Buckling of thin-walled web plates of steel girders can be delayed using bonded glass fiber reinforced plastic (GFRP) stiffeners using the strengthening-by-stiffening (SBS) strengthening technique. The stress state between the bonded adherents (steel web and GFRP stiffener) is complex, varies greatly pre-and post-buckling, and causes adhesion-and/or cohesion-dominant failure modes. Full-scale experiments of SBS-strengthened steel beams showed a need to investigate the fracture mode of the adhesive layer. A finite element model of the full-scale beams was built to study the adhesive layer using sub-modeling techniques considering different steel plate thicknesses, epoxy types, and initial crack to determine the phase angle shift during web buckling. It was observed that the SBS failure is controlled by a mixed mode that starts initially with a phase angle of 29 degrees; i.e., Mode II is the dominant failure mode during the linear phase. Thereafter, Mode I with a 59 degrees phase angle became prevalent during the nonlinear phase of the behavior implying that the buckling-driven failure of web plate changes the phase angle.