258 



CALCULATION OF THE TRANSVERSE STRENGTH 



years after it was explained in the Institution of Naval Architects, is probably the abstract 

 form in which it was then presented. 



Mr. Whiting's presentation of the method is brief and cannot well be understood with- 

 out a study of Marbec's papers. 



Marbec deals first with an independent closed frame ring of any form and of varying 

 section subject to a uniform pressure, external or internal. 



FIG. I. 



-X 



Referring to Fig. I, let p be the pressure per unit length of the ring. The con- 

 tour line represents the neutral axis, which has a total length, measured along the girth, 

 L. At any point A all the molecular stress forces acting on the section can be represented 

 by a resultant force Ra and a couple Ma, but the same result would be obtained if the force 

 Ra were acting parallel with itself at a certain distance from P but rigidly connected with 

 the ring so as to produce the same reaction and moment in the section. In that case we 

 might imagine two equal and opposite forces Ra to be acting at P, of which one might be 

 conceived as a free direct force, the other as forming a couple Ma together with the force 

 acting away from the point P. Ra is called by Marbec "the internal resultant" (la resul- 

 tant e interne). 



The frame ring is characterized by its form and flexibility. The flexibility e at any 

 point is such that the change in curvature produced by a bending moment M is equal to 

 eM. Hence, according to the elementary theory of bending 



E = 



I 



'EI 



being the change of curvature due to a bending moment of unity strength. Put 



sds—dm 



and conceive the flexibility as a sort of density, then dm may be considered as the mass of 

 the elemental arc ds. We may now by integration determine the total flexibility mass of 

 the ring: 



L 



C dm 



m 



and may find its center of gravity, G, as well as its moment of inertia with respect to any 

 axis just as in the case of actual masses. 



