For structural analysis, we considered one span out of five, since the design principle is the same for all of them. The analysis was performed in the Rhino/Grasshoper environment using the Karamba3D module based on the finite element method (FEM).
In order to see how the structure works under its own weight + uniformly distributed load from the roof covering, we took the values from Shukhov's calculations - 42.3 kg/m2. On the diagram of the internal stresses, one can see the work of the main structural elements: the top chord of large trusses is under tension, the lower - under compression. The hinge in the center of the upper chord eliminates the bending moment. The stresses in the gridshell are uniform, mainly axial, with a slight bending at the intersections. The thrust in the transverse direction is taken up by the steel ties.
In order to simulate the real loading of the structure (more critical for vaulted shells), we assumed the uneven snow load, applied to one-half of the structure - 146.7 kg/m2. Under such loading, the left part of the structure deflects, and the right part of it bulges. The upper and lower chords of the large trusses bend, as is illustrated by the asymmetric compression and tension stresses in the chords. The gridshell still has predominantly axial forces without significant moments.
The wind load was calculated on the basis of modern requirements for the calculation of vaulted structures. The normative value of the wind impact is 38 kg/m2. The wind load was applied to the edge facade arches on both sides, with a coefficient of 0.8 on the windward side and -0.4 on the leeward side.
Based on our calculations, the following conclusions can be made:
a) the shape of the gridshell plays an important role in the performance of the structure - favorable axial stresses arise, contributing to the reduction of the cross-section and thus the weight of the elements.
b) the horizontal thrust from the vaulted is almost completely extinguished by the work of the ties, the vertical forces are transferred to the main trusses, which are also responsible for the stiffness of the structure under loads in the longitudinal direction.