THE RANKINE-GORDON FORMULA 861 



But when x = /, y = 0, then - sin nl I cos nl - 



n 



or tan nl =- nl 



This equation must be solved by means of a graph and neglect- 

 ing the zero value, the least value of nl which satisfies the equation 

 is found to be 4-493 radians or 257J. 

 Then n 2 / 2 - (4-493) 2 



= 2-0477C 2 



W/ 2 



Then T7T - 2-0477T 2 



El 



... 2-0477T 2 EI 

 and W = jj 



182. The Rankine-Gordon Formula for Struts. For a very short 

 strut where buckling plays no part, the breaking load should be 

 A/, where / is the crushing strength of the material and A the 

 cross sectional area. For a very long strut where crushing plays 



C7T 2 EI 



no part, the buckling load should be ^ where c is a constant 



depending upon the nature of the ends. 

 Then if W is the load under which a strut of any length gives 



way, and if W = 



' C71 2 EI 



When I is small, W becomes A/ approximately. 

 When I is great, W becomes ^ approximately. 

 This formula therefore makes W approximate to A/ for very 

 short struts, and to ^ for very long struts. 



Thus W 



/here C = , a constant depending upon the material and the 



iture of the ends of the strut. 



Now I = A& 2 where k is the radius of gyration of the section 

 fith respect to that axis about which bending is most likely to 

 ike place that is, the axis about which I is least. 



Then W : 



