be used. These formulas are known as Gordon's and Rankine's. For cast-iron posts, the cross-section being a cross of equal arms. + Metal area × 13330 Safe load in lbs. = 1+ 133 x sq. of total breadth in inches EXAMPLE I. What is the safe load for a hollow cylindrical cast-iron column, 10 feet long, 6 inches external diameter, and 1′′ thickness of shell ? Ans. We must first find the metal area of the cross-section of the column, which we obtain by subtracting the area of a circle of four inches in diameter from the area of one six inches in diameter. The remainder will be the area of the metal. The area of a sixinch circle is 28.27 square inches, and of a four-inch, 12.56 square inches; and the metal area of the column is 15.71 square inches. |