Book format: An electronic version of a printed book that can be read on a computer or handheld device designed specifically for this purpose.
Publisher: RareBooksClub.com (6 Mar. 2012)
By: William Turnbull (Author)
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1832 Excerpt: ...is the next subject that claims our attention. It is affirmed by writers on the resistance of solids, that when a beam or shaft, whose length is greater than its diameter, is subjected to the action of any force which endeavours to twist it round, the line of greatest strain is in the direction of the diagonal of a square: and if a square be drawn on the surface of a beam in its natural form, it will become a rhombus by the action of the straining force (see Tredgold on Cast Iron, art. 229 v): hence it follows, that the quantity of angular motion is double the extension of the length of the beam, therefore we get 7 dpzi 16 /,.... (c) where / is the length of the beam in feet, d its diameter in inches, and p the angle of torsion. It is shewn in the table at page 48, that the relative extensibility of wrought iron, compared to cast iron as unity, is 0-86: hence, the preceding equation becomes, for wrought iron 7dp=l3-76I (d) These two equations are sufficient for computing the angle of torsion, whatever the form of the beam or shaft may be, as is manifest from the circumstance, that no other dimensions enter the equations besides the length / and diameter d: where d may represent either the breadth of a rectangular beam, the side of a square beam, or the diameter of a cylindrical beam, / representing the length in them all. Here follow a few examples to shew the method of reducing the equations. This equation is found in the following manner: 24 / = the length of the beam in inches, of which the diameter is d inches:-jj is the extension in length of cast iron, and-0174533 is the length of an arc of one degree to radius 1: therefore we get M£: =-mim h. the, f 1204 2 ' r torsion: and this reduces to 7df = 16l, the same as we have employed above. Examp...
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