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I was thinking about this and hit a "wall". If you have a vertical rod with constant area that is attached to the ceiling from one point its weight will be:

[itex]w(x)=ρ*x*g[\itex] (where 0 is the end of the bar)

now if you take a differential above x you will have that the downward force that it's experiencing is w(x), but above the dx is w(x+dx). Where did I go wrong here. Is there something I'm not taking into consideration?

Thank you.

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# Statics of bar under own weight.

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