Stability of frame 2

What about roller support? If the roller support provides only compression resistance , it is unstable...

The roller support is providing a horizontal reaction force as shown that's it

As per your assumption 2, if the elements are rigid , yes..still stable.

The horizontal member with gravity load will fall from the roller, which does not provide vertical support. The falling member will cause rotation about the hinge, which has no rotational restraint capacity. So, is it stable?

Thank you for your reply but the two rigid bodies are only connected by two non parallel constraints (ie. the hinge) where is the third one? For a stable system the two rigid bodies should be connected by three constraints

You need to replace the vertical roller to a pin, or horizontal roller, then it is stable. Note the former is a statically indeterminate system.

Below find a solution with selected loading as per ur sketch..

Thank you very much for your input, appreciate it.

I've modified my last response to include the condition below.

retired13 (Civil/Environmental) said:

I've modified my last response to include the condition below.

Click to expand...

Dear retired13, the deflected shape is not applicable since both elements are rigid as per assumption 2.

The tip of L fame will deflect an amount due to gravity load, which will initiate the rotation about the hinge. The rigid bent won't help, as it is standing on a support that is free to rotate. The only chance for this system to survive is the horizontal load is huge, that push the horizontal member tightly against the wall and produces shear friction against sliding. But, the shear friction is usually ignored, as it is unreliable.

Interestingly I see another problem associated to my suggestion to make horizontal roller support - if the horizontal load reverses direction, then again, it is not stable. So, I'll stick to my original suggestion, the roller shall be replaced by a pin. Sorry for the confusion.

Mechanically speaking, the system can stand still with favorable conditions, but it's so called "limiting equilibrium", that is a neither-nor phenomenon - a marble stay on top of a dome.

Thank you very much for your replies

You are welcome. This is a seemly simple, but really tricky problem. When you do design, always keep stability in mind, be conservative.