<p>To strengthen reinforced concrete structures against seismic events, design methods are being established to fit the interiors of existing structures with steel braces or shear walls and to retrofit existing structures with steel braces on the exterior of existing frames for seismic protection. For example, indirect connections that use post-installed anchors are frequently employed in steel-braced frames for seismic retrofits, and many post-installed anchors are required for each existing structure. The connection between the existing structures and reinforcement elements in the seismic retrofitting of concrete construction must be effective in distributing stress. If the strength of the connection is not adequate and if the details are not properly designed, the structure as a whole is not likely to display effective seismic performance. Therefore, we proposed a new method that uses shear connecters with a steel shear key in a frustoconical shape and post-installed anchors for connecting existing concrete to extended concrete. We call this shear connecter the “funnel-shaped post-installed anchor.” In a former study, experiments and non-linear finite element method analysis on the strengthening method that used funnel-shaped post-installed anchors reported that funnel-shaped post-installed anchors with a 45-degree shear key improved shear strength compared with keys with other shapes. However, no shear strength formula has been established for this new type of shear connecter.</p><p>In this paper, based on the mechanisms of resistance and failure mode, we propose the shear strength formula for a shear connecter with a steel shear key having frustoconical shape and a post-installed anchor. This formula assumes tensile failure in the post-installed anchor and bearing failure in the concrete around the shear key. To confirm the accuracy of the proposed analysis model and equation, we investigated the failure mode and the shear strength of the shear connecter using structural tests under a cyclic shear force. The outside diameter of the shear key (50 mm or 70 mm), shape of the surface of the shear key (irregular or flat), material of the anchor bar (SS400 or SNB7), anchorage length of the anchor bar in existing concrete (12d_a or 7d_a), and strength of existing concrete (F_c15, F_c24, or F_c33) were used as experimental parameters. The experiments confirm that the effects on shear strength corresponded to the results of the experiment and calculation model.</p><p>Finally, we proposed a method for evaluating shear strength by considering the mechanical behavior of a rotating shear key in experiments. The calculated shear strength was consistent with the experimental values. </p>