OF SUBMARINES BY MARBEC'S METHOD, 

 or, generally, at any point : 



2 



FIG. 3. 



261 



(14) 



NeutrBl A«<s 



y/orfa/ <?//•"*• 



If A is outside the circle as in Fig. 3, draw a tangent AT to the circle and join OT. 



Then: 



AT= OA- i^^r/- io\ 



but ta = OA has the same value as when A is inside the circle and as given by (13). Sub- 

 stituting in (11') we find: 



2 2 



Hence the bending moment is again found by the formula ( 14) , but is of a sign opposite to 

 that when it is inside. In either case the bending moment is equal to the product of one-half 

 the fluid pressure and the "power" of the point under consideration relative to the circle of 

 polar inertia. 



At the points of intersection between the frame and the circle the bending moment 

 changes sign, its value is zero, and there is no change of curvature. These are points of 

 inflection or nodes, and, since all the nodes must lie on the circle of inertia, it is also called 

 the "nodal circle." 



The resultant of Rx and Ry at any point is R. 



R'= RJ + R; =p'{y-by + f{x-ay = ff^, 



R =pr (15) 



showing that the internal resultant at any point is in magnitude equal to the product of the 

 fluid pressure multiplied by the vector at that point from the center of the nodal circle. 

 The direction cosines of the resultant are : 



^ = - ^zi and A = ^^I^ 

 R r R r 



(16) 



