Set building natural period, soil type, and regional seismic coefficient to calculate design response spectrum Sa(T) and base shear force V in real time. Visualize ground amplification effects and damping ratio sensitivity.
Design Conditions
Site class
Regional seismic coefficient Z
Building natural period T (s)
s
Damping ratio ξ (%)
%
Building weight W (kN)
kN
Results
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Sa (g)
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Cs = Sa/g
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V (kN)
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SDS (g)
Spec
The vertical line marks the current building period T. The Sa value is used for base-shear calculation.
Site
Comparison of Sa and V for the same building under Class I-III site conditions.
Damp
Response spectra as damping ratio ξ varies from 2% to 30%, using the current site class and Z.
What is a Seismic Hazard Response Spectrum?
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The 'Response Spectrum' graph shows period on the horizontal axis and acceleration on the vertical axis—what does this represent?
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Roughly speaking, it's a design guideline that summarizes 'how much a building of a certain period shakes during an earthquake' for each period. For example, a building with a period of 1 second (roughly 10 stories) falls here, and a building with a period of 0.3 seconds (low-rise) falls here. Try changing the ground type on the graph to 'Type 3 (soft ground).' You'll see the peak swell significantly toward the long-period side. Soft ground amplifies slow shaking.
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Looking at the 'Ground Type Comparison' tab, Type 3 has about twice the Sa of Type 1. Can the same building really differ that much depending on the site?
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In practice, the difference can be even larger. Tokyo's alluvial lowlands (along rivers and reclaimed land) often have soft ground, and the design seismic force can be 1.5 to 3 times different from the upland plateaus of Yamanote. That's why before designing a building, it's crucial to first check the ground type through a site boring survey.
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I see 'Base Shear Force V'—does this mean the force in kN applied to the building?
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Exactly. It's calculated as V = Cs × W. Cs is the 'ratio of seismic force to building weight,' and W is the 'building weight.' For example, if W = 2000 kN and Cs = 0.2, a horizontal force of 400 kN acts at the base. This is the starting point for structural design. You can see V increase proportionally when you increase the 'Building Weight' slider.
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In the 'Damping Ratio Sensitivity' tab, the curve's peak gets lower as the damping ratio increases. How do you actually increase damping in practice?
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There are three main methods: ① Damping structures using oil dampers or viscoelastic dampers (ξ ≈ 10–15%), ② Seismic isolation structures that separate the building from the ground using laminated rubber or sliding bearings (ξ ≈ 20–30%), and ③ TMDs (Tuned Mass Dampers) with a weight and hydraulic cylinder at the top of the building. High-rise buildings often use ① and ②; for example, Tokyo Skytree uses ② plus a unique damping core to handle Tokyo's soft ground.
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What is the 'Regional Coefficient Z'? Isn't it the same all over Japan?
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It's a scalar coefficient that reflects differences in earthquake occurrence probability by region. The larger Z is, the larger the design seismic force. Under the Building Standards Law, regions with high seismic risk like Shikoku, Kyushu, and the Tokaido area are assigned Z = 1.0, while relatively low-risk areas like parts of Hokkaido and Okinawa are assigned Z = 0.7–0.9. Even with the same design, the force can vary by nearly 30% depending on where you build.
Physical Model & Key Equations
The design response spectrum $S_a(T)$ is represented by a piecewise-linear model based on site class and regional seismic coefficient.
$$S_a(T) = \begin{cases} S_{DS}\left(0.4 + 0.6\dfrac{T}{T_0}\right) & T \lt T_0 \\ S_{DS} & T_0 \le T \le T_v \\ S_{D1}/T & T \gt T_v \end{cases}$$
$S_{DS} = \tfrac{2}{3} Z F_a \cdot 2.5$ is the short-period design spectral acceleration, and $S_{D1} = \tfrac{2}{3} Z F_v$ is the one-second design spectral acceleration. $F_a$ and $F_v$ are site-class amplification factors.
The damping correction $\eta = \sqrt{10/(5+\xi)}$, where $\xi$ is the damping ratio in percent, adjusts the spectrum for damping ratios other than 5%.
Design seismic force (base shear):
$$V = C_s \cdot W, \quad C_s = \frac{S_a(T)}{g}$$
$V$ [kN] is the horizontal design force at the base of the building, $W$ [kN] is the building weight, and $g = 9.8\,\text{m/s}^2$. This $V$ is used as the design load for columns, beams, and shear walls in structural calculations.
Real-World Applications
Preliminary structural design: Estimate design seismic force quickly from the assumed building period and site conditions, then judge wall quantity, column sizes, and other early design choices. It is especially useful for sensitivity checks across multiple site scenarios.
Seismic assessment of existing buildings: Enter the current building's natural period from an eigenvalue analysis and estimate the strength demand under the current criteria. This supports early screening of retrofit needs and priorities.
