In existing research, the correlation between the resilience performance of the self-centering post-tensioned (SCPT) steel beam-column connections and the inelastic response of the required energy dissipation (ED) system was not addressed. For this purpose, a compact circular hollow steel tube (CHST) is proposed as a replaceable ED system. In the light of existing experimental results, a detailed three-dimensional finite element modeling (3D-FEM) was carried out to identify the response of the compact CHST under half cyclic loading. A lot of numerical work is concluded with the extraction of design charts to determine the axial strain (ΔL/L) of the ED system prior to encountering post-yield buckling. Therefore, in the numerically validated reference SCPT connection, several ED systems predesigned according to the design charts emphasized the capability of design charts to predict and control the resilient response of the connections. The optimum selection of proper inherent depth to thickness (D/t) ratio and length to depth (L/D) ratio of the CHST-ED system can increase the resilience of modern self-centering steel structures.