In ship hull design, longitudinal stiffeners may be twisted or knuckled to keep the continuity of strength along the vessel. This occurs at angled discontinuities such as discontinuous connections at the transverse web between two longitudinal stiffeners having different angles, e.g., a side shell longitudinal stiffener in the rounded part of the ship's hull. Although the criteria for selection of "twist", "knuckle", or "angled discontinuity" as it is should be strength criteria, there are no generalized criteria or published systematic studies, and ship hull designers usually depend on experimental rules. In this study we evaluate and compare the stress magnification factors and define the relative ratio between the stresses in the discontinuity and continuity structures by using finite element analysis from a strength-of-materials point of view. Our results show that under lateral load conditions the stress factor is larger in the twist structure than in the angled discontinuity structure, although under axial load conditions the stress factor in the knuckle and angle discontinuity structures is larger than in the twist structure. Additionally, we propose a formula that estimates the factor in the knuckle structure based on the strength-of-materials approach.