Need help with a Statically Indeterminate System

AI Thread Summary
The discussion focuses on solving a statically indeterminate system involving three steel bars connected to a rigid member K. The user is attempting to determine the forces in each bar and their corresponding elongations using the formula δ = (PL) / (AE). They have derived equations based on moments and force balances but are struggling with the relationships between the points of connection on the rigid member. The complexity arises from the lack of a fixed point, complicating the calculations for elongation ratios. The user seeks guidance on how to proceed with the analysis.
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Homework Statement



Three steel bars are pin-connected to a rigid member K. Determine the force developed in each bar. Determine the load carried be each of the tension members and the elongation of each member

http://img3.imageshack.us/img3/6850/problemdiagram.jpg

Known:
A_A_B = 0.10 in^2
E_A_B = 30E6 psi
A_C_D = 0.20 in^2
E_C_D = 15E6 psi
A_F_H = 0.30 in^2
E_F_H = 10E6 psi


Homework Equations



\delta = (PL) / (AE)


The Attempt at a Solution



Finding the moment about B:
10P_C_D + 20P_F_H = 15(15000)
or
P_F_H = 7500 - (1/3)P_C_D

The equation \delta = (PL) / (AE) yields:
P_A_B = 150,000\delta_A_B
P_C_D = 200,000\delta_C_D
P_F_H = 300,000\delta_F_H

And the sum of forces in the Y direction gives:
P_A_B + P_C_D + P_F_H = 15000


This is where I'm stuck. If any point along K was fixed it would be easy; K is rigid, so then the distance from the fixed point can be turned into a ratio to find the other \delta values. I think all 3 points (B, D, and H) are pulled downward, but I'm not sure what there relation is to each other. Any clues?
 
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Yikes, I think my TEX tags are all messed up. Not sure how to fix it, let me know if you have any questions!
 
Now if it was something like this:
http://img194.imageshack.us/img194/8167/fixedpoint.jpg
I would say sigma_CD = 10(theta) and sigma_FH = 30(theta) and all would be good.


But since it's like this:
http://img199.imageshack.us/img199/9023/nonfixedpoint.jpg
I have another variable in there with x. Now sigma_AB = (x)(theta), sigma_CD = (10+x)(theta), and sigma_FH = (30+x)(theta)

Hmm...
 
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