/sinhQ + sinO 



e\ cosh9 - cosO 

 e e 



(116) 



V"- ' 



3(1-1/ ) L/\/Rh 



The method of calculation has already been discussed in connection with 



Equation (105); the same basic approach applies to Equation (112). 



It is of interest to mention that out of this general solution resulting 



from the use of Equation (101), Reynolds was also able to derive an 



elastic buckling solution by using i/q in place of v and setting Eg « Et = E. 



This solution, similar to that of Von Sanden and Tolke, i.e. , Equation (60), 



is given by Equation (113). 



FAILURE CRITERION FOR COLLAPSE OF 

 AN IMPERFECTLY CIRCULAR SHELL 



44 

 Using classical small-deflection theory, Galletly and Bart carried 



out a theoretical investigation of the effects of boundary conditions and 



initial out-of- roundness on the strength of cylinders subject to external 



hydrostatic pressure. The equations developed by these authors were 



applied to" the case of initially out- of- round cylinders with clamped ends-; 



these equations represented a slightly modified form of those previously 



45 

 derived by Bodner and Berks, working at the Polytechnic Institute of 



74 



