newtonian mechanics - Deformation of an elastic bar

We know that if we fix a bar at one of its ends, then the other one will descend by $s = A \cdot F l^3, A = const.$ (we can assume that $F$ is the gravitational force.

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solidly fixed here

We can assume that we know the descend of the end in this case and mark it by $x$

If we put it freely, like this

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^       ^
held here 

Then I heard we can treat it like two bars solidly fixed in the middle (not sure why)

But what if we fix it at the both ends, like this:

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^       ^
solidly fixed here

How low will the lowest point of the bar descend?