Mechanical and equipment seismic design: Response spectra are also used for nonstructural components such as large machinery, substation equipment, and boilers to estimate design input acceleration from equipment natural period.
Isolation and damping studies: By moving the damping-ratio slider from standard damping around 5% to isolation-level damping around 20-30%, you can see how much Sa decreases and evaluate the benefit of damping devices conceptually.
Frequently Asked Questions
How is a response spectrum different from an earthquake waveform?
An earthquake wave (time history waveform) is an acceleration record on the time axis, while a response spectrum summarizes the "maximum response values" for each period when that waveform is applied to single-degree-of-freedom systems with various natural periods. Since maximum values are more important than waveform details in design, response spectra are widely used. Time history analysis is used for more detailed nonlinear analysis.
How do I find the natural period T of a building?
For a rough estimate, RC structures: T ≈ 0.02 × H (H is building height [m]), steel structures: T ≈ 0.03 × H. For example, a 10-story RC building (height 30 m) gives T ≈ 0.6 seconds. For greater accuracy, eigenvalue analysis (FEM) using stiffness and mass matrices is required, and values vary significantly with wall quantity and foundation conditions. In practice, microtremor measurement is also effective.
How do I determine the ground type?
Under the Building Standard Law, ground type is determined based on the average shear wave velocity Vs (measured by boring surveys and PS logging). Type 1 (bedrock equivalent): Vs ≥ 600 m/s, Type 2 (intermediate ground): 150 m/s ≤ Vs < 600 m/s, Type 3 (soft ground): Vs < 150 m/s (or alluvial layer thickness ≥ 20 m). Desktop estimation is risky, so always use boring survey results.
Can I use the base shear force V directly in design?
The V = Cs × W in this tool is based on elastic response. In actual structural design, it is reduced by the "structural characteristic factor Ds." Ds ranges from about 0.2 to 0.55 depending on frame ductility. Thus, the design lateral force is "V_design = Cs × W / Ds," which is smaller than the elastic V. However, deformation performance (interstory drift) must also be checked, so use an integrated structural calculation program for detailed design.
How much does the design seismic force reduce with a base-isolated structure?
You can check this in the "Damping Ratio Sensitivity" tab. Increasing the damping ratio from the standard 5% to 20–30% (equivalent to base isolation) reduces the peak response spectrum value to about 1/2 to 1/3. Furthermore, by lengthening the period to 2–3 seconds or more using laminated rubber bearings, the spectrum value enters the SD1/T decay region, enabling significant seismic force reduction. This allows smaller structural member sections in the main building, but additional costs for design and maintenance of the isolation layer are required.
How do long-period ground motions differ from ordinary ground motions?
In great earthquakes (M8 or larger), long-period components with periods of 2–10 seconds dominate, causing shaking in ranges not assumed by ordinary response spectra. In the 2011 Great East Japan Earthquake, high-rise buildings in Osaka, 600 km from Sendai, shook significantly, and oil tanks experienced resonance. The spectrum shape of this tool is mainly for short to medium periods, but you can check sensitivity even in the "Period 5 s" slider range. For high-rise building design, compliance with long-period ground motion measures under the 2016 revised Building Standard Law is mandatory.
What is Seismic Hazard?
Seismic Hazard is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Seismic Hazard & Design Spectrum Calculator. Understanding these equations is key to interpreting the results correctly.
$S_a(T) = \begin{cases} S_{DS}\left(0.4 + 0.6\dfrac{T}{T_0}\right) & T \lt T_0 \\ S_{DS} & T_0 \le T \le T_v \\ S_{D1}/T & T \gt T_v \end{cases}$
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Seismic Hazard & Design Spectrum Calculator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.
Read design spectral acceleration Sa(T) in g, seismic coefficient Cs, base shear force V in kN, and SDS plateau value
Worked Example
Five-story reinforced concrete office building in Zone 3, soil class D (stiff clay), natural period T = 1.2 s, 5% damping. Calculator yields Sa(T) = 0.48 g, Cs = 0.044, SDS = 0.52 g. For 2400 tonne building mass, base shear V = Cs × W = 0.044 × 23,520 kN = 1,035 kN. Soil amplification factor Fa = 1.28 increases response; period-dependent reduction R = 8 (special moment frame) reduces demand proportionally.
Practical Notes
Soft clay (Class E) soil amplifies 1.6× compared to rock; verify boring logs and shear-wave velocity before locking soil class
Period elongation from nonlinear response during strong shaking may push structure into longer-period plateau; use pushover analysis to refine T estimate
Base shear V scales linearly with building mass; adding mechanical penthouse or water tanks increases W and amplifies seismic demand directly
Damping below 2% (e.g., tuned mass dampers) and above 20% (lead rubber bearings) require custom spectral shape modifications outside standard code curves