A physics-constrained probabilistic framework for predicting biaxial eccentric capacity of L-shaped composite column

This study develops a physics-constrained probabilistic model to predict the biaxial eccentric compression capacity of multi-limb assembled cold-formed thin-walled steel–concrete L -shaped composite columns (MCTSC-LCC). A dataset containing key design parameters was established based on validated finite element analyses, and a physics-constrained loss function was proposed to train the Physics-Constrained Neural Network (PCNN). Among multiple models, PCNN7 achieved the best accuracy, with an RMSE of 2.28 kN.m and R² of 0.999. SHAP analysis showed that eccentric distance is the dominant factor affecting capacity. To address material and geometric uncertainties, a probabilistic prediction framework based on Latin Hypercube Sampling was established, capturing the distribution characteristics of the capacity. Sobol sensitivity analysis revealed that uncertainties in the steel ratio exert the greatest influence on prediction outcomes, highlighting the need for its precise control in engineering design.