The semi-rigid behaviour of beam-to-column connections has an important effect on the performance of steel frame. This paper proposes a multi-spring component (MSC) model for assessing the rotational stiffness of semi-rigid beam-to-column connections. The main benefit of the MSC model is its ability to easily determine the response of semi-rigid beam-to-column connections in frame analysis. The MSC model is first validated through comparisons with 3D finite element method modelling and experimental test results, where good agreements of load rotation responses are generally observed. Then, using the MSC model, the semi-rigid connections in the frame were modelled by using rotational springs, and the ground floor columns were suddenly removed in sequence. The response of the remaining frame to this sudden removal was obtained through numerical simulation. The results of this simulation showed that the effect of the semi-rigid connection is crucial in the load-distribution and the frame deformation, and the influences of the column loss location and column removal time on frame response were discussed. The MSC model is design-effective and hand-calculable, and thus it brings convenience to the robustness assessment of steel frames suffering single column loss with considering semi-rigid connection and catenary action.