Practical essay on the strength of cast iron, and other metals; containing practical rules, tables, and examples; founded on a series of new ... table of the properties of materials

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. 1831 Excerpt: ...by the revolution-of a semi-cubical parabola round its axis, which is the figure of equal strength for a beam supported in the middle when the weight is uniformly diffused over its length. Then, d3(dc)i P: (:: (d c)s: x3 = K; (dc)W and y = x; also w as. These quantities substituted in Equation i. art. 86, gives » »--rf--x l + 2T+3T + &c. =i7 = DA, the deflexion. (xi.) Here the deflexion is nine-fourths of that of an uniform beam with the load at the extremities. 93c. Case 10. If a beam to support an uniformly distributed load be of equable breadth, but the depth varying directly as the distance from the extremity, as in Fig. 21, Plate III. Then b is constant, and 10 =---; therefore by (Equation i. art. 86.) = D A the deflexion. If the beam had been uniform, and the loads at the extremities, the deflexion would have been only one-third of the deflexion in this case. The cases I have considered are perhaps sufficient for the ordinary purposes of business; the next object is to show how these calculations are affected by changing the position and manner of supporting the beam, or the nature of the straining force; and to compare them with experiments, and draw them into practical rules. For this purpose the most clear and the most useful plan seems to be that of taking known practical cases for illustration. Beams supported in the Middle and strained at the Ends, as in the Beam of a Steam Engine. 94. The distance, F B, Fig. 14. of the direction of the straining force from the centre of motion being constantly the same, the strain will be the same in any position of the beam, (art. 77.) Also, the deflexion from its natural form will be the same in every position, because the strain is the same; and the length does not vary with the position. Now t...