FORMULAS AND TABLES FOR THE SHAFTING OF MILLS AND FACTORIES. BY JAMES B. FRANCIS, CIVIL ENGINEER. [From the Journal of the Franklin Institute.] The following investigation was undertaken at the request of General John C. Palfrey, the Agent of the Merrimack Manufacturing Company, of Lowell, Massachusetts, for the purpose of determining the relative fitness of wrought-iron and steel for the shafting of a cotton factory now erecting by that company. Samples of steel, all of American manufacture, were obtained from different makers, and, together with several samples of iron, were subjected to experiment. The constant expressing the resistance of cylindrical bars to torsion, I deduce from Navier's formula,* in which T= 16 W R (1), Ta constant for the same material. w the weight, in pounds, which if applied at the distance R, in inches, from the axis, will just fracture the bar. л=the ratio of the circumference of a circle to its diameter. d=the diameter, in inches, of the bar at the place of fracture. The bars subjected to torsion were finished in the form of the following diagram, the ends being two inches square, and the middle turned down to a diamenter of inch, in order to insure the fracture taking place in that part of the bar. The weight producing the torsion was applied at the end of a lever, of the effective length of 35-975 inches, fitted to the square boss at one end of the bar. The tendency of the bar to revolve * Resumé des Leçons sur l'Application de la Mécanique, under the action of the weight, was controlled by a worm-wheel about fifteen inches in diameter and one hundred and thirtyeight teeth, fitted to the square boss at the other end of the bar. This wheel could be moved through any arc by means of a worm. As the bar became twisted by the torsional strain, the worm-wheel was moved through an arc sufficient to bring the lever to a horizontal position. A graduated circle on one face of the worm-wheel furnished the means of measuring the arc of torsion. The effective weight of the lever and scale at 35.975 inches from the axis, where the scale was hung on a knife edge, was 48.5 pounds, and was the least effective weight which could be applied to produce torsion. The experiments on deflection were made on round bars turned to a diameter of about one inch. The distance between the points of support was forty-eight inches. Observations were made of the deflections produced by a weight of one hundred and fifty pounds suspended at the middle point between the supports. This weight was not sufficient to cause any sensible set in the bar after the weight was removed; and no sensible increase in deflection was produced by allowing the weight to remain suspended on the bar for several days. The constant E for deflection has been computed by Navier's formula,* 13 W 6πα Ε' (2), in which the distance between the points of support, in inches. w the weight at the middle point between the supports, in pounds. π the ratio of the circumference of a circle to its diameter. d the diameter of the bar, in inches. • See Journal of the Franklin Institute for February, 1862, page 85. DESCRIPTION OF THE BAR. ♪ the deflection at the middle point between the supports, in inches. Experiments on Deflection. Spindle steel, from the Farist Steel Co., Windsor Locks, Conn., from a bar 1 inches in diameter, marked A, 7, 0-995 0.2330 48.0° 3,853,590 53.8° 3,847,530 0.993 0.2310 53.0° 3,918,360 53-7° 3,858,557 0.992 0.2330 0.995 0.2307 54.2° 3,900,420 53.3° 3,892,008 0.998 0.2337 52.2° 3,796,060 49.8° 3,826,641 Bessemer steel, from the works of Messrs. Winslow & Griswold, Troy, 1.000 0.2330 49.4° 3,777,095 1.000 0.2315 52.0° 3,801,566 Several specimens of the steel have been tested for tensile strength, at the works of the South Boston Iron Company, by Mr. F. Alger, in the apparatus designed by Major W. Wade for testing metals for cannon, a description of which may be found in Reports of Experiments on the Strength and other Properties of Metals for Cannon, published in 1856, by authority of the Secretary of War. I find on record many experiments on the fracture of iron and steel by torsion, from which I deduce the following values of T; using the above formula for cylindrical bars, and Navier's formula, for square bars, in which b=the side of the square in inches, and w and R the weight in pounds, producing fracture, and the distance from the axis, in inches, at which it is applied. EXPERIMENTS BY RENNIE, given in the Philosophical Transactions of the Royal Society, for 1818. Bar of English wrought iron, 0.25 inch square, T= 65,982 T= 61,909 T=111,191 Average of 3 bars of iron cast horizontally, 0.25 in. sq. T= 64,776 |