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Lets call length of the inlined bar=L Y of force = y base of triangl= b height of triangle=h angle of bar= a There will be a normal force $F*y/h*cos(a)$ and a horizontal force $F-F*y/h*cos(a)* \mu - N\mu$. But the system will accelerate if If $F_{ef}>N*\mu_{triangle}$ The triangle will topple if $F_{ef}*y>N*b/2$

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UPDATE (I think I misunderstood the constraints in my previous answer) Assuming the greyed out triangle beneath B is rigid and its resting on the horizontal plane with a coefficient of friction $\mu$ the beam is pinned on B and simply resting on A. The force F is large enough, so that the triangle is about to move/rotate. Then it depends on the coefficient ...

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The compressive stress is, of course, a factor, but if we consider a simple brick wall, then this H calculation would not suffice since there is lateral stability to consider as well surely, any misalignment or lateral force e.g. crosswind would compromise height a lot I think.

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