A fracture mechanics based failure prediction strategy for load-carrying composite structures was proposed. This strategy relies on the knowledge of failure modes and local structural details to predict failure based on coupon level test data. The methodology presented here effectively predicted structural failure of a composite hat stringer based on fracture toughness test data. In addition, ply waviness was identified as a critical factor influencing the delamination failure load. The finite element modeling (FEM) technique was used to model the skin-flange region, which included ply waviness effect. The finite element analysis results were used to calculate total strain energy release rate and its Mode I and Mode II components. The finite element analysis predicted unstable delamination growth for positive waviness angles and stable delamination growth for negative waviness angles. The same trends for the relationship between ply waviness angle and the critical load for delamination initiation were observed in the pull-off specimens previously tested. When the test data and the analytical predictions are normalized by their respective no ply waviness one's, the predictions captured the trend of the test results.