Partially self-centering structures are promising seismic resilient structural systems by reducing residual inter-story drifts with low initial construction costs. Comprehensive studies focused on structural design and performance evaluation, but no research was conducted to investigate the design of nonstructural components in partially self-centering structures. This research focuses on developing the probabilistic spectral acceleration demands for the nonstructural design in partial self-centering structures. 320 near-fault recorded ground motions were adopted for considering the uncertainties of seismic excitations. The spectral accelerations of the light nonstructural component were obtained through comprehensive dynamic analyses. The logarithmic normal distribution can be used for describing the probabilistic distribution of floor spectra for partially self-centering structures under earthquakes, validating through the Anderson-Darling test. The influences of design parameters (including structural period, hysteretic parameters, structural damping, the ratio of the structural period to the nonstructural period, and nonstructural damping) on the probabilistic distribution of floor spectra were investigated through parametric dynamic analysis results. Artificial neural network (ANN) models were developed for predicting the probabilistic floor spectra for partially self-centering structures. The analysis results indicate that ANN models can achieve excellent accuracy with a coefficient of determination larger than 0.99. Comparative analysis results reveal that the ASCE method may underestimate the acceleration demand of light secondary systems supported by partially self-centering structures. The developed ANN models were interpreted using the shapely additive explanations. It has been found that the fundamental periods of the main structure and nonstructural components and the response modification factor show significant effects on the median and deviation of the probabilistic floor spectra for partially self-centering structures. The software FloorSpecPS was established to predict the probabilistic floor spectra for partially self-centering structures using the developed ANN models in practical application.