## 5 Dynamic Response of Braced Models
### Shaking Table Testing Results  
The seismic response of braced frames and the local response of NLD obtained from shaking table tests of both case studies are described in this section. Global and local responses of both braced frames were recorded by more than 50 sensors, including load cells, horizontal and vertical accelerometers, and displacement transducers connecting the frame to an external reference structure to record the global seismic behavior and displacement potentiometers for recording the force-displacement behavior of the energy dissipating devices at each story [14; 40]. The time-histories of global drift of the SBF and TBF models are shown in Figure 9. Figure 10 shows the time-histories of demand ductility up to the devices breakage occurred during the test with earthquake input 187 at 100% of PGA level at the second story for HD and at the first story for UFPs. In case of SBF model an interlock limit was activated and the test was stopped for safety reasons. Both braced frames exhibited a complete re-centering capability, with negligible residual inter-story drift and displacements of dampers accumulated during the tests. Up to 50% or 75% of PGA level the global drift reached the design drift, for most severe earthquakes, of both experimental models (0.5% for the SBF model and 1.25% for the TBF model) and the ductility of NLDs slightly exceeds the design values (\(\mu=5\) for the HD devices and \(\mu=4\) for the UFP devices). Figure 11 shows the global response of SBF and TBF models in terms of the time history of the main seismic key indicators (base shear, top displacement, top acceleration, and inter-story drift) for the seismic input 196 at 100% of PGA level. The experimental results show that the base shear recorded by the dynamic actuator of the shaking table and the top acceleration of both the experimental models are of the same order, differences are related to different total mass values of the experimental models. On the contrary, the top displacements and first story drifts are not comparable due to the higher stiffness of the SBF model. The base shear versus top displacement responses highlighted the hysteretic behavior of the SBF model (Figure 10(a)) and the typical flag-shaped behavior of the post-tensioned TBF model, as emphasized in Figure 10(b) from two cycles at highest displacement. Figure 9: Time history of global drifts of **(a)** SBF model and **(b)** TBF model. Force-displacement cycles of HD and UFP dampers placed at each story of the bracing systems of the SBF and the TBF models obtained from shaking table testing for the seismic input 196 at 100% of PGA are compared in Figure 12. The force-displacement curved have been normalized based on the yielding force and displacements obtained by the experimental characterization tests (yield points are indicated in Figure 12). In both cases the NLD dampers showed excellent hysteretic response without significant degradation in strength and stiffness. The force-displacement behavior of HDs and UFPs reflected the behavior of the bare frames with similar of strength due to similar values of story masses (see Table 1) and different values of stiffness (see Figure 4), with HDs stiffness higher than that of UFPs. The displacement time history and the force-displacement behavior of devices of the last test of the seismic sequence (187 at 100% of PGA), during which the failure condition for fatigue was reached by both HDs and UFP, are shown in Figure 13. The use of dissipative bracing system has permitted to achieve a resilient seismic performance of both experimental models without observing structural damages or post-tensioning losses under the seismic sequence composed by more than 20 earthquakes. As shown by photos of Figure 13, the rupture occurred through fracture of the yielding section at ductility values higher than the design ones.