following expression for q; as a function of the critical stress: 



T - 4Sc^(l-Sci.) ~ (81) 



Equation (81) constitutes one of the important relations to be used in the 

 derivation which follows. 



In the preceding it has been shown that, in general, the critical buckl- 

 ing stress for columns is given by 



S^r='^S^r^ (82) 



In the elastic case, T = 1 and Equations (78) and (82) reduce to the well- 

 known results of Euler. 



At this point of the derivation, a basic empiricism is introduced. In 

 the case of plate structures, a slight modification of the form of Equation 

 (82) in which T is replaced by\[T is in better agreement with experiment 

 so that 



S^r = NpScrg (83) 



Trilling and Windenburg offer what appears to be a plausible explanation 

 for the reduction in the critical buckling stress implied by Equation (83) 

 for plate structures in the effect of lateral restraint offered by the second 

 dimension. They go on further to say that "this substitution of ^T^for T 

 in the case of tubes under end-loading is supported theoretically by 

 Geckeler." Although these earlier investigations had not been extended to 



60 



