326 PORTAL WITH POSTS FIXED AT ENDS. Art. 165. 



EIy=y Q R 2 x*-y 2 M 2 x 2 -Q (%x*~y 2 ax 2 } -y 2 Q a 2 x+C 2 . . . (109) 

 y=^y^ when x=a and when x=c 



l =% R^-y 2 M 2 c 2 -Q (l/ 6 c 3 -i/ 2 c 2 



<==% R 2 a*-y 2 M 2 a 2 -Q (i/ 6 a 3 -y 2 a 

 Subtracting 0=%ft 2 (c 3 a 3 ) y 2 U 2 x^(c 2 a 2 ) Q (%c 3 i/ 6 a 8 

 i/ 2 c 2 a+y 2 a 2 c) 

 whence 



) $(c a) 3 



(110) 



Also the equation of the elastic line from F to B Is 



*?*** J2 1 ^ ' X 1 * * * \ / 



El -jr-=R i (cxy 2 x' 2 )MiX+C 3 .. . . (112) 



when 0^=0,=0=^ (c 2 -i/ 2 c 2 ) jtf lC +C 8 and ^^cJ^-i/^c 2 



1 x+C 4 ^ ...... (113) 



y=y 1 when x=a and when ic=c, whence 



r i=R L x. 2 , therefore, R 1 x 2 =^R 1 e and x 2 =^e (115) 



r i =JB 1 e=JB 1 (c a) R i =^QR 2 . Hence 



From which ^=7_1 ^^ 3 3 = _ 3X / (117) 

 From (110) =1 ,,, . J ( !~^ (c+ 



Solving for x we get ^ = 3a-4-c (118) 



When c=2a or a=%c, ^^a (119) 



(#j would eriual y 2 a if /? did not deflect.) 



When ca that is the portal is a single strut a plate girder 

 for example (see Art. 170) Xj=y 2 a (120) 



