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This study investigates the structural performance of a novel modular sleeve connection equipped with a wedge locking mechanism, developed to enhance the reusability of steel structures within a circular construction framework. Nonlinear finite element analyses were carried out in Abaqus to examine the baseline configuration, where the beam and column are joined through a prefabricated welded sleeve–wedge assembly. Two variants were evaluated: a reference model without stiffeners and a modified model reinforced with transverse stiffener plates. The results show that stress concentrations in the unstiffened model are primarily located at the sleeve corners, leading to localized yielding under increasing loads. The inclusion of stiffeners helps redistribute stresses and delays plastic strain development, though yielding remains confined within the joint. Practical considerations highlight limitations of the welded one-piece assembly, particularly with respect to fabrication tolerances and on-site adjustability. Despite these drawbacks, the findings demonstrate the potential of wedge-based sleeve connections for demountable steel structures and establish a foundation for further developments involving bolted, more modular configurations.