Vertical earthquake vulnerability of long-span spherical lattice shells with low rise-span ratios

Abstract This paper presents an approach for quickly predicting vulnerable areas of long-span spherical lattice shells under vertical earthquakes using the equivalent continuum analogy. According to the moment theory from classical shell mechanics, the equations for locating the position of maximum nodal displacement are deduced in the elastic range, while considering the heterogeneity in equivalent stiffness. Based on the plastic limit analysis theory, a defined relative stiffness index is proposed by integrating the curvature variation over the corresponding node-bearing area to predict the position of maximum nodal displacement in the plastic range. Several spherical single-layer lattice shells are analyzed using the finite element method to verify the proposed method, and the relative stiffness index, which could be used as an indicator to validate and adjust structural design configurations. As a large-span shell is expected to perform better when each ring has a similar equivalent stiffness index, thereby avoiding abrupt changes in stiffness. The case study indicates that the vulnerable area in such a long-span single-layer lattice shell can be predicted and controlled based on the relative stiffness index values. Additionally, the desired seismic damage-endurance capacity can be obtained by adjusting the relative stiffness index of each ring to ensure that the structure is sufficiently resilient. The method for predicting displacement-based vulnerable areas using the equivalent continuum analogy provides a practical tool for a quick assessment of preliminary design schemes of new lattice shells and can be also applicable to existing and ready-for-retrofit lattice shells.