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Early-stage damage detection for bridges requires continuously sensing strain over large portions of the structure, yet with centimeter-scale resolution. To achieve sensing on such a scale, this work presents a sensing sheet that combines CMOS ICs, for sensor control and readout, with large-area electronics (LAE), for many-channel distributed sensing and data aggregation. Bonded to a structure, the sheet thus enables strain sensing scalable to high spatial resolutions. In order to combine the two technologies in a correspondingly scalable manner, non-contact interfaces are used. Inductive and capacitive antennas are patterned on the LAE sheet and on the IC packages, so that system assembly is achieved via low-cost sheet lamination without metallurgical bonds. The LAE sheet integrates thin-film strain gauges, thin-film transistors, and long interconnects on a 50-μm-thick polyimide sheet, and the CMOS ICs integrate subsystems for sensor readout, control, and communication over the distributed sheet in a 130 nm process. Multi-channel strain readout is achieved with sensitivity of 18 μStrain RMS at a readout energy of 270 nJ/measurement, while the communication energy is 12.8 pJ/3.3 pJ per bit (Tx/Rx) over a distance of 7.5 m.