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The following is an indeterminate frame consisting of two beams that are rigidly connected to each other at the corner support.

enter image description here

I want to find the support reactions.

enter image description here

As far as I can see, this is a symmetric structure with symmetric loading (please do correct me if I am wrong).

And as I understand it, a symmetric structure with symmetric loading has symmetric reactions.

From here, the chain of logic I would follow is:

  1. The corner roller support has a vertical reaction (V2) of 0, for symmetry to be possible.
  2. Similarly, H1 = 0, for symmetry.
  3. V1 = - H2, again for symmetry of reactions.

Then, from equilibrium, we can say:

enter image description here

However, this is incorrect. The mark scheme for this question has a different solution.

Could someone please tell me where in my process I have made a mistake?

EDIT: This is what the mark-scheme says: enter image description here

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1 Answer 1

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The members and loads of the frame are symmetric about joint "B", but the supports are not, which is the source that causes non-conforming deflections when loaded. The sketches below depict each case of the deflection of the frame.

enter image description here

ADD:

The roller support at "B" is free to move in x-dir. The sketches below show the lateral displacement and corresponding joint rotation due to the respective loads "F" and "H".

enter image description here

Simplified Frame Model:

enter image description here

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  • $\begingroup$ Thank you for your reply. Could you please take a look at the edit I've added? It shows the deflected shape which the markscheme contains, and it appears to be invoking symmetry. Do you think you could offer some clarification about that? $\endgroup$
    – VJ123
    May 12, 2022 at 15:06
  • $\begingroup$ You've neglected the roller support at "B", at which the rigid bent will move laterally for both loads. You can't solve it by symmetry and ignore the additional forces contributed by the displacements. However, in this case, you can place a vertical reaction at "C" to represent the vertical reaction at "B". Now you have a symmetrical frame as shown as the simplified model. The additional forces due to displacements will be there but hidden in the rigid frame analysis. $\endgroup$
    – r13
    May 12, 2022 at 18:56
  • $\begingroup$ Thanks for that! $\endgroup$
    – VJ123
    May 13, 2022 at 10:18

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