From several years now at CEA/Saclay has been lunched a program that aims at developing design tools and technologies for conduction-cooled MgB2 magnets. In the framework of this program, a device for investigating the circumferential strain dependence of the critical current density in MgB2 wires and tapes has been designed. It has to be integrated into the existing test facility which provides 600 A dc current power, 3 T background field, and is conduction-cooled down to 4 K by a two-stage GM cryocooler. In this device a new spring geometry is investigated, where the conductor is tested in a magnet-like configuration by applying a uniformly distributed circumferential strain (up to 1$\%$) to a ring-shape spring. The paper focuses on the mechanical design, analytic calculations, and numerical simulations of the spring geometry. Moreover, experimental tests on a mock-up model of the device are performed in order to validate the working principle and the materials properties.