Triple metals

Two metal sticks A and B are fixed on the left wall in the above diagram. The lengths and the linear expansion coefficients of A and B are \(3L\), \(\alpha\) and \(L\),\(2\alpha\), respectively. A third metal stick C with length \(3L\) is fixed on the right joint bar on which the right end of B is also fixed. Suppose that there is a temperature change \(\Delta T\) which is the same for all of A, B and C, and the distance between the wall and C remains constant, which is \(L_0\) as shown in the diagram. What is the linear expansion coefficients of the metal C?

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