WEIGHT AND SUPPORT IN SHIPS. 
463 
and from them we obtain the following limits. For shearing-forces the maximum lies 
between one half and three fifths of the displacement, and for bending-moments between 
one seventh and one sixth of the product of the displacement by the length. These are, 
of course, to be regarded simply as limiting values ; in practice they can scarcely occur, 
because no ship is likely to rest at the extremities only without having a moderate base 
of support. The amount of the strains actually experienced would depend, obviously, 
upon the length of the base of support and its greater or less nearness to the bow and 
stern. 
When a ship ashore rests upon a middle support and has her ends unsupported, which 
in the other extreme position she can occupy, she is, as I have said, less severely strained 
than when resting on the ends only, the reason for this fact being that the heavy weights 
carried in the amidship portion are comparatively close to the point of support in one 
case, whereas in the other they are much more distant. The greatest difference in 
strains should consequently be looked for in ships having very concentrated weights 
amidships ; and it is interesting to remark that while such a concentration has been 
shown to be beneficial in reducing most of the principal strains experienced by ships 
afloat, it is the cause of the increase in sagging-strains in ships ashore. A ship having 
her weights uniformly distributed throughout the length would be subject, when sup- 
ported at the middle only, to hogging-moments equalling in amount the sagging- 
moments incidental to support at the extremities. Actual ships, however, have not 
any thing like a uniform distribution of weights, and the greatest weights are usually 
found near the middle. In spite of the increase in the severest exceptional strains thus 
caused, however, it cannot be doubted that the ordinary distribution of the weight is 
beyond comparison better than uniform distribution would be ; for its beneficial effect, 
in reducing strains in ships afloat, is continually called into play, while the other effect 
is seldom, if ever, produced. 
In order to show the relative magnitude of the classes of exceptional strains in ships 
ashore, I will again take the three typical ships and give a few quantitative results. The 
only explanation required of the method I shall follow is that when a ship is supported 
on a single point, vertically below her centre of gravity, the maximum shearing-force 
will equal the weight of either the fore or the after body, and the maximum bending- 
moment will equal the product of the weight of one of these bodies by the distance of 
its centre of gravity from the point of support. The previous investigations therefore 
supply all the data required for the further calculations. 
In the ‘Minotaur’ the after body is the heavier, and its weight, 5070 tons, constitutes 
the maximum shearing-force. The product of this weight by the distance of the centre 
of gravity of the after body from the transverse plane passing through the centre of gra- 
vity of the whole ship, 81 feet, gives us : 
Maximum hogging-moment =5070 tons X 81 ft. 
= 410,600 foot-tons (in round numbers); or about 
= displacement in tonsX of the length in feet, 
3 s 2 
