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We present a novel concept of quasi-distributed flexible optical fiber extensometers fully compensated from thermal variations. Developed for structural health monitoring applications, the sensors are composed of a combination of intrinsic Fabry-Perot cavities as long-base extensometers, and point-like Bragg gratings inserted along the same fiber used as temperature sensors. This configuration enables a high degree of multiplexing, thus quasi-distributed sensing, and very efficient temperature compensation. Both types of sensors are read by a fiber-optic low-coherence interferometer, used in an original way to measure simultaneously the length variations of the cavities and the wavelength shifts of the Bragg gratings. Finally, we present the experimental validation of the whole measurement system, suitable for concrete structures instrumentation, as it includes an original optical fiber sheath packaging the optical fiber as a flexible sensor.