Response Spectrum Curves [FEA]
A Response Spectrum Curve is the design spectrum: the peak acceleration a single-degree-of-freedom oscillator of a given period experiences under the design earthquake. The RSA case looks up each mode's period on this curve, scales the mode by the resulting spectral acceleration, and combines the modal responses.
The curve is input data only. It adds nothing to stiffness or mass and generates no load until an Eigenvalue & RSA case references it.
Data
Period/Frequency: Whether the curve's X axis is expressed as period (seconds) or frequency (Hz).
Engineering influence. The two are reciprocals, so selecting the wrong one does not merely rescale the curve — it reverses it, mapping long-period modes onto the short-period end of the spectrum and vice versa. The result is not obviously wrong: a plausible set of forces comes out, but the flexible modes are assigned the accelerations belonging to stiff ones. Design spectra are most often published against period; check which convention your source uses.
Points/Equations: Whether the curve is defined by tabulated points or by a code equation.
Engineering influence. Tabulated points are explicit and reviewable, which suits a site-specific spectrum. An equation form generates the curve from code parameters and stays consistent if those parameters change. Neither is more accurate; the equation form is less prone to transcription error, the tabulated form easier to audit against a published figure.
Period/Frequency vs Acceleration: The tabulated curve itself — the pairs of X value and spectral acceleration.
Engineering influence. This is the substance of the object. Its shape drives everything: a design spectrum characteristically has a short-period ramp, a constant-acceleration plateau, and a descending branch beyond a corner period. Where the structure's fundamental period falls on that shape governs the demand — a period on the plateau attracts the maximum acceleration, while a longer period on the descending branch attracts substantially less. This is exactly why base isolation works, and why a small error in modelled stiffness can move a structure between two very different parts of the curve.
The tabulated range must cover the structure's periods. Values beyond the last tabulated point are not extrapolated meaningfully, so a curve that stops at 2 seconds applied to a structure with a 4-second isolated period will not give sensible demand for that mode. Include enough range at both ends.
Interpolation between points is linear, so a curve defined with too few points cuts corners on the plateau and can under- or over-state acceleration for a period that falls between them.
Units matter and are easy to get wrong: a spectrum published in g must be converted to the model's acceleration units, or scaled through the RSA case's direction scale factor. A spectrum left in g in a model expecting in/s² understates demand by a factor of ~386.
Results sensitive to it: every RSA force, displacement and reaction, in direct proportion.
Verification
Plot the curve and compare it against the published design spectrum. Shape errors, unit errors and reversed axes are all obvious visually and nearly invisible in a table.
Confirm the curve contains points at all before running an RSA case.
Check the X-axis convention against the source, and confirm the plateau is at short periods rather than long ones — a reversed axis puts it at the wrong end.
Confirm the tabulated range spans the structure's periods, including the longest mode of interest.
Check the peak spectral acceleration against the expected value for the site — typically a few times the peak ground acceleration.
Verify units by hand: read the acceleration at the fundamental period, multiply by the participating mass, and compare against the reported base shear.
Cross-check an RSA result against a time-history analysis using a record compatible with the spectrum; they should be the same order of magnitude.
Common mistakes
An empty curve, giving an RSA case that reports zero everywhere with no error.
Period and frequency interchanged, reversing the spectrum and assigning stiff-mode accelerations to flexible modes.
Leaving the spectrum in g in a model whose acceleration units are not g, understating demand by a large factor.
A tabulated range that does not cover the structure's periods, particularly for isolated or long-period structures.
Too few points, so linear interpolation cuts across the plateau or the corner.
Using the same spectrum for the vertical direction without the reduction the code requires.
Transcribing a spectrum from a figure without plotting the result to check it.
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