> 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/loads-fea/dynamic-loads-fea/eigenvalue-rsa-cases.md). # Eigenvalue & Rsa Cases An Eigenvalue case computes the structure's natural periods and mode shapes — the free-vibration properties that govern all of its dynamic behaviour. Adding response spectrum curves turns the same case into a **Response Spectrum Analysis (RSA)**, which combines the modal responses against a design spectrum to estimate peak seismic demand without integrating in time. The case reads **mass** from the model (self-weight plus Nodal Mass objects assigned to it) and **stiffness** from the current model state. It generates no load of its own; RSA produces a set of peak responses rather than a single equilibrium solution. {% hint style="warning" %} **RSA results are peak magnitudes, not a snapshot.** They are combined statistically across modes, so the reported values do not occur simultaneously and are not in equilibrium: reactions will not sum to any applied load, and signs are conventionally positive. Do not expect a check that works for a static case to work here. {% endhint %} ## Modal Parameters **Analysis Type:** Selects what the case computes — a normal modal extraction or a buckling analysis. *Engineering influence.* Modal extraction solves the free-vibration eigenproblem for periods and mode shapes. Buckling instead solves for the load factor at which the structure becomes unstable under the applied load pattern, and requires the Applied Load and Buckling Load Factor fields below. The two share the machinery but answer completely different questions. **# of Mode Shapes:** The number of modes to extract. *Engineering influence.* Too few modes truncates the response and **understates** demand, most noticeably in the stiff directions and near supports where high-frequency modes contribute. The standard acceptance criterion is that the retained modes capture at least about **90% of the participating mass** in each direction of interest — check the participating mass ratios rather than picking a number. Increasing the count costs solution time and never makes the answer worse. A value of 0 extracts nothing and the case cannot solve. **Gravity:** The gravitational constant in the model's length units per second squared, used to convert **weights** into masses. *Engineering influence.* This scales the entire mass matrix, so an incorrect value shifts every period by `√` of the error and invalidates the whole analysis. Leaving it blank or zero is safe — it falls back to standard gravity in the project's length unit — but an explicitly wrong value (32.2 in an inch model, where 386.09 is expected) rescales everything by a factor of twelve with no warning. **Type of Modes:** The extraction method — Eigen, or one of the Ritz variants (WYD, LWYD, QSRV). *Engineering influence.* **Eigen** vectors are the true natural modes and are what you want when the physical periods matter. **Ritz** vectors are load-dependent: they are generated from a specific load pattern and concentrate on the modes that pattern actually excites, so for the same number of vectors they typically capture far more participating mass than eigen modes do. For seismic work Ritz vectors usually give better results for fewer vectors; for reporting natural frequencies, use Eigen. Ritz methods require the **Applied Load** below to define the pattern. **Applied Load (Ritz / Buckling):** The load case that supplies the pattern for Ritz vector generation, or the load pattern whose buckling factor is sought. *Engineering influence.* For Ritz, the vectors are tuned to this pattern, so it should represent the loading the analysis is about — a poor choice produces vectors that miss the response of interest. For buckling, this defines the load whose multiplier the analysis reports; the buckling factor is meaningless without knowing which load it multiplies. **Pre-stress Load (Stress-Stiffened Modal):** A load case whose axial forces are used to build a geometric stiffness that modifies the modal solution. *Engineering influence.* Axial force changes a member's effective bending stiffness: tension stiffens, compression softens. Including a prestress or dead-load case here produces **stress-stiffened** modal results, which matter for cables and stays (whose stiffness comes almost entirely from tension) and for slender compression members (whose periods lengthen under load). Leaving it empty analyses the unstressed structure, which for a cable-stayed bridge gives periods that are far too long. **Pre-stress Load Factor:** A multiplier on the prestress load used for stress stiffening. Scales how much geometric stiffening is included; 1 uses the case as-is. **Centering Frequency (Ritz QSRV Method):** The frequency the QSRV Ritz method centres its vector generation around. Only meaningful for that method; set it near the frequency range that dominates the response of interest. **Buckling Load Factor:** Reports the computed factor by which the Applied Load must be multiplied to cause buckling. *Engineering influence.* This is **output**. A factor below 1 means the structure buckles under less than the applied load; a large factor means buckling is not critical. Interpretation depends entirely on which load case was applied — the same structure has different factors for different patterns. Linear buckling overestimates capacity for real, imperfect structures, so the factor is an upper bound. ## RSA Curves **Curve in Dir. 1 / 2 / 3:** The response spectrum applied in each of the three directions. **Scale in Dir. 1 / 2 / 3:** A multiplier on each curve. *Engineering influence.* A case with **no curves assigned is a pure modal analysis** — it reports periods and mode shapes and no seismic demand. Assigning curves turns on the RSA combination. The scales apply code-required factors — importance factors, response modification, or the reduced factor commonly applied to the vertical component. Response scales linearly with them. Directions 1 and 2 are usually the two horizontal directions with the same spectrum, and direction 3 the vertical with a reduced one. {% hint style="danger" %} An RSA case whose curve contains **no points** produces spectral accelerations of zero and therefore **zero displacements and forces** — with no error. A result of exactly zero from an RSA case is almost always an empty curve, not a structure that does not respond. {% endhint %} **Dir. Angle:** The angle between the spectrum's direction 1 and the global X axis. *Engineering influence.