The present work treats the problem of the dynamic behavior of a vertical slender structure subject to combined axial and transverse motions. The solution method is based on a Galerkin-type semi-analytical formulation. The responses to sinusoidal monochromatic excitation are assessed with respect to the significance of each mode and their spectral content. As a result, a reduced, yet nonlinear, lumped model for each one of the significant modes of the structure is generated. The parameters of these fixed-structure models can be determined systematically by two methods relying on the spectral analysis of the numerically calculated modal responses of the structure. The resulting models constitute an explicit input-output relationship between the imposed motions and the modes of the structure, useful for stability analysis, design and control.