# Building Earthquake Simulator - Modes, Response Spectrum, Base Isolation, TMD

> Simulate a multi-storey building in an earthquake: mode shapes, Newmark time history, response spectrum, base isolation and tuned mass dampers (Taipei 101).

- URL: https://qilingtools.com/en/physics/seismic-isolation
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Model an N-storey building as floor masses joined by storey springs, set the mass, stiffness, damping and a soft ground storey, and see its mode shapes and periods. Then shake it with a random earthquake (Kanai–Tajimi site filter), a sine sweep or a near-fault pulse, integrated step by step with Newmark-β, and watch it sway with each storey coloured by drift. Further tabs explain response spectra and the 1985 Mexico City resonance, compare a base-isolated building with a fixed-base one side by side, and tune a roof mass damper with Den Hartog's formulas.

## How to use

1. Pick a preset (3, 10 or 30 storeys, soft first storey, approximate Taipei 101) or set storeys, mass, stiffness and damping
2. Open Modal analysis to watch the first mode shapes and read periods and effective mass
3. In Time history choose the motion, site and PGA, then play or drag along the chart to any moment
4. In Spectrum & resonance compare site spectra with the building periods and try the 1985 Mexico City preset
5. In Base isolation and Tuned mass damper adjust the isolated period or mass ratio and compare accelerations, drifts and frequency response

## Features

- Eigenvalue analysis of an N-storey shear building: periods, animated mode shapes, participation and effective mass
- Newmark-β average-acceleration time history; seeded random quakes plus sine sweep, pulse and steady sine
- 5%-damped pseudo-acceleration spectrum with the building periods marked and four site types to overlay
- Side-by-side animation of fixed-base and base-isolated buildings with roof acceleration, drift and isolator displacement
- Roof TMD with Den Hartog optimal frequency and damping ratios, frequency response with and without it, approximate Taipei 101 model
- Inter-storey drift coloured by damage level, with a bar chart of each storey's peak

## FAQ

### Why did mostly mid-rise buildings collapse in the 1985 Mexico City earthquake?

Mexico City sits on soft clay from an old lake bed with a site period of about 2 seconds, which amplified waves near that period several times and kept shaking for one to two minutes. Buildings of 6 to 15 storeys started with periods of about 0.6 to 1.5 seconds; as they cracked they softened and their periods moved right onto the 2-second peak, so damage made the shaking worse. Low houses and very tall towers had periods away from the peak.

### How does base isolation reduce earthquake forces, and when does it not help?

Laminated rubber bearings are soft sideways, stretching the building period from about 1 second to 2 to 4 seconds, where most earthquakes have much lower spectral acceleration. The superstructure then moves almost as a rigid block, so storey drifts and floor accelerations drop sharply, at the cost of tens of centimetres of movement at the isolation level. On a soft site whose own period is near 2 seconds, lengthening the period can land on the spectral peak instead; the tool shows this amplification directly.

### How does a tuned mass damper work?

A mass near the top is tuned close to the building's first-mode frequency. As the building sways the mass lags by about 90 degrees, and its spring and damper draw vibration energy out and dissipate it, splitting the sharp resonant peak into two lower ones. Den Hartog's optimum f = 1/(1+μ) and ζ = √(3μ/8(1+μ)³) makes the two peaks equal. It works best on narrow-band, sustained motion such as wind sway and helps less with a short pulse-like earthquake.

### What is inter-storey drift and how much is dangerous?

It is the horizontal displacement of one floor relative to the floor below, divided by the storey height, and it measures how much columns and walls are distorted. For reinforced-concrete frames, roughly below 0.5% is essentially undamaged, 0.5–1% means light damage such as partition cracking, 1–2% moderate to severe damage, and above 2% is near collapse. The tool colours each storey by its current drift and shows the peak over the whole record.

### How does this differ from real seismic design?

The model is a linear-elastic shear building with one horizontal degree of freedom per floor. It ignores bending, torsion, soil–structure interaction and yielding of members, the ground motions are synthetic rather than recorded, and Taipei 101 is only a rough 20-mass model built from public figures. It is meant for understanding periods, resonance, isolation and dampers, not for code design.

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