Vacuum breakdown is one of the main limitations to the operating accelerating gradient in radio frequency linear accelerators. Recent studies of copper cavities have been shown that harder copper conditions more quickly and can reach higher accelerating gradients than soft copper cavities. Exploiting this advantage requires the development of assembly methods that do not involve the copper-softening high-temperature heating cycles that are used in for example bonding and brazing. A shrink-fit method, which was already implemented successfully in the operation the IPM linac, is proposed for the construction high-gradient test S-band standing wave structure operating at 2998.5 MHz. The three cells cavity is designed to have a maximum gradient in the middle cell that is twice that of the adjacent cells. Mechanical considerations relating to the shrink-fit construction method have been performed using Ansys. To validate the simulations and ensure the feasibility of construction by shrink-fit method, a sample cavity was constructed and cold tests was performed.