This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
The crushing strength of any body is in proportion to the area of its section, and inversely as its height. In tapered columns, the Strength is determined by the least diameter.
When the height of a prism or column is not 5 times its side or diameter, the crushing strength is at its maximum.
Experiments upon cast-iron bars give a crushing stress of 5,000 lbs. per square inch of section as just sufficient to overcome the elasticity of the metal; and when the height exceeds 3 times the diameter, the iron yields by bending.
When it is 10 times, it is reduced as 1 to 1.75; when It Is 15 times, it is reduced as 1 to 2; when it is 20 times, it is reduced as 1 to 3; when it is 30 times, it is reduced as 1 to 4; and when it is 40 times, it is reduced as 1 to 6.
The experiment of Mr. Hodgkinson have determined that an increase of strength of about 1/8 of the breaking weight is obtained by enlarging the diameter of the column in its middle.
In cast iron columns of the same thickness, the strength is inversely proportional to the 1.7 power of the length nearly. Thus in solid columns, the ends being flat, the strength is as d3.6 / l1.7, l representing the length, and d the diameter.
Hollow columns, having a greater diameter at one end than the other, have not any additional strength over that of uniform cylindrical columns.
Experiment upon wrought iron give a mean crushing stress of 74,250 lbs. per square inch. Cast iron is decreased in length nearly double what wrought iron is by the same weight; but wrought iron will sink to any degree with little more than 26680 lbs. per square inch, while cast iron will bear 97500 lbs. to produce the same effect.
A wrought bar will bear a compression of 1-863 of its length, without its utility being destroyed.
With cast iron, a pressure beyond 26680 lbs. per square inch is of little, if any, use in practice.
For equal decrements of length, wrought iron will sustain double the pressure of cast iron.
Glass and the hardest stones have a crushing strength from 7 to 9 times greater than tensile: hence an approximate value of their crushing strength may be obtained from their tensile, and contrariwise.
Various experiments show that the power of stones, etc., to resist the effects of freezing is a fair exponent of that to resist compression.
 
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