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Collapse oj Short Thin Tubes. 565 



six diameters. In fig. 6 we have the calculated hyperbola 

 extended beyond the length of six diameters. The particular 

 curves of figs. 6 and 7 are for 1-inch and 3-inch tubing of 

 thicknesses of t/d='024,5 and '0227, but the tubes of other 

 diameters and thicknesses show similar characteristics. It 

 is seen that, for lengths greater than six diameters, the 

 hyperbola thus calculated shows pressures increasingly less 

 than those given by experiment. At this length of six 

 diameters there thus appears to be a " critical length." The 

 curve at this length bends rapidly towards the horizontal 

 [especially and particularly so] in the case of the thick tubes. 

 In the case of the thinnest tubes both for the 1-inch and the 

 2-inch tubes, that is, for tubes in which the ratio of t/d is '001, 

 the agreement with the hyperbola is not so good and, indeed, 

 the maximum bend seems to occur at a much shorter length. 

 While the curves show much uniformity and the same 

 characteristics are found in the 1-inch and the 2-inch tubes 

 for this thickness, yet the percentages of error for such low 

 pressures of collapse are necessarily greater. 



(3) The experimental curves of this investigation are not 

 in agreement with the Southwell formula L = k ^d 3 /t, 

 which Cook has used. This is shown in typical cases in 

 figs. 6 and 7, where the curves for L=l*75 ^d*/t are drawn 

 for the 1-inch and 3-inch tubes having a ratio t/d of *0245 

 and '0227. On the same figures we have the rectangular 

 hyperbolas drawn through the experimental point fcr a 

 length of six diameters. If we write the formula L = k v ^, t 

 in the form 



L= -M_ 



~ s/tjd' 



we see that the critical length should increase directly as 

 the diameter, and inversely as the square-root of t/d. It is 

 evident that the length corresponding to the critical bend 

 does vary as the diameter of the tube, but the curves do not 

 show that the thinner tubes have the longer critical lengths. 

 Indeed, the very thin tubes for both the 1-inch tubes and 

 the 2-inch tubes rather indicate a shorter critical length 

 than a length of six diameters. It will be remembered that 

 Cook was unfortunately limited by his apparatus to lengths 

 of less than four diameters, and so his curves could not show 

 the above. 



The experimental curves for seamless steel tubes, for 

 which the ratio t/d is between '024:5 and '015. thus show 

 that there is a " critical w bend at the length of about six 

 diameters, the part of the curve for the shorter lengths being 



