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The correct definition and measurement of the thermomechanical properties of the superconducting cable used in high-field magnets is crucial to study and model the behavior of the magnet coil from assembly to the operational conditions. In this paper, the authors analyze the superconducting coil of the main dipoles for the Large Hadron Collider. They describe an experimental setup for measuring the elastic modulus at room and at liquid nitrogen temperature and for evaluating the thermal contraction coefficient. The coils exhibit strong nonlinear stress-strain behavior characterized by hysteresis phenomena, which decreases from warm to cold temperature, and a thermal contraction coefficient, which depends on the stress applied to the cable during cooldown.