286 



TESTING OF STRUTS. 



collapse. Of these, Euler's formula, deduced from theo- 

 retical considerations, is true only for long struts, whose 

 ratios of length to diameter are much beyond what exist 

 in practice. On the results of the experiments of Eaton 

 Hodgkinson, Gordon based his well-known formula; 

 llankine modified Gordon's formula and reduced it to a 

 form which is more generally applicable; Johnson has 

 devised what he calls a parabolic formula ; and besides the 

 classic experiments of Hodgkinson, those of Christie, 

 Davies, and later of Considere and Tetmajer have 

 contributed to the determination of the empirical con- 

 stants used in these formulas. 



ms////s 





^B 



ft 



' 



Y/ ?////// 



P 

 FIG. 149. 



It will suffice here to indicate the process of reasoning 

 leading up to Rankine's formula. 



The pillar, under an axial load P, may be held in 

 position in one of three different ways. 



In Fig. 147 the pillar, of length I, is provided with 

 rounded ends or hinges, so that there is no constraint. The 

 length I is the effective length, and is between the outsides 

 of the rounded ends or between the centres of the pin 

 joints. 



In Fig. 148 the pillar is shown as being provided with 

 feet, by means of which the ends are constrained and 



