15 



Theoretical Values: 



(a) 



p = 10.2* 



(b) 



p = 8 



2* 



(O 



p = 6.1 



Experimental Values: 





(a) 





(b) 







(c) 



Model Size I 





6.1 





3.9 







3.35 



II 





7.0 





5.1 







4.15 



III 











6.0 







— 



IV 





9.5 





7.2 







— 



FIG. 



7. Summary of Experimental 

 Data. 



The entirely disproportionate value of Ilia 

 is omitted here. Fig. 7 gives a general idea 

 of the distribution of these values. Here we 

 see that the calculated values may very well 

 be regarded as obtainable asymptotic limits. 

 There remains only the question as to what 

 causes the smaller models to collapse so far 

 below the theoretical collapsing pressure. 

 It seems most probable that the welding of 

 the thin plating disturbs the symmetry of the 

 circular form, or the homogeneity of the ma- 

 terial itself. It is certain that in the 

 case of buckling with higher number of lobes, 

 even very slight irregularities may have a 

 decisive effect. 

 The second group of experiments concerns tubes with the wall thickness-ratio 

 h/a = 0.00406, x = h 2 /3a 2 = 5.49** 10" 6 

 and with frame spacing of 400, 500, and 600 mm (15.7 in., 19.7 in., 23.6 in.) and 

 a tube radius of 800 mm (31.5 in.). In both the first two cases the frames 

 failed under the test. In the third case, likewise, it must be assumed as certain, 

 because of the magnitude of the observed buckling pressure, that the limit of 

 strength was reached through failure of the frame. 



[Translator's Note: It is understood that the testing arrangements were such 

 as to make it impossible to observe the inside of the model during the testsj 



As we know from a theory which will not be further discussed here, if the 

 frames are too weak, the buckling pressure must correspond to that of a tube with 

 an effective length of double the frame spacing or even higher. We can, therefore, 

 test the reliability of our theory by computing the buckling pressure for tubes of 

 the length 1 = 800, 1000 and 1200 mm and compare them with the test results. With 

 help of the graph we find: 



et= 2.51 (3) dC= 2.09 

 n = 8 n = 7 



(1) 



(2) 



ot= 3.14 

 n = 8 



Further calculation shows: 

 (1) f= 0.134 



f,= 1.24 



,= 1.2 



