Again, let it be required to form a hoop of iron 3 inch in thickness, and 16 inches outside diameter. 16.5-875-15.625, or 1 foot 35 inches; opposite to which, in the Table of Circumferences, is 4 feet 1 inch, independent of any allowance for shutting. The length for angle iron, of which to form a ring of a given diameter, varies according to the strength of the iron at the root; and the rule is, for a ring with the flange outside, add to its required interior diameter, twice the extreme strength of the iron at the root; or, for a ring with the flange inside, subtract twice the extreme strength; and the sum or remainder is the diameter by which to determine the length of the angle iron. Thus, suppose two angle iron rings similar to the following be required, the exterior diameter a B, and interior diameter c D, each to be 1 foot 10 inches, and the extreme strength of the iron at the root c d, e d, &c. of an inch. A c d c d B c D d c d twice =13, and 1 ft. 103 in. +13=2 ft. 1 in., opposite to which, in the Table of Circumferences, is 6 ft. 4 in., the length of the iron for CD; and 1 ft. 10 in.-13-1 ft. 8 in., opposite to which is 5 ft. 51 in., the length of the iron for a B. But observe as before, that the necessary allowance for shutting must be added to the length of the iron, in addition to the length as expressed by the Table. area of circle from which rn ps,, V X, Then, 122.75 × 79.5=9758 525 square inches, as a rectangle. And deduct the area of the coke space, and the difference of area between the semicircle formed by the two back corners, and that of a rectangle of equal length and breadth; Then 46.75 x 37.25=1731-4375 area of r, n, s, t, in sq. ins. 32-252 x 7854 = 408.4 area of half the circle rn. 2 Radius of back corners=4 inches; consequently 82 x 7854-25 13, the semicircle's area; and 8 x 4=32-25-13-6.87 inches taken off by rounding the corners. Hence, 1731-4375 +4084 + 6·87=2146·707, and 10027-325-2146-707-7880 618 square inches, or whole area in plan, 7880-618 × 32 the depth=252179.776 cubic inches, and 252179.776 x 003607 (see Table of Approximations, page 30)=909.61245 gallons. |