* Rotates the excitation directions, which is how a skewed bridge is analysed along and across its bearing lines rather than along the global axes. For a skewed or curved structure the response varies with this angle, and codes commonly require several angles to be checked because the governing direction is not obvious. ## RSA Combination **Damping Ratio:** The modal damping assumed when combining. *Engineering influence.* Damping is embedded in the spectrum itself, and this value governs the **correlation** between modes in the CQC combination: higher damping increases correlation between closely-spaced modes and generally increases the combined result. The default 0.05 (5%) matches the damping most design spectra are published for. Using a value inconsistent with the spectrum's basis double-counts or omits damping. **Modal Comb. Method:** How responses from different modes are combined — CQC, SRSS, ABS, or the ten-percent rule. *Engineering influence.* **SRSS** (square root of sum of squares) assumes modes are independent and under-predicts when periods are closely spaced. **CQC** (complete quadratic combination) accounts for cross-correlation between close modes and is the general-purpose choice; it reduces to SRSS when modes are well separated. **ABS** (absolute sum) assumes all modes peak together — very conservative and rarely required. Structures with closely-spaced modes, which includes most skewed and curved bridges, are exactly where the choice matters. **Spatial Comb. Method:** How the three directional results are combined — typically ABS, SRSS or CQC3. *Engineering influence.* This implements the directional-combination rule the code requires (the familiar 100%/30% style rules, or SRSS). **CQC3** additionally searches over the angle of incidence to find the critical orientation, which is valuable for skewed structures where the governing direction is not aligned with the model axes. ABS is the most conservative. **γ – (CQC3):** The ratio between the two horizontal spectra used by the CQC3 method. Only meaningful when CQC3 is selected. ## Mass Source **Self Mass Factor:** A multiplier on the mass derived from the structure's own self-weight. *Engineering influence.* Codes commonly require a portion of live load to be included in seismic mass, or a factor applied to superimposed dead load. A factor of 1 uses the structural self-weight as-is; 0 removes it entirely, leaving only Nodal Mass contributions — which produces a nearly massless model with implausibly short periods. **Mass Case 1–5:** Load cases whose applied vertical load is converted into additional mass for this analysis. **Mass Case 1–5 Factor:** The multiplier applied to each of those cases when converting its load to mass. *Engineering influence, both.* Self-weight alone is rarely the whole seismic mass. Superimposed dead load, ballast, equipment applied as surface load, and the code-required fraction of live load are all applied as *loads* rather than modelled as structure, and this is how they contribute inertia — the same case can act as a gravity load in the static analysis and as mass here, without being modelled twice. The factor is where the code's fraction is expressed: a live-load case included at 0.2 contributes a fifth of its load as mass. A factor of 0 contributes nothing, so a Mass Case named but left at zero factor is a silent omission. Leaving all five empty means the mass is self-weight plus Nodal Mass only, which for most bridges **understates** the seismic mass. Adding mass lengthens periods, and because spectral ordinates fall with period beyond the plateau, the effect on force demand can go either way — it is not conservative in one direction. Take care not to double-count load that is already carried by modelled elements with density. **# of Nodal Mass:** Reports how many Nodal Mass objects this case actually picked up. **Output, not input.** *Engineering influence.* This is the verification field for nodal mass. A count lower than expected almost always means a Nodal Mass row has no Analysis Case assigned, since a case only collects masses that point at it. ## Settings **Structure Group:** The part of the structure active for this case. Leave empty for the whole model. **Is Active:** Whether the case is solved. Inactive cases are skipped silently. ## Verification * Check the periods against expectation or a hand estimate before trusting anything downstream. A fundamental period that is wildly off means mass or stiffness is wrong, and every RSA result inherits that error. * Check **modal participating mass ratios** reach about 90% in each direction; if not, increase the mode count. * Animate the mode shapes and confirm they are physically sensible — a first mode that is a local vibration of one member rather than global movement usually means a missing connection. * Confirm **# of Nodal Mass** matches the number of mass objects you created. * Confirm total model mass against a hand take-off. * For RSA, verify the spectrum curve actually contains points and plot it. * Compare CQC against SRSS; a large difference indicates closely-spaced modes and confirms CQC is the right choice. * For a stress-stiffened case, compare periods with and without the prestress load; cables should stiffen markedly. ## Common mistakes * **An empty response spectrum curve**, producing exactly zero displacements and forces with no error. * **Too few modes**, understating demand — especially near supports. * **Wrong Gravity value**, rescaling the entire mass matrix and every period. * **Nodal Mass objects with no Analysis Case assigned**, so they are silently excluded. Check the count. * **Expecting RSA results to be in equilibrium.** They are statistically combined peaks; reactions will not sum to an applied load. * **Using SRSS on a structure with closely-spaced modes**, under-predicting the combination. * **Omitting the prestress load for a cable-stayed structure**, giving periods far too long. * **Self Mass Factor at zero**, leaving a nearly massless model. * **No Mass Cases named**, omitting superimposed dead load from the seismic mass entirely — or naming one and leaving its factor at zero, which contributes nothing. * **Checking only the global axis directions** on a skewed bridge, missing the governing angle. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. 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