188 PRESENT STATUS OF THE CONCRETE SHIP. 



Under this assumption the increase of the torsion due to dynamic action appears to 

 be such that the resulting lengthwise diagram for the maximum torsional moments is 

 a parabola, the maximum ordinate of which is given by formula ( i ). The torsion is 

 maximum at or near the center, zero at the ends. It is emphasized that /in ( i ) is 

 the transverse moment of inertia of the actual water-line section. 



When the total torsional moments in the various sections have been found, the 

 next step is to determine the internal distribution of stresses caused by the torsional 

 moment in each section. As in the case of a shaft, the torsion stresses are essentially 

 shears in transverse and longitudinal sections, though longitudinal tensions and com- 

 pressions may occur locally, say, where the section changes. Longitudinal tensions 

 and compressions would also occur in the abnormal case of a deckless ship, in which 

 the torsional resistance would consist of a resistance against bending of each side of 

 the ship, the one side upwards and the other side downwards. In order that the tor- 

 sional stresses shall not be large, it is essential that one or more shells are formed by 

 sides, bottom and deck, or by sides, bottom, decks and longitudinal bulkheads. These 

 cases may be considered the normal ones, and these are the cases in which the essen- 

 tial effect is shears in the transverse and longitudinal sections. These shears can be 

 evaluated by analysis, either by the principle of consistent deformations or by the 

 principle of least work. If only a single shell resists torsion the stress may be ex- 

 pressed by a simple formula which will be given. The notation is : — 



A = area enclosed by the center line of the cross-section of the shell ( for in- 

 stance, cross-sectional area of the ship). 



T = total torsional moment. 



5" = shear per unit length of circumference of shell. 



The formula is then — 



S = T/2A 



{A measured in square feet, T in Ib.-feet gives S in Ib.-feet.) 6" is a constant all 

 through the circumference. One central longitudinal bulkhead would not change the 

 conditions, as, on account of the symmetry, it would not itself carry any torsional 

 stress. Two longitudinal bulkheads would release the sides of, say 8 per cent of the 

 torsional stress (typical case), but would increase the stress in the central parts of 

 bottom and deck by about the same amount. 



Finally, the torsional shears should be combined with the shears of the regular 

 vertical shear action. The regular vertical shear and the torsional shear do not be- 

 come maximum for the same wave condition, hence the combination of the two 

 effects cannot consist of a simple addition. We assume the conditions to be such 

 that a 30° angle between wave crest and ship gives maximum torsional stress (this 

 assumption is on the safe side, as slightly lower resulting values are found when the 

 angle is smaller). Further, it is assumed that the wave section in the direction of the 

 ship has top and trough at the same points for maximum regular shear and maxi- 

 mum torsional shear. This assumption is also on the safe side. It is then found that 

 the following formulas for the combined effect give very close approximations. The 

 notation is : — 



