This article presents a simple engineering procedure to assess the fracture failure in the welded connection between a concrete-filled square hollow section and an open flange H-section, so as to enhance the ductility of the composite connection. This procedure predicates on an elliptical fracture envelope and a generalized yield model proposed and verified in previous studies. The experimental program compares the performance of a BASE specimen without openings in the flange of the connected H-section and two specimens (denoted as B1 and B2) with openings introduced near the connection. The numerically computed fracture index and yielding index for all specimens agree with the physical failure mechanisms observed in the test. This study demonstrates that openings in the flange of an H-section improve effectively the ductility of the highly stiffened connection between a concrete-filled tube and an open flange steel beam.