The design and effectiveness of fatigue load-dominated multi-membered tubular structures, such as offshore jackets, largely hinges on the fatigue performance of welded regions due to stress concentrations, necessitating the use of thick steel members. To address these challenges and reduce overall steel consumption, an innovative bonded joining technology known as wrapped composite joints demonstrating superior fatigue performance has been identified as a potential solution. Offshore conditions introduce combinations of different loading directions, resulting in complex stress states at the root of the composite wrap. This necessitates understanding the influence of such multi-axial loads on the static fracture resistance of the steel-composite wrapped joints. In this regard, interaction criterion exponents play a key role in understanding the correlation between different loading conditions. Ongoing research on wrapped composite joints focuses on these exponents, highlighting that delamination near the steel-composite interface stems as the main failure mechanism. In this context, this paper will develop a finite element (FE) model of X-shaped wrapped joint imposing fracture to the composite material and will study the superposition principle that exists between combined axial and bending loads. Combinations of load cases will be simulated to derive the interaction criterion exponents defining the failure envelope of such steel-composite wrapped joint. Modification to the current design recommendation is proposed with alternative an criterion with a good fit that aids in the design.