A method for quantifying the overall Poisson's ratio of a rod undergoing torsional loading is proposed and applied for a concentrically compound rod with inner core and outer shell of similar shape but opposite Poisson's ratio signs. Results show that a concentric compound rod with auxetic core exhibit same effective Poisson's ratio signs but with greater magnitude under torsional loading than under axial loading. However, a concentric compound rod with auxetic shell exhibits a range of volume fraction whereby the overall auxeticity of the rod is loading mode dependent, i.e., it behaves as a conventional rod under axial loading but as an auxetic rod under torsional loading. Hence a compound rod with conventional core and auxetic shell can be used as a smart structure that gives different response depending on the type of loading imposed on it.