Building Response

Four shear buildings stand on the same shaking ground. Each storey is a lumped mass joined by a hysteretic spring; the equations of motion are integrated live (RK4) under the chosen ground record.

Playback speed 1× Motion exaggeration 20×

Ground motion

Record type Peak ground acceleration 0.35 g Magnitude (duration) 6.8 Dominant ground frequency 1.5 Hz

Buildings

Storeys 10 Stiffness & strength factor 1.00× Damping ratio ζ 3.0 %

Selected building Base isolation Tuned mass damper

Show Mode shapes Response spectrum

Mode shapes

Why resonance matters

Every building has natural periods at which it prefers to swing; a taller, more flexible building has a longer one (roughly 0.1 s per storey). When the ground shakes at a frequency close to a natural frequency each swing adds to the last and the response is amplified by about 1/(2ζ). Short stiff buildings are hit hardest by quick, high-frequency shaking, tall ones by slow, long-period shaking.

Damage is colour-coded by peak inter-storey drift: green below 0.2 %, yellow near 1 %, red from 2.5 %, and a storey collapses at 4 %. Springs yield at 0.7 % drift and keep only 5 % of their stiffness afterwards. Base isolation lengthens the period of a low-rise building far beyond the ground's energy; a tuned mass damper on the roof soaks up energy in the first mode.