## 2 Dynamic Response of a Multi-Story STMF with SMAs  
### Description  
A benchmark nine-story, five-bay structure with STMFs of open Vierendeel type, studied by [PERSON] and [PERSON] [20], was selected to examine its behavior incorporating STMFs with X-diagonal Ni-Ti SMA bars as dissipation devices in a pin-ended special segment under seismic loading. Standard profiles of the US steel industry were used for the members of the frame, which are given in detail in the publication mentioned above. The structure is 45.70 m in length and 39.90 m in elevation and it consists of five 9.14 m wide bays on each floor. The levels of the structure are numbered concerning the ground level. The 9 th level is the roof and under the ground level, there is a basement. The floor-to-floor height of the basement is 4.30 m, for the 1 st floor is 5.50 m, and for the 2 nd through 8 th floors is 4.30 m. The height of the truss is 1.20 m and the length of the special segment is 2.43 m. Columns are made of 355 MPa steel, placed in strong axis bending. Column bases are pinned and secured to the ground. Concrete foundation walls and the surrounding soil are assumed to restrain the structure at the ground level from horizontal displacement. The original structure was designed according to the performance based design procedure (PBDP), aiming to achieve a predictable and controlled yield mechanism through the formation of plastic hinges at the four corners of the chord members of each special segment. A thorough description of PBDP is given (among others) in the work by [PERSON] et al. [21] and the review article of [PERSON] [22]. Members outside of the special segment need to remain elastic and are designed to resist the gravity loads and the maximum expected vertical shear strength (\(V_{ne}\)), developed at the midpoint of special segments when the frame reaches its target drift and the desirable collapse mechanism, i.e., the formation of plastic hinges. The original structure is modified by placing SMA bars as dissipation devices in pin-ended chord members in the special segment. All members' sections are kept the same as derived from the design of the conventional structure. Both structures, the conventional and the proposed one, are modeled using SeismoStruct 2024 software [23]. Columns of both structures were modeled as elastic elements. Chord and truss members outside of the special segment of the conventional structure were modeled as elastic elements except for the chord members in the special segment, which were modeled as inelastic elements with concentrated inelasticity within a fixed length. On the contrary, chord and truss members outside of the special segment of the proposed structure were modeled as inelastic elements while chord members in the special segment were modeled as elastic elements with moment releases at both ends. Chord members support gravity loads as well. Simple connection details were considered for girder-to-column moment connections. Double channels were used for all truss members. The undeformed shape of the conventional structure without SMAs and without incorporating a pin-ended special segment is depicted in Figure 1.  
Regarding the inelasticity of selected members, the FE procedure adopted was the more recent forced-based (FB) formulation, a brief description of which can be found in the software's user manual. Moreover, the damping ratio used in the analyses was equal to 5%, a value typical for steel structures. The SMA rate-independent constitutive law se_sma2 (of [PERSON] et al. 2013 [24]) embedded in SeismoStruct was used. SMAs were modeled via SeismoStruct as truss elastic elements since they undergo only axial deformation. They were considered to be made of a circular solid section, to have a length of 2.71 m, a Young's modulus of 35 GPa, 300 kPa forward and reverse transformation stress, 373 kPa forward transformation finishing stress, and 150 kPa reverse transformation finishing stress.