COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 223 
ew niethod of rigorous investigation for stability problems in general, It 
obtains the general formula 
t Al d' 1 Kk — | all 
p= 2H— | - : ope ae 
P d | wae 1) 16 ny 3 l—m 4d | 
where « = number of lobes in collapsed cross-section and i is proportional to 
the length of the flue, the ratio depending on the terminal conditions. It is 
shown that the above formula leads to a result differing from that of Prof. 
Love (see No. 12) for the rate of decay of end effects. _ 
Southwell, R. V. 1913 On the Collapse of Tubes by External Pressure. ‘ Phil. 
‘ Mag.,’ May 1913. 
An attempt to meet the difficulties suggested by A. B. Basset. (See 
No. 1.) An investigation of the strength of short tubes is also given leading 
to the formula given in No. 17. 
19 Stewart, R. T. 1905-6 Collapsing Pressures of Bessemer Steel Lap-welded 
Tubes 3 to 10 inches in diameter. ‘Trans. Am. Soc. 
Mech. Eng.,’ 1905-6, vol. 27, pp. 730-822. 
Over 500 tests carried out on lap-welded steel tubes. It was found that 
the length of tube between transverse joints tending to hold it to circular 
form has practically no influence on collapsing pressure so long as length not 
less than about six diameters. 
The formula 
p = 1,000 ¢ - f1- 1,600 7.) 
for values of p less than 581 Ib. and values of | less than -023, and p 
_ 
ow 
= 86,670 5 — 1,386 for values of p and 5 greater than the above, are given. 
It is also pointed out that the formula 
3 
p = 50,210,000 (4 ) 
represents very nearly the results of the tests on tubes in which © ig less 
than -023. A series of curves is also given, showing the inapplicability of the 
older formule of Fairbairn, Nystrom, Grashof, Unwin, Belpaire, Wehage, 
Clark, &c., to modern tubes. 
20 Stewart, R. T. 1907 Collapsing Pressures of Lap-welded Steel Tubes, ‘ Trans. 
Amer. Soc. Mech. Eng.,’ 1907, vol. 29, pp. 123-130. 
The effects of the distortion due to successive re-tests on the collapsing 
pressures of 10-inch lap-welded steel tubes. The following formula is given : 
— 47°55 ed 
a 0-0926 7° — 0-874)!-# + 47-55 
where p, = collapsing pressure of normally round tube, 
p, = that of distorted tube, 
M = ratio of max. to min, diameter. 
21 Stewart, R. T. 1911 Stressesin Tubes. ‘ Trans. Am. Soc. Mech. Eng.,’ 1911, 
vol. 33, pp. 305-312. 
An investigation showing that the stresses in the wall of a tube exposed 
to an external fluid-pressure are of the same character as those in a column 
having fixed ends. 
22 Unwin, W.C. 1875 Resistance of Flues to Collapse. ‘ Proc. Inst. Civ. Eng., 
vol. 46, p. 225, 1875. 
Showed, from shape of collapsed tube, that when length exceeded a 
certain value, strength would become constant. Deduced the formula 
from analogy to struts, 
