## A text-book of the strength of materials and of stresses in structures; for use in scientific high schools and schools of technology

### Thomas William Mather

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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. 1897 Excerpt: ...I---f-= 4 12--(3t + t,,), and the required moment about the neutral h3 axis e e is I--( 3 b + bt)--A z2 In the accompanying figures, the moment of inertia about a specified axis is given, and also expressions for the area and distance c from the outermost fiber to the neutral axis, this axis being designated by the line ee. Many other sections might be I Y given, which however would be of "--" f-but little real use. Commercial forms, such as "I" or "deck" beams, vary much in shape; and manufacturers usually give moments of inertia, areas, and weights in their trade catalogues. Fig. 49 represents a section of an iron "I beam," and Fig. 50, of a deck beam, the two forms most commonly used as beams. The following table is taken from the catalogue of Carnegie Bros. & Co. Other manufacturers produce similar beams, but with dimensions more or less changed. The last column gives values (I1) for the moment of inertia about the axis YY. When, however, an irregular form is used, the moment of inertia of which cannot be readily found from tables, or by direct calculation, the following graphical method may be employed. Let Fig. 51 represent a Jrail, the dimensions of which are known. Make the line AB equal to the entire depth and draw any line, whose length is b inches, at right angles to it, the distance from the base CD being x inches. The moment of this Fig. 51. line with respect to CD is bx2. Assuming any convenient scale, lay off a c equal to bx2. At any other point distant xt inches from CD, where the width is bt inches, the moment is Pt x. Lay off a equal to this, to the same scale, and determine the point Gi In a similar manner find a sufficient number of points to construct accurately the curve Acc2B. By means of a ...

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