Structural analysis stiffness method

[mdub12]

http://www.flickr.com/photos/53948823@N08/6193375731/

I need to solve this problem but with member 2 as L+e instead of L, and omit the load..

Since I only see one degree of freedom, i don't know how to set up the matrix to solve for the 3 forces.

I have K₁₁ = EA/L + (EA/(L+e))cos²(30) + EA/L cos²(60) but since there is only 1 DOF and no loads, i don't have much to make a matrix equation with..

I tried moving the roller to the right ecos(30) and trying to solve for the forces like that, but couldn't get much.. any ideas?

 

[mdub12]

I figured it out..

A_D = A_dm + kD

A_D = 0

K₁₁ = EA/L + (EA/(L+e))cos²(30) + EA/L cos²(60) = 2EA/L

A_dm = PL/EA = ecos(30) --> P = EAe√3/2L

--> D = √3e/4

A_R1 = A_rm + F_rD

A_R1 = EA√3e/4L
A_R2 = -5EAe/8L
A_R3 = EA√3e/8L