Abstract：Traditional methods for analyzing the P-Δ effect in tall structures often struggle to account for time-varying axial forces, potentially underestimating the impact on structural safety. This paper employs the weak form quadrature element method (QEM) to establish Hermite-type quadrature element models for both distributed mass structural systems and systems with concentrated masses. A high-order, precise analytical method for the P-Δ effect in tall structures is developed. The method is applicable to structural systems with abrupt mass changes and can handle time-varying axial forces induced by arbitrary axial loads. High-precision solutions for the P-Δ effect are provided without requiring iterative calculations, accurately revealing the influence patterns of vertical loads and time-varying axial forces on the characteristics of tall structures. Comparative analysis of three different types of cases verifies the feasibility and accuracy of the proposed method. Numerical analysis results demonstrate that this method achieves high-precision P-Δ effect analysis. For both uniformly distributed mass and systems with concentrated masses, using just one quadrature element yields highly accurate dynamic response results. The computational time required is significantly less than that of traditional P-Δ effect analysis methods while maintaining the same level of accuracy.
2025, Vol. 46 
