Art. 165. PORTAL WITH POSTS FIXED AT ENDS. 



327 



These would ordinarily be the limits for the relation between 

 a and c, and x would only vary from 0.6a to 0.5a. Even if a 

 were only ^ c (which limit would very seldom be reached) x l 

 would be only 0.670. 



In order that the above equations may be applicable (see 

 Art. 164) M^^X^i^(iQ^)>%ff(a--i) (121) 



(See Equations (114) and (116) ). 



(122) 



D may be a direct stress or a reaction. Special precautions 

 must be taken in the construction if it is desired to have a reac- 

 tion which will make the end of a column "fixed," since an ex- 

 ceedingly small change in the direction of the axis of the column 

 will destroy this condition. In truss bridges we must depend 

 upon the direct stress in the post to fix its ends. 



D is made up of T 7 , (Fig. 217) except at B, the dead load 

 stress in the post, and in some cases, also the live load stress. 

 (164.) 



In Fig. 217 putting the forces H and V, and H' and T 7 ' at a 

 and a' respectively, and taking moments of the external forces 

 about the point of inflection in aF 



(c-x,) 



V = 



or 



= [ (R+P) (c-x^-H'fr-a'+xS-x 



when c=c', V'=V, and 



=-y= [(R+P) (c-x 1 )-n f (x^-x 1 



when c=c' and x =x^ 



=_V= [(R+P) (c-X! 



i +R 1 ')] (124) 



1 +R 1 ')] (125) 



(126) 

 (127) 



From equations (114) and (116) R : = 2 ( c a) ' and 



