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The present paper describes a device structure for controlling and measuring strain in graphene membranes. We propose to induce strain by creating a pressure difference between the inside and the outside of a cavity covered with a graphene membrane. The combination of tight-binding calculations and a COMSOL model predicts strain induced band gaps in graphene for certain conditions and provides a guideline for potential device layouts. Raman spectroscopy on fabricated devices indicates the feasibility of this approach. Ultimately, pressure-induced band structure changes could be detected electrically, suggesting an application as ultra-sensitive pressure sensors.