324 



PORTAL WITH POSTS FIXED AT ENDS. 



Art. 165. 



165. General Case of Portal with Posts Fixed at Both 

 Ends. In Fig. 217 assume F to deflect as much as B, that is, 

 the bracing to be rigid. So far as the post is concerned, we 

 have the case of a beam fixed at both ends, a load at a distance 

 a from one end and supports not on a level, as shown in Fig. 218. 



Since there is no moment at the points of contraflexure 

 (89) the reactions H, H', V, and V, Fig. 217, may be supposed, 

 when convenient, to act at the points of contraflexure. 



Fig. 2.8. 



Taking moments about the point of contraflexure nearest 

 a, Fig. 218, we have, 



M 2 R 2 x l =0 or. M 2 =R 2 x l (94) 



and for the equation of the elastic line (81) we have 



El ^-=y 2 R 2 x 2 -M 2 x+(C=Q) (96) 



cix 



Substituting for M 2 from (94) and making x=a 



(99) 



Similarly if the shear It./ is in a' F' 



c/)., ..(100) 



If FF' is rigid, y l =y l ' and we have, after substituting for 

 R 2 and R 2 their equivalents, H and H'. 



