w(x,e) 



where 



f 1^1 



(x) + C-> sm — + Co sin -— 



(160) 



u, (x) = COJ 



2qL 



V (x) = w,(x) = sin -~- 

 1 1 2qL 



> < X < qL 



(161) 



a^(x) = 



V (x) = w (x) = 1 



qL^ < x < ( L^- qL^) 



U (x) = COS 



(x-L +2qL ) 



2qL. 



v^(x) = w (x) = sin 



(x-L^ + 2qL^) 



2qL, 



where 



(162) 



(L^-qL^) <x <L^ (163) 



x,e are the axial and circumferential coordinates, respec- 



tively 

 a, V, and w are the axial, tangential, and radial displacements, 



respectively 

 Ap Bj^, . . . etc. are arbitrary coefficients 



l-i-^ is the bulkhead spacing, and 



q is an arbitrary number which permits the formation of 



a straight central portion of variable lengths as shown 

 in Figure 18. 



101 



