This section is from the book "The Tinman's Manual And Builder's And Mechanic's Handbook", by Isaac Ridler Butt. Also available from Amazon: The Tinman's Manual And Builder's And Mechanic's Handbook.
[From Adcock's Engineer.']
According to Tredgold's and Duleau's experiments, a piece of the best bar-iron 1 square inch across the end would bear a weight of about 77,373 lbs., while a similar piece of cast-iron would be torn asunder by a weight of from 16,243 to 19,464 lbs. Thin iron wires, arranged parallel to each other, and presenting a surface at their extremity of 1 square inch, will carry a mean weight of 126,340 lbs.
List of woods, arranged according to their strength.-Oak, alder, lime, box, pine (sylv.), ash, elm, yellow pine, fir.
A piece of well-dried pine wood, presenting a section of 1 square inch, is able, according to Eytelwein, to support a weight of from 15,646 lbs. to 20.408 lbs., whilst a similar piece of oak will carry as much as 25,850 lbs.
Hempen cords, twisted, will support the following weights to the square inch of their section:
3-inch to 1 inch thick, 8,746 lbs.; 1 to 3 inches thick, 6,800 lbs.; 3 to 5 inches thick, 5,345 lbs.; 5 to 7 inches thick, 4,860 lbs.
Tredgold gives the following rule for finding the weight in lbs. which a hempen rope will be capable of supporting: Multiply the square of the circumference in inches by 200, and the product will be the quantity sought.
In the practical application of these measures of absolute strength, that of metals should be reckoned at one-half, and that of woods and cords at one-third of their estimated value.
In a parallelopipedon of uniform thickness, supported on two points and loaded in the middle, the lateral strength is directly as the product of the breadth into the square of the depth, and inversely as the length. Let W represent the lateral strength of any material, estimated by the weight, b the breadth, and d the depth of its end, and l the distance between the points of support; then w = fd 2b ÷ I.
If the parallelopipedon be fastened only at one end in a horizontal position, and the load be applied at the opposite end, W = fd2b ÷ 41.
It is to be observed that the three dimensions, 6, d, and /, are to be taken in the same measure, and that b be so great that no lateral curvature arise from the weight; f in each formula represents the lateral strength, which varies in different materials, and which must be learnt experimentally.
A beam having a rectangular end, whose breadth is two or three times greater than the breadth of another beam, has a power of suspension respectively two or three times greater than it; if the end be two or three times deeper than the end of the other, the suspension power of that which has the greater depth exceeds the suspension power of the other four or nine times; if its length be two or three times greater than the length of another beam, its power of suspension will be ½ or 1-3 respectively that of the other; provided that in each case the mode of suspension, the position of the weight, and other circumstances be similar. Hence it follows that a beam, one of whose sides tapers, has a greater power of suspension if placed on the slant than on the broad side and that the powers of suspension in both cases are in the ratio of their sides; so, for instance, a beam, one of whose sides is double the width of the other, will carry twice as much if placed on the narrow side, as it would if laid on the wide one.
In a piece of round timber (a cylinder) the power of suspension is in proportion to the diameters cubed, and inversely as the length; thus a beam with a diameter two or three times longer than that of another, will carry a weight 8 or 27 times heavier respectively than that whose diameter is unity, the mode of fastening and loading it being similar in both cases.
The lateral strength of square timber is to that of a tree whence it is hewn as 10: 17 nearly.
A considerable advantage is frequently secured by using hollow cylinders instead of solid ones, which, with an equal expenditure of materials, have far greater strength, provided only that the solid part of the cylinder be of a sufficient thickness, and that the workmanship be good; especially that in cast metal beams the thickness be uniform, and the metal free from flaws. According to Eytelwein, such hollow cylinders are to solid ones of equal weight of metal as 1.212:1, when the inner semi-diameter is to the outer as 1: 2; according to Tredgold as 17: 10, when the two semi-diameters are to each other as 15:25, and as 2: 1, when they are to each other as 7: 10.
A method of increasing the suspensive power of timber supported at both ends, is, to saw down From 1/3 to ½ of its depth, and forcibly drive in a wedge of metal or hard wood, until the timber is slightly raised at the middle out of the horizontal line, By experiment it was found that the suspensive power of a beam thus cut 1-3 of its depth was increased 1-19th, when cut ½ it was increased l-29th, and when cut 3-4th through it was increased 1 .87lh.
The force required to crush a body increases as the section of the body increases; and this quantity being constant, the resistance of the body diminishes as the height increases.
According to Eytelwein's experiments, the strength of columns or timbers of rectangular form in resisting compression is, as
1. The cube of their thickness (the lesser dimension of their section). 2. As the breadth (the greater dimension of their section). 3. inversely as the square of their length.
Cohesive power of Bars of Metal one inch square, in Tons.
Iron. Swedish bar.....
Do., Russian bar.....
Do., English bar.....
Do, sheer ................
Copper, cast ...............
Brass, cast, yellow .
Tin, cast .................