Practical Essay on the Strength of Cast Iron and Other Metals Volume 1

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. 1842 Excerpt: ...is 4/6 rf2 (1-qp3) (a-1)2. hence we have the equation (n--l)2 (1--qp3) = 1---/ to determine the place of the neutral axis; or This formula is complicated, but it affords some curious results. If we make p = o, we have the strength of a bar with its neutral axis at C, and the depth A C is '( '--)' VI + VI-q/ where d is the whole depth. And if AE = D B, then A C = % d, when the neutral axis is at C. The neutral axis may be at any point that may be chosen between the point C and half the depth, by varying the values of q or p for that purpose. If we make d j = '75, and= 5, then A M = yr, and DF = C M; also, AE = DB. The strength is fbd2 _ 6x2-4/_W-(xxv) The figure is drawn in these proportions, 6 is the whole breadth D B, and d the whole depth. Its strength is to that of the circumscribing rectangle shown by the dotted lines as: 1 or as 5: 12. These equations show the relation between the strength of beams, and the weight to be supported in some of the most useful cases when the load is applied as in fig. 14; but previous to considering how these equations will be effected by varying the mode of supporting the beam, it will be desirable to give some rules for estimating the deflexion of beams. 120. The deflexion of a beam supported as in fig. 16, Plate II., is caused by the extension of the fibres of the upper side, and the compression of those on the under side; the neutral line ABA' retains the same length. If we conceive the length of a beam to be divided into a great number of equal parts, and that the extension, at the upper side of the beam, of one of these parts is represented by a b, then the deflexion produced by this extension will be represented by de, and the angles acb, dee, being equal, we shall have b c: dc:: ab: d e; the smallness of the a...