332 PORTALS POSTS PARTIALLY FIXED. Art. 167. 



In this value of D, V is neglected. With this mean value, call in sr 

 HH' in (158) find an approximate value of V from (124). 

 The second term will become zero, but this will be a close approx- 

 imation of V. With this value of V find D and D' and M 2 and 

 MS. Substituting the latter in (155) or (156) we get H', and 



With these approximate values of H and II' we get from 

 (154) and (158) values of ^ and z/, R t and / These in (124) 

 give a new value of V. This should not differ much from the 

 lirst approximation. Generally the effect of a change in V on H' 

 can easily be seen without again going through the entire calcu- 

 lation. 



167. General Case of Portal with Posts Partially 

 Fixed at Both Ends. In this case both x l and x 2 will be 

 less than in the first case with both ends of the columns fixed. 



The distribution of the load between #and H' may be found 

 as follows : 



When x>a, 



EI^R^c-x) -M t .......................... (160) 



El ^R^cx-lx*) -M l x + C 1 .'. ................ (161) 



(162) 



When x=a and x=c in (162), y=y 1 , and 



C t =pf ^c+a) -^(cs+ac-ia*) .. .............. (163) 



When x<a, 



EI d = M 2 -Hx ............................... (164) 



(165) 

 4 =0) ............. (166) 



When x=Q, y=0, and C 4 =0. 



When x = a, from (165) =- from (161) 



-a) ..... (167) 



