12 



If we proceed purely analytically, without the use of tables, we must use 

 the equation 



P = f S f-^^]=|6 2a ,[,-Mu] (17, < 



in the unelastic region, which follows from the substitution of Eq. (15) in 



Eq. (13) and the elimination of k. The value of y must here be determined by the 



equations in Section 1. The numerical values in Eq. (17) are for medium steel. 



3. COMPARISON with EXPERIMENTAL RESULTS. 



Two series of experiments were carried out in 1918 with large medium steel 

 tubes welded along the longitudinal seam, and subjected to external water pressure. 

 The first series included tubes with the wall thickness-ratio 



h/a = 1/400 = 0.0025; x = h 2 /3a a = 2.083 * 10" S 



and the three length ratios 



a/1 = 400/120, 400/180, 400/240 whence, 



eC =Ta/l = 10.47, 6.98, 5.24 



We obtain from the graph, Fig. 4, at the ordinate h/a = 0.0025, the values of 

 the number of lobes, n, in the three cases: 



(a) n = 16 (b) n = 14 (c) n = 13 

 [Translator's Note: For case (c), n lies so close to the border line between 12 

 and 13 that practically it might be either. Actually, n = 12 is determinativej 



The experimental number of lobes from the tests on four different sizes of 

 models of diameters 800, 1200, 1600, 2400 mm (31.5 in., 47.2 in., 63.0 in., 

 94. 5 in. ) are 



Case (a) 

 n = 17 



17 1 5 I3---U 



16 



We may conclude, therefore, that the agreement is almost exact. In addi- 

 tion it is worthy of note that the agreement appears to improve for the larger 

 models. The differences between the number of lobes observed in the various sizes 

 of models, as well as the departures from the calculated number, hardly exceed the 

 limits of unavoidable experimental error. Fig. 6 shows the buckled model in 

 experiment IVa. 



Model Size 





I 



(D = 800 mm) 



II 



(D = 1200 mm) 



III 



(D = 1600 mm) 



IV 



(D = 2400 mm) 



(b) 



(c) 



= 15 



n = 14 



15 



13 



14 - 15 





14 - 15 





