Optical fiber sensors are ideal for monitoring continuous deterioration conditions of civil infrastructure, especially of long-span bridges. Typically, a network of sensors is used to measure the strains or low frequency vibrational response of the structure. In this work, we demonstrate dynamic spectral demodulation of fiber Bragg grating (FBG) sensor responses with a stabilized Michelson interferometer for monitoring mechanical strains in a model of long-span bridge. A series of experiments has been performed, including the measurements of the natural resonant modes of the model bridge, impact response of a bridge member and acoustic emissions in a fractured aluminum bar. The experimental results not only reveal that dynamic spectral demodulation of FBG strain responses at frequencies extending up to about 3.5 MHz is possible, but also suggest that the method may be suitable for monitoring high frequency mechanical strains in civil structures that result from cracking or impact loading, thus providing a tool for local detection of structural damage.