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This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L)$ and with control functions in $H^2(0,T)$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.