Effects of supporting-substructure lateral stiffness on the internal forces of grid structures

The substructure, which supports the grid structure, significantly affects the overall stability and safety of the system by contributing lateral stiffness. This paper evaluates the safety performance of a failed grid structure and identifies a design flaw in which fixed displacement supports were improperly applied as boundary conditions. This misapplication resulted in a substantial deviation between the calculated internal forces and the actual forces observed in the structure, leading to an underestimation of the compression levels in the top chord members. A parametric analysis was performed to assess the influence of varying boundary conditions on the internal forces within the grid structure. The analysis reveals that the internal forces change logarithmically with variations in the lateral stiffness of the supports and show an approximately linear positive correlation with the span of the structure. The maximum stress in the structure decreases initially and then increases as the lateral stiffness of the supports increases. Increasing the lateral stiffness of the supports generally reduces the maximum stress in the structure; however, an optimal stiffness value may exist where the maximum stress is minimized. In cases of asymmetrical lateral stiffness, the maximum stress is primarily influenced by the section of the structure with the lowest stiffness. Thermal stresses are concentrated in regions around the supports with the higher constraint and display a clear logarithmic relationship with changes in lateral stiffness.