For most design and recertification work on tubular structures, it is not practical to determine the joint hot spot stresses experimentally or using detailed finite element analysis. Therefore, parametric equations were developed in the past for various joint geometries to relate stress concentration factors around the joints to basic joint geometrical parameters. Such parametric equations have limited applications to reinforced joints because the nature of reinforcement varies and may be difficult to represent by a generic set of geometric parameters. In this paper, a new method is introduced to include local joint stiffness in the parametric equations represented by a generic characteristic of the joint determined by modal analysis. The parametric equations produced in this paper can be applied to any reinforced T-joint regardless of the nature of reinforcement. This is especially useful in those cases where the exact nature of reinforcement is not known, for example, hidden in the interior or deteriorated through age or fabrication error. The dimensionless joint stiffness parameter can be calculated by a simple modal test and a beam model without needing to know the nature and details of the reinforcement.