11 × √ 92 1.46 inches. Example 3. The force of the steam being sixteen pounds per circular inch, and the diameter of the piston twenty-four inches, the diameter of a cast iron connecting rod should not be less than The middle is commonly expanded into a form of greater lateral strength, and in all cases should be of larger diameter than the ends, in the proportion of about one-tenth. 507.-For air pump rods, the pressure of the atmosphere and the diameter of the pump must be taken, instead of the force of the steam and the diameter of the cylinder. Parallel motion rods should be three-sevenths of the diameter of the piston rod, except in the case of that for steam boat engines, when there is lateral stress. Connecting rods for giving motion from the cross-head to beams, or to cranks, should be seven-tenths of the diameter of the piston rod. 508.-Of the strength of arms of beams, cranks, &c. It may be assumed as a principle that a beam of uniform thickness should not be of less thickness than one-sixteenth of its depth, otherwise it is liable to overturn; besides, in cast iron it is not safe to trust the strength of a casting, which is not a sixteenth part of its depth in thickness. Now for the case, when the velocity is the same as that of the piston D P l = 212 b d 2,* and when 16 b = d, and 12 /= =n D, it becomes for cast iron That is, when D = the diameter of the piston in inches, and d = the depth of the beam in inches, and the breadth one-sixteenth of that depth, n the number of times the diameter is contained in the length from the centre of motion to the point where the force is applied, and P double the force of the steam in the boiler, in pounds per circular inch. The depth at the end should be half the depth at the centre of motion, and the breadth uniform, and an access of strength may be given by forming the section, so as to increase the thickness at the edges to one-ninth of the depth, or till the parts between be reduced to the thickness of one-sixteenth of their width. For wrought iron put 240 instead of 212, and for wood sixty-four instead of 212. * Practical Essay on Strength of Iron, art. 116. 509.-Example 1. Beams.-An engine beam is three times the diameter of the cylinder, from the centre to the point where the piston rod acts on it, the force of the steam in the boiler is fourteen pounds per circular inch, its double is twenty-eight, and the diameter of the piston is twenty-four inches. In this case 81 D d, or d= 19.4 inches, and the mean breadth is 1.22 inches, and the breadth at top and bottom 2.16 inches. If of wrought iron with the same proportions, 78 D d, and the breadth one-sixteenth of the depth. Of wood with the same proportions, 78 D = d, but the breadth one-fourth of the depth. 510.-Cranks. A crank should embrace a shaft, so that its depth at the shaft should be 15 times the diameter of the shaft; hence, if S D be the diameter of the shaft, the depth of the crank must be 1.5 S D, but since (art. 508,) D P 1 = 212, b d2, we have Example 2. A crank shaft is equal in diameter to 31 times the diameter of the cylinder, and the force of the steam in the boiler being fourteen pounds per circular inch, or P = twenty-eight pounds, required the breadth of the crank at the shaft, its radius being 2.5 feet. In this case · ·6 l = b in inches; and as 7 = 2·5 feet, it is 6 × 2·5 = 1.5 inches, and the depth is 1.5 × ·31 × 30 = fourteen inches. 511.-Wheel arms. The arms of wheels may be considered in respect to strength only; and if the rim be of equal strength, then a wheel should in all cases have six arms, when it is of sufficient magnitude to require its strength to be found by rule. With this condition we have 2 D2 P R = 212 × 6 b ď2, or D2 P R = 3 × 212 b ď. If we consider the arms to be one-third of the breadth of the wheel, and allow as excess of strength, that which is added to give it lateral strength, then When R the radius is = 1, and P = 28 twice the force of the steam in the boiler, K K as inserted along with the proportions of teeth in the table, (art. 513.) 512. The teeth of wheels will be most conveniently given in a tabular form, with a correction for curvature in determining their breadth, which is not included in the formula in my treatise on cast iron. The first column shews the stress on the teeth in pounds; the second the horses' power nearly equivalent, when the velocity is three feet per second; the third column the pitch; the fourth the thickness; and the fifth the breadth of the teeth: the sixth column shews the greatest depth of the middle of the arm at the base in the direction of the wheels' motion, when that part is one-third of the breadth of the teeth, and the radius is one foot; hence, being multiplied by the square root of any other radius in feet, it will be the depth for it: the seventh column shews the breadth of the rib which strengthens the arm; and the eighth the diameter of a cylinder, when the force of the steam is thirty-five inches of mercury in the boiler, and the teeth move at the same velocity as the piston. For any other velocity the stress will be found by (art. 500.) 513.—A Table of the Strength, &c. of Teeth and Arms for Wheel Work. 514.-The strength of beam gudgeons may be determined by the rule, P D2 854 de.* It reduces to * Essay on Strength of Iron, art. 139. For low pressure and the length should be not less than eight-tenths of the diameter. steam, twice its force is twenty-eight pounds per circular inch, or P = 28, and therefore in that case, one-sixth of the diameter of the cylinder should be that of the gudgeon. For pins for connecting rods where the bearing is double, the stress is reduced onehalf, and 515.—The strength of shafts. The shafts are supposed to be supported so as to render the lateral stress as small as possible, then the resistance to twisting alone has to be considered, and as no part of the shaft should be less than the bearings or journals, therefore allowing one-sixth for wear R D2 P = 960 d3 ;* when the shaft revolves in the same time, the piston makes a double stroke, and if the radius R n D, we have = If it revolve N times while the piston makes a double stroke, then (art. 500,) we have For wrought iron the divisor should be 1080 instead of 960. Example. What should be the diameter of a shaft of cast iron, when the crank arm is equal to the diameter of the cylinder, double the force of the steam in the boiler twentyeight pounds per circular inch, the piston thirty inches in diameter, and one revolution of the shaft made in the same time as a double stroke? In this case n and N are each equal one, hence, |