To find the weight of a cast iron beam of given dimensions. Rule.-Multiply the sectional area in inches by the length in feet, and by 3.2, the product equal the weight in lbs. Ex. Required the weight of a uniform rectangular beam of cast iron, 16 feet in length, 11 inches in breadth, and 14 inch in thickness. 11 x 1.5 x 16 x 3.2=844.8 lbs. Resistance of bodies to flexure by vertical pressure. When a piece of timber is employed as a column or support, its tendency to yielding by compression is different according to the proportion between its length and area of its cross section; and supposing the form that of a cylinder whose length is less than seven or eight times its diameter, it is impossible to bend it by any force applied longitudinally, as it will be destroyed by splitting before that bending can take place; but when the length exceeds this, the column will bend under a certain load, and be ultimately destroyed by a similar kind of action to that which has place in the transverse strain. Columns of cast iron and of other bodies are also similarly circumstanced, this law having recently been fully developed by the experiments of Mr. Hodgkinson on columns of different diameters, and of different lengths. When the length of a cast iron column with flat ends equals about thirty times its diameter, fracture will be produced wholly by bending of the material; -when of less length, fracture takes place partly by crushing and partly by bending: but, when the column is enlarged in the middle of its length from one and a half to twice its diameter at the ends, by being cast hollow, the strength is greater by 4th than in a solid column containing the same quantity of material. To determine the dimensions of a support or column to bear without sensible curvature a given pressure in the direction of its axis. Rule.-Multiply the pressure to be supported in bs. by the square of the column's length in feet, and divide the product by twenty times the tabular value and the quotient will be equal to the breadth multiplied by the cube of the least thickness, both being expressed in inches. of E; Note 1.-When the pillar or support is a square, its side will be the fourth root of the quotient. 2. If the pillar or column be a cylinder, multiply the tabular value of E by 12, and the fourth root of the quotient equal the diameter. Ex. 1. What should be the least dimensions of an oak support, to bear a weight of 2240 lbs. without sensible flexure, its breadth being 3 inches, and its length 5 feet? Tabular value of E = 105, Ex. 2. Required the side of a square piece of Riga fir, 9 feet in length, to bear a permanent weight of Dimensions of Cylindrical Columns of Cast Iron to sustain a given load or pressure with safety. 12 1716 1697 1672 1640 1603 1561 1515 1467 1416 cast iron columns 18 feet in length, 8 inches in diameter, and the metal 1 inch in thickness; what weight may Ex. Wanting to support the front of a building with Practical Utility of the preceding Table. E 98 STRENGTH OF MATERIALS. I confidently expect each column capable of supporting without tendency to deflection? Opposite 8 inches diameter, and under 18 feet=1097 = 657 cwts. Note. The strength of cast iron as a column being 1.0000 Elasticity of torsion, or resistance of bodies to twisting. The angle of flexure by torsion is as the length and extensibility of the body directly, and inversely as the diameter; hence, the length of a bar or shaft being given, the power, and the leverage the power acts with, being known, and also the number of degrees of torsion that will not affect the action of the machine, to determine the diameter in cast iron with a given angle of flexure. Rule.-Multiply the power in tbs. by the length of the shaft in feet, and by the leverage in feet; divide the product by fifty-five times the number of degrees in the angle of torsion; and the fourth root of the quotient equal the shaft's diameter in inches. Ex. Required the diameters for a series of shafts 35 feet in length, and to transmit a power equal to 1245 lbs., acting at the circumference of a wheel 2 feet radius, so that the twist of the shafts on the application of the power may not exceed one degree. |