> For the complete documentation index, see [llms.txt](https://docs.openbrim.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.openbrim.org/templates/openbrimfea/result-combinations-fea/equivalent-stiffness-fea.md). # Equivalent Stiffness \[FEA] An Equivalent Stiffness point condenses the stiffness of a whole region of the model into a single 6×6 stiffness matrix, expressed at the centroid of a chosen set of nodes. It answers the question "if I replaced everything attached here with one equivalent spring, what would its stiffness be?" Typical uses are handing a foundation or substructure stiffness to a separate superstructure model, providing a soil-structure interaction stiffness to another engineer or another package, checking the stiffness a bearing or an expansion joint actually sees, and reducing a detailed local model to a boundary condition for a coarser global one. This is a **reporting** object. It computes and stores a result during analysis; it adds nothing to the stiffness matrix, no mass, and no load, and it does not change any other result in the model. ## Data **Nodes:** The set of nodes defining the point. Supplied as a comma-separated list of node names. The equivalent stiffness is computed at the **centroid** of the listed nodes, and the resulting 6×6 matrix relates forces and moments at that centroid to translations and rotations there. The choice of nodes therefore determines both *where* the stiffness is reported and *which* part of the structure is being condensed. *Engineering influence.* Listing a single node gives the stiffness the structure presents at that joint. Listing the full set of nodes across an interface — every node on a pier-to-deck connection, say — gives the stiffness of that interface as a whole, with the nodes treated as one point at their centroid. Because the centroid is a plain geometric average of the listed node positions, adding or removing nodes moves the reference location and changes the reported matrix: the coupling terms between translation and rotation are measured about that point, so a centroid that is not where the receiving model expects its boundary produces a matrix that is correct but not usable as-is. A list that names a node that does not exist, or is empty, yields no result rather than an error. The matrix is computed per analysis case, so results are reported against the case that was run. Related parameters to consider together: the boundary conditions of the region being condensed — a region that is fully restrained elsewhere will report a very high stiffness, and one that is under-restrained may report a near-singular matrix with very small or zero diagonal terms in the unrestrained directions. The condensation reflects the model as built, including any restraints, springs and constraints acting on it. Results sensitive to this parameter: only the reported stiffness and flexibility matrices. Nothing in the parent analysis changes. ## Verification * Check the diagonal terms of the reported matrix for physical plausibility: they should be positive, and their relative magnitudes should reflect the structure — a slender pier is much softer laterally than vertically. * Apply a unit load at the same location in the full model and compare the resulting displacement against the corresponding flexibility term. This is the most direct check and should match closely. * Confirm the reported reference location is where you expect. If it is not, the node list is including or excluding nodes you did not intend. * Check symmetry: the matrix should be symmetric to solver precision for a linear elastic model. A markedly non-symmetric result indicates a nonlinearity or a modelling problem in the condensed region. * Substitute the matrix into the receiving model as a spring and confirm that model's displacements at the interface reproduce the detailed model's. * Hand-check a simple case: for a single cantilever pier, the lateral term should be close to `3EI/L³`. ## Common mistakes * **Expecting it to change the analysis.** It is a reporting device; adding one does not stiffen or soften anything. * **Naming an inconsistent node set**, so the centroid falls somewhere physically meaningless — for example mixing nodes from both ends of a pier and reporting a stiffness at its mid-height. * **Transferring the matrix to another model without accounting for the reference location**, losing the translation–rotation coupling and typically under-predicting the receiving model's rotations. * **Condensing a region that is under-restrained**, giving near-zero stiffness in the free directions and, if used as a boundary condition, a receiving model that is unstable. * **Reading the matrix from the wrong analysis case**, particularly in a staged model where the stiffness of the region changes stage by stage. * **Assuming the matrix is valid for a nonlinear structure.** It is a linearized stiffness about the analysed state, and it does not carry gapping, yielding or contact behaviour with it. --- # Agent Instructions This documentation is published with GitBook. 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