334 PORTALS POSTS PARTIALLY FIXED. Art. 167 



revised and again applied in (174), neglecting the second term, 

 which is small. Now having a close approximation of V, we 

 can find approximate values of D 2 and D 2 ' ', M 2 and M 2 ' from 

 (179), (178), (175), and (176). From (172) or (173) we can 

 find the corresponding value of H'. From (175) and (176) we find 

 the first approximate values of x l and a:/. Now a revised value 

 of V can be found and applied to get as before new values of 

 H' ', H, x lf and /. This process may be continued until the 

 required degree of accuracy is attained. 



The stresses for this case are found in exactly the same 

 manner as for the first case, but the formulas in the recapitu- 

 lation of Art. 165 have to be modified, because RL and Q are 

 different. We have: 



H(a-x 1 ) =/J 1 (e-x 2 ) ............................... (181) 



and R^^^k.D^M,... . .......................... ... .(182) 



from which R^ = [H(a -xj + Af J ....................... (183) 



and* 2 = . . ..(184) 



Ri 



Q=R l +H ........................................ (185) 



^-[H(a-x l ) +MJ ........ (186) 



Horiz. Comp. B'F =R+P + R l +R l ' =R+P+--[H(a+x l ) 



'+x l ') +Af 1 +Af 1 ']. . . . (187) 



FF' =H' +#/ =H' + [H f (a r -z/) +M /] . , . . (188) 



e 



The maximum stress in the posts may be gotten from equa- 

 tions (135) to (138) inclusive, remembering that H and H' are 

 not the same as in (186), (187), and (188). 



When the wind blows in the opposite direction the same 

 remarks apply as in Art. 165. 



168. Particular Cases of Stresses in Portal Bracing. 



We shall now apply the general formulas which have been devel- 

 oped, to the usual particular cases of construction of portals. The 

 various cases will be distinguished by numbers followed by the 

 letters a, b, and c. The letter a denotes that both ends of the posts 

 are fixed; the letter b that the posts are fixed at their tops, and 



