Mechanics and Strength of Materials

PREFACE

In the following pages are compiled a number of concise tables and diagrams relating to mechanics and the strength of materials, carefully selected from MACHINERY'S monthly Data Sheets, issued as supplements to the Engineering and Railway editions of MACHINERY since September, 1898. Several additional tables also are included.

In order to enhance the value of the tables, brief explanatory notes have been provided wherever necessary. In some of these notes references are made to articles which have appeared in MACHINERY, and to matter published in MACHINERY'S Reference Series, giving additional information on the subject. These references will be of considerable value to readers who wish to make a more thorough study of the subject. In a note at the foot of each table, reference is made to the page on which the explanatory note relating to the table appears.


MECHANICS

Rules and Formulas in Mechanics

On pages 4 to 11, inclusive, is given a collection of rules and formulas in mechanics, covering the subject in a comprehensive manner. The subjects treated are work, momentum, energy, centrifugal force, center of gravity, moment of inertia, radius of gyration, falling bodies, accelerated motion in. a straight line, pendulum, inclined plane, friction, moments, safety valve, prony brake, strap brake, tackle-block, epicyclic gears, countershaft, crank and connecting-rod, toggle-joint, differential pulley, suspended cable, friction clutch, parallelogram of forces, triangle of forces, polygon of forces, and stresses in a crane. [MACHINERY'S Reference Series No. 5, First Principles of Theoretical Mechanics.]


Forces on Inclined Planes

On pages 12 and 13 a table is given to find the force required for moving a body along an inclined plane. The friction on the plane is not taken into account. The first column in the table gives the per cent of grade, or the rise in feet per 100 feet. The second column gives the angle in degrees and minutes corresponding to this rise. The third and fourth columns give the sine and cosine of the angle, and the fifth column the pull in pounds required for moving one ton along the inclined surface. The last column gives the perpendicular pressure on the plane per ton.

For example, assume that it is required to move a body weighing two tons along an inclined plane having a rise of 10 feet in 100 feet. What power would need to be exerted, the friction not being taken into consideration? To find the answer from the table, locate 10 in the left-hand column; following the line from 10 horizontally, we find that the power necessary for one ton is 199.2 pounds, and hence for two tons, 398.4 pounds. Of course, as the friction must be taken into consideration, the power required to pull the load will have to be increased according to the character of the sliding surfaces.


Calculating  Centrifugal Force

Centrifugal force, as it is somewhat vaguely called, is not really a force re siding in the revolving body and tending to urge it away from the center; it is rather the extraneous force which has to be exerted to restrain the body in its circular path, and prevent it from following the tangential direction which it constantly tries to take in accordance with Newton's law, viz., that a moving body will continuously follow a straight line, unless acted upon by some outside force. This restraining force is directly proportional to the radius of the circle described by the center of gravity or center of mass of the revolving body, its weight (or more strictly, its mass), and the square of the number of revolutions per minute.