OF SUBMARINES BY MARBEC'S METHOD. 



263 



case the radius of the nodal circle, which is the radius of gyration about O as a pole, must be 

 the same as that of the circle of the neutral axis. Hence the bending moment is everywhere 



FIG. 4-. 



Neutral A\;& 

 and 

 Nodal Circle 



zero. For instance, in Fig. 4 the center of gravity of the ring is in the vertical axis but 

 above the center of the circle formed by the neutral axis, while O is found in that center and 

 hence M is everywhere equal to zero. This is important, because it shows that it may be pos- 

 sible by proper construction to reduce the bending moments very considerably in noncircular 

 frame rings by so designing them that the neutral axis shall be circular or nearly so. Actually 

 the bending momentswould not be exactly zero, because the pressures referred to or projected 

 on to the neutral axis would not be uniform, but by proper adjustments it should be possible 

 to reduce the bending moments to a minimum. 



If a portion of a ring with circular neutral axis is entirely inflexible, we have e = 

 for that portion, but it is still true that the center of the nodal circle coincides with the center 

 of the circle formed by the neutral axis and the bending moments are zero. This case 



riG. 5. 



Neutral f^*- 



Nodaf Circle 



