Statically Indeterminate Bar with alternating area and length

[hboyd3]

http://img197.imageshack.us/img197/5981/probie.png

So first I did a force balance (dF_x=0)

P=P_B-P_C=8.5kN

R_D= R_A - P
R_A = R_D + P

I know the total change in length is equal to 0, so

d_AB + d_BC + d_CD = 0

==>

(R_A*L₁)/(E*A₁) + (P*L₂)/(E*A₂) + ((R_A-P)*L₁)/(E*A₁) = 0

but when I do the algebra I can never get it to work. my numbers never match the answer no matter which way I approach it. I can do problems with only 2 different sections but this 3 sectioned one has me baffled.

the answers are
R_A= 10.5kN to the left
R_D= 2kN to the right

anyone have any insight?

 

[PhanthomJay]

You are assuming that the force in the middle segment is P. It is not. Cut a section (Free Body Diagram) thru the middle bar and determine the force in that bar as a function of the known and unknown variables.