In this study, it is shown that under very weak dynamic and quasi-static deformation that is orders of magnitude below the yield deformation of the equivalent stress-strain curve (around 10(-3)), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10(-7) and 10(-4). These observations support the concept of universal behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.