The Influence of Second-Order Effects on the Critical Load Multiplier and Natural Frequencies of a Low-Rise Steel Dome

This study investigates the influence of loading pattern, analysis level, and nodal connection stiffness on the stability and dynamic behaviour of a low-rise steel dome. Three joint configurations and two loading scenarios, symmetrical and asymmetrical, were analysed. Structural stability was evaluated using linear buckling analysis, second-order analysis, full geometrically nonlinear analysis. Dynamic properties were determined by modal analyses performed with and without the geometric stiffness matrix. The results show that the structural response is governed primarily by the asymmetric distribution of axial forces. For the model with pinned joints, a 68.4% decrease in the critical load multiplier is observed. Modal analysis revealed that asymmetric loading not only reduced the first natural frequency but also fundamentally changed the modal structure. Global vibration modes disappeared, modal mass became distributed over a large number of modes, and the Modal Assurance Criterion remained below 0.11, confirming a qualitative change in the vibration mechanism. In contrast, symmetrical loading caused only minor frequency reductions while largely preserving the mode shapes. The results demonstrate that linear analyses may significantly overestimate the stability and dynamic performance of low-rise steel domes under asymmetric loading. Accurate assessment therefore requires second-order effects, geometric nonlinearity, and geometric stiffness to be considered.