## 6 Conclusions  
This paper presents a new displacement-dependent damper, referred to as the Stainless-Steel Tube-in-Tube Damper (SS-TTD), for the passive control of structures subjected to seismic loadings. The SS-TTD consists of two tubes (inner and outer tubes) arranged in a telescopic configuration that can be installed in a frame structure as a conventional brace. The source of energy dissipation is the plastic deformation of stainless-steel strips achieved by opening slits in the walls of the outer tube. Stainless steel is used because its inherent energy dissipation capacity is larger than low-yield or mild steel, and is more durable against corrosion, thus reducing maintenance costs. The height-to-width ratio of the steel strips is made as large as possible?within the dimensional requirements imposed by architectural constraints?to guarantee a flexural-type yielding mode and to enhance the energy dissipation capacity. Three SS-TTDs were built and tested under dynamic and static cyclic loads. In the dynamic tests, the new dampers were installed in a RC waffle-flat plate structure and subjected to several ground motion simulations on a shaking table. In the static tests, the dampers were subjected to cycles of constant amplitude until failure. From the tests the following conclusions can be drawn:  
* The new damper exhibits a stable hysteretic behaviour until failure, with minor reduction of the peak strength under repeated cycles of constant amplitude. * For realistic values of the maximum ductility demand (3-9), the force-displacement curves are exempt from geometric nonlinearity effects that cause spurious increases of the restoring force; such geometric nonlinearities start at a displacement ductility larger than about 12. * The force-displacement curve of the SS-TTD was split into the so-called skeleton part and the Bauschinger part, and the ultimate energy dissipation capacity of SS-TTD in each part was quantitatively evaluated; furthermore, a procedure to predict the failure of the damper based on this decomposition is proposed. * The ultimate energy dissipation capacity of the SS-TTD, expressed in terms of the amount of energy that can be dissipated consuming only the Bauschinger part, is 3- and 16-fold higher than that of slit-type plates made of mild steel and high-strength steel, respectively. Further, the cumulative ductility of the SS-TTD exceeds by more than four times the values reported in the literature for similar slit-type steel plate dampers. * Two numerical models are proposed to characterise the hysteretic behaviour of the SS-TTD: a polygonal model based on the decomposition into the skeleton and Bauschinger parts of the force-displacement curves, and a smooth model that uses the Bouc-Wen formulation. Although both models adequately reproduce the response obtained experimentally, the former predicts the energy dissipation path and failure of the damper better, while the latter reproduces the shape of the hysteretic loops more accurately. Figure 24: Comparison between test and numerical model simulations: (**a**) SS-TTD4 normalized \(Q\)-\(\delta\) curves, (**b**) SS-TTD4 energy dissipation paths, (**c**) SS-TTD5 normalized \(Q\)-\(\delta\) curves, (**d**) SS-TTD5 energy dissipation paths, (**e**) SS-TTD6 normalized \(Q\)-\(\delta\) curves, (**f**) SS-TTD6 energy dissipation paths. **Author Contributions:** [PERSON] conceived the damper and experimental campaigns as principal investigator of the grant funding the project; [PERSON] performed the static tests, participated in the shaking table tests, and processed the experimental results; [PERSON], [PERSON] and [PERSON] analysed the experimental results and obtained the conclusions; all authors contributed to writing the paper. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Spanish Ministry of Economy and Competitivity, grant number MEC BIA2017 88814 R, and received funds from the European Union (Fonds Europeen de Development Regional).