Materials of engineering. v.3; A treatise on brasses, bronzes and other alloys, and their constituent metals Volume 3 - Softcover

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 edition. Excerpt: ...or as, shown by M. Navier, to the axis through the centre of gravity. The quantity J J y2 dy dx, which is always a factor in this expression, is the " moment of inertia." The data to be here given are experimentally obtained figures, derived from tests of pieces of rectangular section; other forms will be considered later. 162. Formulas for Transverse Loading are deduced in all works on resistance of materials. For cases of rupture, when the beam is supported at the ends and loaded in the middle, for rectangular bars, M=-Pl=rRbd; and R = 4 0 2bd2 for non-ductile materials, and it may be assumed, in all cases in the engineer's practice, that the material tested is in practice either sufficiently elastic and rigid to justify the use of this formula, or is to be loaded only within its elastic limit. Then the formulas for other cases become: (1.) Beam fixed at one end, load at the other: (7.) Fixed at one end, supported at the other, load at the middle: All of these equations are, of course, "homogeneous." Replacing bd2 by o.59/3, transforms these quotations so as to apply very exactly to circular sections. 163. The Modulus of Rupture, R, being obtained by experiment and inserted in these formulas, the maximum load that a beam will support, when of similar shape and of that material, becomes calculable. The value of the modulus of rupture is readily determined by experiment from the formula: R=rAp+yw when the weight of the beam, W, is taken into account. When the dimensions all become unity, we have, neglecting W, that is to say, the modulus of rupture is one and a half times the load which would break a bar unity in length, breadth and depth, supported at the ends and loaded in the middle. For British measures, it is 18 times the...