ON STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 467 



of failure characteristic of tubes under compression, in which either 

 wrinkles are produced in the walls or the wall ' caves in ' in several places 

 round the circumference). 



When proper precautions are taken to secure accurate loading, experi- 

 ments lead to the following conclusions for tubes of mild 'Mi-A in 

 which the elastic limit and yield are nearly identical. 



(1) For tubes in which ^ is greater than 0'006, yield precedes coUapse 

 by wrinkling. 



(2) For tubes in which p is greater than approximately 0'044, complete 



collapse occurs at higher stresses than the yield, whilst thinner tubes 

 sustain the yield stress and collapse immediately by the walls ' caving 

 in.' 



It has been shown by the author that the yield stress in compression 

 is the upper limit of strength for a strut of ductile material ; hence it 



follows that the strength of a tubular strut in which ^ > 006 is the same 



as that of a solid strut having the same ^ and the same yield stress pro- 

 vided the end connections are satisfactory. 



In all struts the strength is decreased by the efiects of eccentricity 

 of loading and initial curvature. For struts having free ends these can 

 be readily allowed for by the following modification of Perry's formula : 



p = average stress. 

 p^ = yield stress in compression. 

 Pe = Euler value. 

 ca 



a = distance of the extreme fibre from the centre of area of the cross- 

 section. 

 AC = radius of gyration in plane of bending. 



c = equivalent curvature ^= Cy -\- Ji. 



C| = initial curvature = distance of the centre of area of the middle 

 section from the line through the centres of area of the ends. 



h = initial eccentricity of loading. 



An alternative formula can be obtained by replacing the curvature 

 term by an eccentricity term of the same amount, as suggested by 

 Southwell, and using Smith's formula 



^ Pr 



1+,. sec^^^. 



8 = equivalent eccentricity = h -\- c^. 



