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A helical nanowire can be defined as being a nanoscopic rod whose axis follows a helical curve in space. In the case of a nanowire with asymmetric cross section, the helical nanostructure can be classified as normal or binormal helix, according to the orientation of the cross section with respect to the helical axis of the structure. In this work, we present a simple model to study the elastic properties of a helical nanowire with asymmetric cross section. We use the framework of the Kirchhoff rod model to obtain an expression relating the Hooke's constant, h, of normal and binormal nanohelices to their geometric features. We also obtain the Young's modulus values. These relations can be used by experimentalists to evaluate the elastic properties of helical nanostructures. We showed that the Hooke's constant of a normal nanohelix is higher than that of a binormal one. We illustrate our results using experimentally obtained nanohelices reported in the literature.