AN ANALYSIS OF TESTS OF WATER-TIGHT BULKHEADS. 87 



no distinction is made between these cases (Fig. i , a and Fig. i , 6 or c) , since 

 the same sizes of bars are recommended whether the bars are " efificiently 

 connected to the intercostals between the floors in vessels having ordinary 

 floors," or whether they are "secured with eflicient brackets to the inner 

 bottom in vessels having cellular bottoms." 



In case of stiffeners supported at both ends and at an intermediate 

 point the statements made in last year's paper (see the Transactions, 1909, 

 page 393), concerning bracketing of a stiff ener, which is continuous over the 

 middle point of support, should, in the light of the above discussion on 

 brackets, be amended to read, that the best solution is obtained by bracket- 

 ing at all three points and not only at the ends, since the stiffener will thus 

 be reinforced at the middle point where a great bending moment is found. 

 If only one bracket is fitted at the middle point, it should be fitted below 

 rather than above this point. 



b. FORMULAS FOR THK CAS^ WHEN THE LEVEL OF THE WATER IS BELOW 



THE TOP OF THE STIFFENER. 



This case was omitted in last year's paper, but as it occurs in the 

 present analysis, and as it may occur in many other cases, the solution 

 is given in the Appendix. 



C. FORMULAS FOR TENSION AND BENDING COMBINED. 



The solution of this problem given in last year's paper may be much 

 simplified in cases where the maximum elastic deflection, d, of a stiffener 

 is known, as in case of the analysis of a given test. As shown in the 

 Appendix, we may then with sufficient accuracy calculate the tension, 

 T, under the supposition that the stift'ener has deflected as it would do 

 under pure bending with the same maximum deflection and under a uni- 

 form load. 



This supposition furnishes us in all cases with a simple equation of 

 the first degree in T. The expression for T depends only on the elasticity 



of the material and on the ratio between the deflection and the length, -, 



and is thus entirely independent of how the deflection has been produced, 

 and of the moment of inertia of the stiffener. 



The tension so found is likely to be an outside maximum value, for 

 the supports of a stiffener are rarely absolutely immovable, nor are the 

 attachments absolutely rigid, such as supposed in the formulas. 



By applying this method to actual bulkhead tests it is found, that with 



