As the key part of the force-transfer path in a steel frame, a reasonable modeling method of beam-to-column connections in the structural analysis model is crucial. From the designer’s perspective, a rational and accurate classification of beam-to-column connections is an invaluable basis for improving modeling efficiency and design accuracy. Although some investigations led by Eurocode 3 (EC3) have provided a systematic and quantitative approach for classifying beam-to-column connections, it is not sufficiently developed for general steel braced frames. In this paper, based on a modified analytical model of the beam-to-column connection substructure that accounts for the effect of braces, the rotational stiffness demand of the beam-to-column rigid connection is derived from the perspectives of structural lateral stiffness and stability. The quantitative relationship is established between the rotational stiffness demand and the relative stiffness of the braces. The accuracy and reasonability of the proposed analytical model and stiffness demand are verified using finite element models (FEMs) at both the story and structure levels. Particularly, the effect of the non-linear behavior of beam-to-column connections on the structural response under high-intensity earthquakes is further comparatively analyzed in the context of seismic design. The results demonstrate that, a beam-to-column connection can be modeled as a continuous rigid connection in non-linear analysis only if it simultaneously satisfies the following requirements: the rotational stiffness meets the demand proposed in this study, and the bending capacity is designed to be overstrength compared to the beam cross-section.