of this may be found in Reference 8; however it is of interest here to give 

 the end result which can be expressed by the following convenient formula; 



Lg = LFi+b (22) 



In Equations (15) through (22) the following F functions (graphical 

 solutions for which were first developed by Krenzke and Short in Reference 

 10) have been introduced for ease of calculation: 



■^1^(0)1^°^^ T]^9 - cos Ti^O 



/2> 



(23) 



^2 = 



cosh T] sin T) sinh tj cos tj 



■ — — + 



/2> 



:24j 



"3% 



0.91 



cosh T] sinh r\ cos t] sin t] 



/2> 



(25) 



NO. 91 



cosh:]! 6sinq2® sinhtij^Scosij^Q 



^2 



T]l 



/57 



(26) 



where: 



D 



coshT]j6sinhT)-^e cosT]2esinq2^ 



L ^1 ^2 - 



-^ = i^f^^'(-r) 



(27) 



e = ^3(l.v2)^ 



27 



