An empirical methodology for bend stiffener sizing

A flexible riser hanging from an offshore platform may experience excessive curvatures at the hang-off zone due to the stiffness discontinuity between the riser and its attachment point. To mitigate this issue, a bend stiffener is typically installed to gradually increase the bending stiffness of the riser’s upper section, thereby limiting the curvature. Previous studies have modeled a bend stiffener, often with a conical profile, as a cantilever beam. The structural analysis of this beam results in a second-order nonlinear differential equation with variable coefficients. While an explicit analytical solution for this equation is not available, a numerical solution can be obtained using advanced mathematical algorithms, which can be implemented through commercial or open source software. This paper introduced an empirical procedure for designing a bend stiffener. The riser’s hang-off section, including the bend stiffener, is modeled as a cantilever beam. It is assumed that at a certain distance from the tip of the bend stiffener, the bending moment of the riser approaches zero. At this “zero-moment” point, the axial tension force and rotation angle of the riser can be obtained from global dynamic analyses of the riser. The procedure begins by determining the length of the riser section between the zero-moment point and the tip of the bend stiffener. With this length known, the shear force, tension force, and bending moment at the tip of the bend stiffener can be calculated based on the equilibrium of the riser section. The second part of the procedure involves estimating the dimensions of the bend stiffener, particularly the length and outer diameter of its conical section. To avoid relying on advanced mathematical algorithm, the bend stiffener is simplified as a series of short segments, with each segment modeled as a cantilever beam with a constant cross-section. Starting from the tip of the bend stiffener, the length and outer diameter of each successive segment were estimated iteratively from equilibrium, deformation equations, and material mechanics. The proposed empirical procedure was compared with previous studies and validated using finite element analysis simulations. Results showed that the empirical procedure offered a practical tool for the preliminary design of a bend stiffener.