Art. 165. PORTAL WITH POSTS FIXED AT ENDS. 



32o 



(ia o 

 H 



multiplying both sides of the equation by -77- 



1 

 Now H+H'=R+P .............................. (102) 



or ff'+'^j/ H'=R+PQTH f ( 1+ jp)*=R+P from which 



(103) 



If the posts have the same cross section 1=1' and they drop. 

 If the supports are on a level a=a' and (103) becomes 



H' _ R+P ..(104) 



-/ (j^-^) 



J'^o^t 



If a = a r and x 1 =x 1 ', (103) becomes 



H > = ?_l ==(R+ P)_J_ 7 ................ (105) 



Y + l 



In this case when / =/' we have H =H f =%(R +F) ........ (106) 



This case is treated in Art. 169. 



(102 and (103) determine H and H' when x^ and x/ are 

 known. For the conditions given these depend upon the rela- 

 tion between c and a and c' and a' . The relation between c, 

 a, and x l will now be found. 



M K>a = ^j-^E 2 x-M 2 -Q (x-a) ............. (107) 



This is the equation of the elastic line from F to B. 



...... (108) 



The first members of equations (96) and (108) are equal 

 when x=a,. Hence CV= y 2 Qa-. 



