Bars and rod

Bars and rod

Two cylindrical horizontal bars are fixed one above the other; the distance between the axes of the bars is $\ 4d$ , where $\ d$ is the diameter of the rod. Between the bars, a cylindrical rod of diameter $\ d$ is placed as shown in Figure (this is a vertical cross-section of the system). The coefficient of friction between the rod and the bars is $\ µ = 1/2$ . If the rod is long enough, it will remain in equilibrium in such a position. What is the minimal length $\ L$ of the rod required for such an equilibrium?

You can express your answer in the form $\ L=xD$ , where $\ x$ is a positive, real number. Find $\ x$ .