Analysis of key elements of truss structures based on the tangent stiffness method

In recent years, the topic of progressive structural collapse has received more attention around the world, and the study of element importance is the key to studying progressive collapse resistance. However, there are many elements in truss structures, making it difficult to predict their importance. The global stiffnessmatrix contains the specific information of the structure and singularity of thematrix can reflect the safety status of the structure, so it is useful to evaluate the key elements based on the global stiffnessmatrix for truss structures. In thispaper, according to the tangent stiffness-basedmethod for the element importance, the square pyramid gridwas chosen as an example, and the distribution rules of key elements under different support conditions, stiffness distributions, and geometric parameterswere studied. Then, three common symmetric grid forms, i.e., diagonal square pyramid grids, biorthogonal lattice grids, and biorthogonal diagonal lattice grids, were selected to investigate their importance indices of elements. The principle in this work can be utilized in progressive collapse analysis and safety assessment for spatial truss structures.