# Eigenvalue & Rsa Cases Eigenvalue analysis computes the natural frequencies and mode shapes of the structure. Response Spectrum Analysis (RSA) uses these mode shapes combined with a design response spectrum to estimate the peak dynamic response (forces and displacements) due to earthquake loading. ## Modal Parameters **# of Mode Shapes:** The number of vibration mode shapes to compute. More modes capture higher-frequency response but increase computation time. For RSA, enough modes should be included to capture at least 90% of the total mass participation in each direction. **Gravity:** The gravitational acceleration value used to convert weight to mass for the eigenvalue analysis. Mass = Weight / Gravity. **Type of Modes:** The method used to compute mode shapes. Options include Exact (full eigensolution), Ritz (load-dependent Ritz vectors which can be more efficient for RSA), and Ritz QSRV (Quasi-Static Ritz Vectors centered around a target frequency). **Applied Load (Ritz Method):** The load pattern used to generate Ritz vectors. This is only required when the Ritz method is selected. The Ritz vectors are generated based on the spatial distribution of this load pattern. **Centering Frequency (Ritz QSRV Method):** The target frequency around which the Ritz vectors are centered. This is only required when the Ritz QSRV method is selected. Modes near this frequency are computed more accurately. ## RSA Curves Response spectrum curves define the spectral acceleration as a function of period for each direction of earthquake loading. **Curve in Dir. 1:** The response spectrum curve for the primary horizontal earthquake direction (typically longitudinal). Select from the defined spectrum curves in the project. Right-click any RSA Curve or Mass Source field for actions including quick selection of available spectrum curves and mass case assignments. **Scale in Dir. 1:** Scale factor applied to the response spectrum in Direction 1. Used to adjust the spectral accelerations (e.g., for importance factors or site coefficients). **Curve in Dir. 2:** The response spectrum curve for the secondary horizontal earthquake direction (typically transverse). **Scale in Dir. 2:** Scale factor applied to the response spectrum in Direction 2. **Curve in Dir. 3:** The response spectrum curve for the vertical earthquake direction. **Scale in Dir. 3:** Scale factor applied to the response spectrum in Direction 3. **Dir. Angle:** The angle that defines the orientation of Direction 1 relative to the global X axis. This allows the earthquake directions to be rotated relative to the global coordinate system. ## RSA Combination **Damping Ratio:** The modal damping ratio used for all modes in the RSA analysis. Typical values are 0.05 (5%) for concrete structures and 0.02 (2%) for steel structures. This value is used to read the spectral acceleration from the response spectrum curve at each mode's period. **Modal Comb. Method:** The method used to combine modal responses. Options typically include CQC (Complete Quadratic Combination, recommended for structures with closely spaced modes) and SRSS (Square Root of Sum of Squares, suitable when modes are well separated in frequency). **Spatial Comb. Method:** The method used to combine responses from different earthquake directions. Options are ABS (sum of absolute values), SRSS (Square Root of Sum of Squares), and CQC3 (Menun & Der Kiureghian, 1998), which accounts for correlation between the ground motion components along the structure axes and automatically finds the critical angle. **γ - (CQC3):** The ratio of the minor (intermediate horizontal) input spectrum to the major input spectrum. Only the ratio γ is supplied; the program finds the critical angle and reports the maximum response for each component. Used only when Spatial Comb. Method is set to CQC3. ## Mass Source Defines the mass sources used in the eigenvalue analysis. The total mass includes the structure self-weight (scaled by the self mass factor) plus mass from specified load cases. **Self Mass Factor:** Multiplier applied to the structure's self-weight mass. Use 1.0 to include full self-weight mass, or 0.0 to exclude it. **# of Nodal Mass:** The number of additional nodal mass definitions used in the eigenvalue analysis. **Mass Case 1:** The first load case whose loading is converted to mass for the dynamic analysis. For example, a superimposed dead load case can contribute additional mass. **Mass Case 1 Factor:** Scale factor applied to the mass from Case 1. Use 1.0 for full contribution. **Mass Case 2:** The second load case contributing mass to the dynamic analysis. **Mass Case 2 Factor:** Scale factor applied to the mass from Case 2. **Mass Case 3:** The third load case contributing mass to the dynamic analysis. **Mass Case 3 Factor:** Scale factor applied to the mass from Case 3. **Mass Case 4:** The fourth load case contributing mass to the dynamic analysis. **Mass Case 4 Factor:** Scale factor applied to the mass from Case 4. **Mass Case 5:** The fifth load case contributing mass to the dynamic analysis. **Mass Case 5 Factor:** Scale factor applied to the mass from Case 5. ## Settings **Structure Group:** The FE group defining which elements are active (have stiffness and mass) during this analysis. If left empty, all elements in the model are included. **Is Active:** Controls whether this analysis case is included in the analysis run. 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