A Treatise On The Principles And Practice Of Dock Engineering

RISE OF GATES. 323 That is (since the water pressure on any surface is proportional to the square of the depth), the pressure on A D is to that on A B in the same ratio as the depth A C to the depth A B. Having divided the sectional area of material required into equal portions, the cesses or girders can be located at the centres of pressure of the respective zones. Rise of Gates.—The ratio which the versed sine or rise of a pair of gates bears to the span varies in practice between the limits of one-third and one-sixth. The best proportion is a matter of individual experience and local requirements, rather than of theoretical calculation. Much depends upon the nature of the material of which the gate is constructed, its distribution and maximum resistance to stress, but the practical exigencies of the situation often outweigh them all in importance. It has been stated that the most economical rises are about one-third and one-fifth for cylindrical and straight gates respectively.* But gates are rarely constructed with parallel faces, and the disposition of the material may be, and often is such, that the longitudinal axis, which is the true curve of the gate, follows a path in no way concentric with either of the faces. Further, it should be noted that mere economy in gate construction is a question of minor importance to those of stability, durability, and convenience. A great rise, combined with cylindrically-curved backs, calls for long and deep recesses in the side walls, and exposes a large gate surface to contact with passing vessels. On the other hand, at graving dock entrances the rise of the gates adds somewhat to the available length of the dock. Considering the question for a moment merely from the point of view of the amount of stress due to different ratios of rise to span, let us refer to the closely approximate formula already devised for the value of the resultant stress in terms of the rise and span of the gates, viz. :— R \16r 4/ Re-arrange and let r = vs, so that v may have any value, integral or fractional, of which the latter alone calls for serious considération. Then „ wh2 R= ^ x 1 + 4 F3 8^ S' In this equation we have an expression for the resultant in terms of the water pressure per unit length of the gate ^Yj-^> multiplied by a coefficient involving the rise and span of the gates only. Now assign to v a series of values ranging from 4 to 1—that is, from x^ to unity—and calculate therefrom the corresponding values for the coefficient 1 + 4u2 8 V * Min. Proc. Inst. C.E., vol. xviii., p. 474 ; vol. xxxi., p. 344.