Presets
Playback
Building and ground motion
Pick the excitation type, switch protection systems on and drag the sliders.
Layers
Model checks
The science
Shear-building model
Each floor is a lumped mass m joined to the one below by a spring of storey stiffness k. With the ground moving by xg(t) the relative displacements x obey M x'' + C x' + K x = -M 1 ag(t). For a uniform N-storey building the natural frequencies are ωj = 2√(k/m) sin((2j-1)π/(2(2N+1))); the first mode dominates the response.
Resonance
A steady sine base motion of amplitude ag at frequency f gives a roof amplitude |H(f)| ag, where H comes from solving (K - ω2M + iωC) X = -M 1. Near f1 the amplification is about 1/(2ζ), which is why a 3 % damped frame shakes more than 15 times harder at resonance. The green curve in the middle graph is this transfer function, the yellow line marks the forcing.
Soft storey, isolation, TMD
A weak ground storey concentrates drift there (inter-storey drift ratio = Δx / storey height). A base-isolation layer lowers the system to a very low frequency (0.3-1 Hz) so the building rides above most earthquake energy. A tuned mass damper (mass ratio μ, frequency f1/(1+μ), damping √(3μ/(8(1+μ)3))) removes energy from the first mode.
Honest simplifications: linear elastic behaviour (no yielding, cracking or collapse), stiffness-proportional damping, rigid floors, the synthetic earthquake is filtered noise (not a real record), ground displacement is shown only as a schematic jolt. Not a design tool.
What to try
- Resonance preset: the roof swings far more than the table because forcing equals f1.
- Soft-storey preset: storey 1 turns red while the others stay calm.
- Base-isolated preset: drifts nearly vanish, the isolation layer takes the motion.
- Tuned mass damper preset: compare the amplitude with the TMD switched off.