and since 



"E A 

 the above equation leads to the following expression for the critical buckl- 

 ing stress: 



d =7r^Ep^ (73) 



where 



^ ^NA• 



When the nondimensional variables 



cr _ 1 



^cr " "37" ' ^E " "^ \j E 



are introduced, the Euler formula can be written simply as 



(74) 



"E X| 



(75) 



The Euler formula, Equation (73), is a special case of the more 

 general Considere-Engesser formula which may be written as 



^.. " ^^E/>2 



(76) 



where E is known as the reduced modulus and is a function not only of the 

 slope of the stress-strain diagram but, strictly speaking, also of the shape 

 of the column cross section. However, it has been shown from rather 

 extensive tests that the effect of the column cross section on E does not 



58 



