An analysis of tests of WATER-TIGHT BULKHEADS. 105 



Third Case — Elastic String {curve 2, fig. 7). 



This case is given because it furnishes an outer value of the elongation 

 and hence of the tension for a given maximum deflection. As explained 

 in last year's paper (Appendix II, page 422), we have here: — 



y=^^ (9) 



which gives- 



T2=—p'PAE (10) 

 24 



^ = ^ (II) 



8T ' ^ ^ 



whence- 



8AE8^ A 4 17^" 



T2 = — r7^ = 2.67 AE- (12) 



Comparing now the three values of T as found by (4), (8) and (12) 

 we see that Tj is about seven per cent, greater than Tj and Tj about two 

 per cent, greater than T^. 



The actual curve of deflection when tension is included will, for a given 

 value of d, both in the first and second cases, fall somewhat outside the 

 respective curves for pure bending o and i, and in case of stiff eners with 

 very small moment of inertia the actual curve of deflection will approach 

 curve 2, which gives the absolute maximum value of the tension. (See 



Fig. 7.) 



With the stiffness usually possessed by bulkhead stiffeners the curve 

 of deflection for a given value of d will probably always fall very near the 

 curve for pure bending, and we may therefore assert that the tension, as 

 determined by (4) and (8) on the basis of a given deflection, is not likely 

 to differ more than a few per cent, from tlie true value in all ordinary cases. 



As shown on Fig. 8 the curve of deflection for a certain increasing load 

 is very nearly of same length as that for the same uniform load, being 

 inside the latter curve at the upper part and outside at the lower part. 

 For combined uniform and increasing load the curve of deflection is inter- 

 mediate between the two first named ctirves. We may thus without 



