AbstractThe determination of the long-term extreme distribution for a wave-loaded structure requires computing the second-order statistics of the responses and their time derivatives under various short-term sea states. In a spectral context, these statistics are typically obtained on a modal basis by integrating the power spectral densities of the corresponding responses over frequency. In this paper, a semianalytical approximation is developed for computing these integrals with the aim to reduce the computational cost of each short-term analysis. To do so, a state-space formulation is considered for the equations of motion, and the general framework provided by the multiple timescale spectral analysis is implemented. It hinges on the existence of distinct peaks in the integrands to express the variances and the covariances of the modal state responses as the sum of two components with simple expressions: the resonant and the loading component. New techniques are investigated to formulate them. For the former, the structural kernel is expanded in partial fractions while it is fitted by a monomial of a given degree for the latter. The resulting decomposition is validated on a minimalistic example first and is then verified on a simplified model inspired by the Bergsøysund Bridge, which is an actual floating pontoon bridge located in Norway.