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The series connected hybrid (SCH) Magnet developed at the NHMFL will provide high field (36 T), high field quality (1 ppm stability and homogeneity) and a moderately large bore (40 mm inside the resistive shim coils) for users interested in medium resolution NMR studies. The SCH comprises a superconducting outsert built with Nb3Sn cable-in-conduit conductor and a resistive insert using Florida-Bitter technology. The insert and outsert magnets are connected electrically in series, which mitigates many of the engineering challenges for such systems, but mechanical design of the structural components linking these remains critical to the performance of the superconducting outsert. We present detailed design and analysis of these components with an assessment of their ability to meet the functional requirements presented by potentially normal, off normal and fault conditions during operation.