The ERIES-ALL4wALL project, “Smart ALLoys for WALLs,” aims to understand and improve the seismic performance of reinforced concrete (RC) building core walls, which are poised to become increasingly vital as the global building stock is expected to double by 2060. This paper presents preliminary results and findings relative to the dynamic testing of two large-scale RC U-shaped core walls, which were tested in the National Laboratory for Civil Engineering (LNEC), in Lisbon. The first unit, UWS1, used conventional steel reinforcement, while the second (UWS2) incorporated largely-debonded iron-based shape memory alloy (FeSMA) rebars. The latter were heated via Joule effect to apply a pre-stress aiming at reducing residual displacements. The units were subjected to alternating uni- and bidirectional ground motions. This paper presents the full time-histories of the wall collar’s relative displacements in both orthogonal directions, along with the corresponding torsional rotations. The article also examines the maximum and at-rest residual displacements, comparing them with those anticipated from quasi-static reverse-cyclic tests. It concludes with a preliminary discussion of unexpected structural behavioral features of UWS2, which are attributed to electrical insulation deficiencies that led to difficulties with the resistive heating system in three of the four wall cross-sectional corners.