Consider a cylinder of height h, diameter d, and wall thickness t pressurized to an internal pressure Po (gauge pressure, relative to the external pressure). The cylinder consists of material with Young’s modulus E, Poisson’s ratio ν, and density rho. Derive expressions for the axial and hoop strains of the cylinder wall in terms of the can dimensions, properties, and internal pressure. You may assume plane stress conditions. Assume a strain gage is bonded to the cylinder wall surface in the direction of the hoop strain. The strain gage has nominal resistance R0 and a Gage Factor GF. It is connected in a Wheatstone bridge configuration where all resistors have the same nominal resistance; the bridge has an input voltage Vin. (The strain gage is bonded and the Wheatstone bridge balanced with the vessel already pressurized.) Required:
Develop an expression for the voltage change ΔV across the bridge if the cylinder pressure changes by ΔP.