j4 MK. IS. \. SiMTWVKLL ON THE GENERAL THEORY OF ELASTIC STABILITY, 

 so that, finally, 



T- ^ < 1U > 



This result leads to a simple method by which the collapsing loads of short struts 

 may be obtained graphically from the compressive stress-strain diagram. A full 

 explanation is given in the paper to which reference has already been made, and a 

 comparison, showing satisfactory agreement, is made with the results of experiments. 

 One conclusion of some practical importance may be noticed : the curves of collapsing 

 stress show that great ductility of material is by no means desirable in struts, 

 the primary requisite being a high elastic limit. 



Need for Further Research. Conclusion. 



With slight modification, the theory just given for short struts might be applied to 

 the problem of circular rings under radial pressure ; but these appear to be the only 

 cases in which we can at present discuss the stability of overstrained material. In 

 any problem dealing with plates or shells distortion from the equilibrium position 

 must introduce new stresses, in directions perpendicular to that of the stress which 

 has caused elastic failure. The circular type of distortion in a tubular strut, for 

 example, will introduce " hoop " stresses, and at present we have no knowledge of the 

 corresponding stress-strain relations when " set " has occurred. 



This and many other stability problems may be regarded as special cases of a 

 general problem, viz., the determination of the changes of strain which occur when an 

 infinitesimal stress-system, defined by principal stresses g, r, s, is impressed upon a 

 material already overstrained by a simple stress p. The problem is not simple, and 

 its solution would probably entail much theoretical and experimental work ; but this 

 would be justified by the importance, both for theory and practice, of its applications. 



In conclusion, the author desires to express his indebtedness to Profs. LOVE and 

 HOPKINSON, for valuable criticism and advice ; to Mr. L. S. PALMER, for the photo- 

 graphs reproduced in fig. 2 ; and to Messrs. H. J. HOWARD and D. P. SCOTT, for 

 assistance in the prosecution of the experiments described on p. 223. He also takes 

 this opportunity of thanking Messrs. Stewarts and Lloyds, Ltd., of Glasgow, for 

 gifts of very accurate steel tube for experimental purposes. 



