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.
Multiply the weight to be supported in pounds by the length of the cylinder between the supports in feet; divide the product by .6 of the value of material, and the cube root of ¼ of the quotient will give the diameter.
Note,-When the cylinder is loaded uniformly along its length, the cube root of half quotient will give the diameter.
What should be the diameter of a cast-iron cylinder, 2 feet between the supports, that will support 54000 lbs. without permanent injury?
64000X2 800
----------=800, and 3√- = 5.85 ins.
.X225 4
And what its diameter if loaded uniformly along its length? 800+2 -------=100, and 3√ 100=4.64 ins.
 
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