# Frame Deflection

1. Aug 1, 2012

### zzinfinity

I had this as an exam question in my first Structural Analysis course, and couldn't figure it out. The frame is supported by 2 cantilevers at points A and D. The top member is perfectly rigid, that is EI=infinity. E is constant. Solve for the deflection at point B and the reactions at A and D.

Could someone give me an idea of how you could approach this? My Professor said it could be solved in 3 or 4 lines but I sure don't see how. Thanks

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2. Aug 1, 2012

### PhanthomJay

The horizontal load distributes to each column in accordance with the relative stiffnesses of each (the column with the higher EI hogs a greater share of the load since deflections at B and C must be equal). Also, because of the infinite beam stiffness, there can be no rotation of joints A and C, so each column is fixed at the base and "guided" at the top. I assume that you can then use beam tables for reactions and deflections?
Note I am assuming rigid connections between beam and column, and not pin connections. This is not that fully clear from the sketch.

3. Aug 1, 2012

### zzinfinity

Thanks for your response! However I made a mistake. The frame is supported by 2 pin supports, not cantilevers. Yes the connections between the beam and columns are rigid so the angle between the beam and columns is 90 degrees. The only table provided have the fixed-end moment equations, but I thought the FEM in each member would be zero since there is no load applied any where along the members.

The way I tried to approach this problem was the slope-deflection method but didn't now how to deal with the infinite EI.

When you say more of the load goes to the column with the higher stiffness, is it a direct proportion? Is the load on the right column exactly 3 times the load on the left column?

Thanks!

4. Aug 1, 2012