BBB, is termed a curve
The stresses at a transverse section due to bending are obtained from the usual formula M =y, where M is the bending moment, I
the moment of inertia of the section about the neutral axis, y the distance from the neutral axis of the point at which the stress is required, and p the intensity of stress. In calculating I, a deduction from the area of plating in tension is made for rivet holes, and only the continuous longitudinal portions of the structure are assumed effective in resisting bending.
The stresses • obtained by this method undergo considerable variation with class and size of ship. As regards the former, it is evident that the actual straining actions upon a ship necessarily vary with the type; and the stresses allowable, as calculated on a uniform basis of applied forces, must vary accordingly. The variation due to size is less obvious, but it is clear that the larger the ship, the less is the probability of encountering waves as long as herself ; and, moreover, the proportion of height to length of the largest waves is generallyless than that assumed. For these reasons greater calculated stresses are allowable in large ships than in small ships or in those of moderate size. The limiting stress frequently adopted for small ships is 6 tons per sq. in., which may be increased for portions in tension to 8 tons with high tensile steel ; on the other hand, the calculated stresses in the largest vessels frequently exceed 8 tons compressive and to tons tensile.
The above method is that now universally adopted for comparing the stresses in ships caused by longitudinal bending; although imperfect, it affords a reasonable basis of comparison between the longitudinal strengths of vessels, especially when, as is generallyon TorpedoBoat Destroyers (see Trans. Inst. Nay. Archs., 1905). The principal dimensions of the " Wolf " are—length 210 ft., breadth 21.7 ft., draught 5 3 ft., and displacement 36o tons, with a coal capacity of 8o tons. Two sets of experiments were made—(i.) under a hogging moment when supported in dock on two cradles to ft: wide, spaced 26 ft. apart centre to centre, and equidistant from the ship's centre of gravity, bunkers empty ; (ii.) under a sagging moment when supported by similar blocks 120 ft. apart, bunkers full. The distribution of weight and buoyancy had previously been determined for each case so that the pressures on the blocks and the bending moments caused thereby could be accurately; obtained. When thus supported the waterlevel in the dock was gradually lowered; and for successive waterlevels spaced 6 in. apart the extension or compression of the plating was measured at various points of the structure by Stromeyer's strain indicators; the vertical deflections at various points of the length were also recorded. The observations were repeated several times, and the following are the general results:
(a) In the sagging condition the neutral axis was actually situated 755 ft. above the keel; the calculated distance was 7 8 ft. deducting rivet holes in parts in tension and 7 7 ft. without such deduction. In the hogging condition the observed height was 7.2 ft., those calculated as before being 7 5 ft. and 7 6 ft. All shell and deck plating, gunwale and keelson angles, and the side girders and angles were included in the calculation for the moment of(inertia. The calculated and observed positions of the neutral axis are thus in fairly close agreement.
(b) The actual vertical distribution of strain over a transverse
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