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• CFD predicts pure hydrodynamic loads on truncated cylinders. • A phase-decomposition method was developed for a shallow-draught cylinder. • Cylinder draught strongly scales linear loads; smaller effect on nonlinear loads. • New finding: 2nd-harmonic force, unlike other harmonics, increases at shallower draughts. • Pitch angle chiefly affects impact and secondary load cycle events. Under severe ocean-wave conditions, nonlinear hydrodynamic forces on marine structures are critical for analysis and design. While such nonlinear loads on fixed monopile-type offshore wind turbine foundations have been widely investigated, the corresponding behaviour for truncated cylinders-potential floating offshore wind turbine platforms-remains insufficiently understood. In this work, a Computational Fluid Dynamics (CFD) model is employed to simulate a nominally rigid cylinder to provide the pure hydrodynamic load. The loads on the truncated cylinder are analysed within a Stokes-type perturbation expansion. A phase-decomposition method is then applied to cleanly separate the individual linear and nonlinear (higher-harmonic) force components so that they can be analysed independently. The effects of cylinder draught and static pitch angle are investigated. The draught is found to have a stronger influence on the linear force than on most higher harmonics; notably, the second-harmonic component increases for shallower draughts in certain wave regimes, a behaviour not previously reported. In contrast, pitch angle primarily affects the higher-order components linked to wave impact and secondary load cycle events. These results demonstrate the influence of geometry and orientation on nonlinear wave loading experienced by truncated cylinders and provide guidance for the design and assessment of floating offshore wind platforms.