Abstract: Objective To address the stress concentration induced by web openings in deck transverse beams of roll-on/roll-off (Ro-Ro) ships, an interpretable and computationally efficient method is proposed for predicting the circumferential stress distribution around openings. Methods The circumferential stress is formulated as a periodic function on the circular domain and compactly represented by a truncated Fourier series with fixed-dimensional spectral coefficients. The theoretical spectrum derived from Vierendeel mechanism theory is adopted as a mechanical baseline. A spectral-domain residual learning network is constructed to perform data-driven corrections to the theoretical spectrum, and a harmonic confidence weighting scheme is introduced to emphasize dominant low-order modes while suppressing high-order noise. Results On the test set, the model achieves a peak stress RMSE of 31.121 MPa, a relative mean curve error of 0.133, and a median peak-angle error of 2°. Compared with pointwise-supervised curve regression models, the proposed approach reduces the curve error by 63.96%, the peak-angle error by 84.62%, and the peak-value error by 9.22%. Relative to frequency-domain supervised models, the curve error is reduced by 48.45% and the peak-angle error by 84.62%. Conclusions Spectral-domain encoding combined with theory-based residual learning enables stable characterization of circumferential stress patterns and peak stress angles, providing an interpretable and rapid assessment tool for early-stage decisions on opening layout and reinforcement extent.