## 1 Introduction
Crescent shaped braces (CSBs) were recently used for seismic retrofitting as hospital in order to connect the steel moment-resisting frames with two external reinforced-concrete cores [27; 28; 29; 30]. CSBs are characterized by a geometrical configuration which is \"ad hoc\" defined in order to provide the structure with prescribed multiple seismic performances, within the performance based seismic design framework. U-shaped hysteretic dampers included in a damping box located at the middle of a diagonal brace are proposed in [31] to improve the performance of moment-resisting frames. The experimental behavior of a self-centering timber brace that employs the resilient slip friction joint (RSFJ) for energy dissipation is investigated in [32]. Steel frame braced with tension-only pseudo-elastic nickel-titanium (NiTi) shape memory alloy (SMA) wires was developed in [33] for seismic retrofit applications. Specific codes are adopted worldwide to regulate the use of these seismic-resilient devices. AASHTO Guide Specification for Seismic Isolation Design [34] was the first code which established rules for the dimensioning and the use of anti-seismic devices. This document was firstly focused on isolation systems, then recommendations to energy dissipating devices were also extended. Nowadays the regulation of anti-seismic devices has been included in national standards, as example the Italian seismic code NTC 2018 [35], the European Standards EN 15,129 [36] and the American Standards ASCE/SEI 7-10 [37] and guidelines such as the American FEMA 461 [38]. These codes specify the performance requirements of nonlinear displacement dependent device in order to reproduce the actual working conditions of the devices, covering all the stages of the life cycles. In general, in case of metallic dampers the velocity has negligible influence and quasi-static tests can be carried out to establish their performance capability. The test procedure shall include the steps listed in the codes unless otherwise prescribed in the design specifications. Based on the results of two experimental campaigns performed at the structural laboratory of University of Basilicata (Italy), in the present work the attention is focused on cyclic performance of steel flexural NLD dampers installed in V-inverted dissipative bracing systems considered for a steel frame (JetPacs project) [39] and for a post-tensioned timber frame (Pres-Lam project) [24; 40]. Respect to previous papers the novelty of this study is the comparison of the complete seismic sequence of shaking table test results of two different experimental braced frame models including NLDs. The main objective is to assess the reliability of current seismic codes in terms of cyclic testing required for type tests and factory production control tests of NLD. In particular, hysteretic dampers (HD) considered for the steel braced frame (SBF) and U-shaped flexural steel plate (UFP) dampers used for the timber braced frame (TBF) have been analyzed. The capability of both devices to dissipate energy is due to the nonlinear behavior when stressed beyond elastic limit, moving the yielding point along the flexural plates. Quasi-static cyclic tests of both NLDs were performed to characterize the force-displacement behavior of dampers using testing protocols proposed by the American guidelines and European codes. Then, the experimental results of the shaking table tests performed on both specimens are compared in terms of global seismic behavior of the structures and local response of dampers. Almost the same random seismic sequence composed by over 20 consecutive seismic inputs, obtained from the same set of 7 natural earthquakes at various intensities, has been considered for both frame models. In this paper, the experimental results have been investigated in terms of number of cycles to failure of HD and UFP devices, i.e., the number of fatigue cycles at which the rupture of a device happened.