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Embedded Column Base (ECB) connections in seismically resistant steel moment frames are commonly designed to be stronger than the connected column, to protect them from inelastic actions. This relies on estimation of demands induced by the column and the strength capacity of the connections themselves. However, recent research indicates that prevalent approaches may be unconservative for both demand and capacity estimation, with the consequence of unintended damage/failure of the connection. Motivated by the above, this research (1) characterizes the seismic demands induced in ECB connections, and (2) evaluates various strength models for these connections, in support of improved design approaches. This is done through a virtual test program that uses validated continuum finite element simulations of interactive column-ECB subassemblies. The results suggest that the current design approaches for ECB connections are unconservative, i.e., they underestimate demands while also overestimating the ECB resistance, with the possibility of unintentional nonlinear behavior within the embedded portion of the ECB connection. This is undesirable, because the ECB connections are not usually detailed to provide plastic deformation capacity. A method is proposed to provide improved estimates of the anticipated flexural demands of non-dissipative ECB connections, along with recommendations regarding the strength models. To accomplish this, the method incorporates local cross-sectional slenderness, gravity-induced axial load demand in conjunction with load combinations imposed by current seismic design standards. The sensitivity to the steel column material grade, the imposed loading history, and axial load demands is studied, and limitations of the approach are outlined.