Interactively calculate simplified design response spectra based on Japan's Building Standard Law and ASCE/SEI 7. Compare Sa, Sv, and Sd as damping and site class change.
Ground Motion & Site Conditions
Damping Ratio ζ
Primary damping ratio
%
Steel: 2%, RC: 5%, base isolation: 20%
Spectrum Type
Structural Natural Period
Natural period T
s
Low-rise RC: 0.1–0.3s / high-rise: 3–5s
Sa = — m/s²
Results
—
Natural period T [s]
—
Sa [m/s²]
—
Sv [m/s]
—
Sd [m]
Response Spectrum (Multiple Damping Ratios)Acceleration spectrum Sa [m/s²]
Spectrum
Resonance Animation — Structural Motion under Ground Excitation
1.00
Natural period T [s]
5
Damping ratio ζ [%]
0.0
Ground PGA [m/s²]
0.0
Roof displacement u [cm]
1.0×
Response amplification
Resonance status: evaluating…
Target building (current T)Reference building (stiff / short-period)Ground motion
As the building's natural period T approaches the dominant ground-motion period, resonance produces much larger motion. Increasing damping reduces the response.
Student: What is a seismic response spectrum? I have seen the graph in textbooks, but I am not sure what engineers use it for.
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Professor: It is a compact summary of how strongly structures with different natural periods respond to the same earthquake. The horizontal axis is natural period and the vertical axis is peak response. Move the natural-period slider and the corresponding point follows the curve; its $S_a$ value can be used to estimate equivalent seismic force from $F = S_a \times m$.
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Student: The graph also shows velocity Sv and displacement Sd, not just acceleration Sa. When should each one be used?
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Professor: Sa is commonly associated with member force and shear demand, Sv with perceived motion and nonstructural damage, and Sd with clearance, pounding, and isolator stroke. Increase the primary damping ratio from 5% to 20%; as in a highly damped isolation system, all three spectra decrease markedly.
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Student: Why is the design curve smooth when spectra calculated from individual earthquake records are jagged?
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Professor: Design spectra smooth and envelope the variability of many records. Change the site class from stiff Class I to soft Class III and note the stronger long-period demand. That trend represents the greater susceptibility of long-period structures to amplification on soft soil, an effect that design provisions must address.
Frequently Asked Questions
Increasing damping lowers the spectrum across the period range. Softer sites amplify longer-period response, while stiff sites emphasize shorter periods. Use the real-time comparison to examine the differences.
The approximate pseudo-spectrum relationships are Sd = Sa / ω² and Sv = Sa / ω, where ω=2π/T. Compare all three measures to understand force, velocity, and displacement demand over the period range.
Use the Building Standard Law spectrum for Japanese building approval and ASCE/SEI 7 for U.S. design or international comparisons. Apply the governing project code and its site-specific parameters.
No. This simplified model is intended for preliminary studies and parameter exploration. Final design requires a detailed site classification, project-specific design ground motion, the governing code, and review by a qualified engineer.
Engineering Applications
Seismic Design of Buildings:Estimate the fundamental period, read the corresponding $S_a$ from the design spectrum, and derive an equivalent lateral demand for preliminary member sizing under the applicable building code.
Base-Isolated and Damped Structures:Isolation lengthens the period and often provides 20–30% equivalent damping. The lower spectral demand illustrates the basic isolation effect, while isolator stroke is assessed from the displacement spectrum $S_d$.
Critical Facilities (Plants and Hospitals):Evaluate seismic demand on critical nonstructural components such as petrochemical piping and tanks or large hospital equipment. Component period, damping, and $S_v$ help characterize the expected response.
Ground-Motion Characterization and Site Amplification:The spectrum indicates which structural periods are most affected by a ground motion. Comparing site classes also quantifies the amplification of longer-period components on soft soil.
Common Misconceptions and Limitations
Keep several limitations in mind. First,“a design spectrum is not an exact prediction.”The smooth curve is a representative design model derived from many records; an individual record can contain peaks well above it. Final design must use the code-prescribed factors, combinations, and strength checks.
Second, understandthe limitations of the SDOF model.The simulator represents a structure with one mass and one spring, whereas real buildings have multiple degrees of freedom and higher-mode effects. Slender towers, for example, may have significant second- and third-mode response. Use this result as a first-mode estimate.
Finally, avoiduncritical parameter selection.Response is sensitive to damping. Typical assumptions vary—from roughly 2% for steel and 5% for reinforced concrete to 10–20% or more for isolation systems. Always select a value appropriate to the actual structure rather than relying on the default.
Select the ground-motion level and site class from the drop-down menus.
Set the damping ratio from 1–30%. Typical starting values are 2% for steel, 5% for RC, and 20% for base isolation.
Use the spectrum buttons to switch among Sa (acceleration), Sv (velocity), and Sd (displacement).
Move the natural-period slider from 0.05–5s to calculate and plot Sa, Sv, and Sd at the selected point in real time.
Worked Example
Consider a six-story steel office building with 5% damping on Class III soft soil. At T=1.2s under the strong-motion setting, Sa is about 457cm/s² (≈4.57m/s²). Multiplying by mass gives a preliminary horizontal foundation demand. Raising damping to 10% reduces Sa to about 373cm/s², illustrating the benefit of added damping.
Engineering Notes
Site Class A represents rock and is dominated by periods below 1s, while soft-soil Class D is dominated by long-period ground motion above 2s; high-rise buildings must be checked for Class D conditions.
Damping includes material behavior and friction from nonstructural components; for existing-building assessment, prefer measured values when available.
When applying ASCE/SEI 7, obtain the U.S. seismic-map values Ss (1-second period) and S1 (0.2-second period) separately, then apply the spectrum modification coefficient Fa.
Use conservative assumptions and, in final design, evaluate damping or isolation measures that avoid or reduce resonance demand.