REFERENCEFIXED
T₁—s
Undamped natural periods
Peak roof |u|— mm
250 t / floor · 100 MN/m · 5% damping
CHANGE A PARAMETER. SEE THE RESPONSE.
Building dynamics, in motion.
One ground motion. Two structures. Explore what changes.
Linear elastic model
Modified building
m
t
50 t1,000 t
k
MN/m
10 MN/m400 MN/m
ζ
%
0%20%
TRY A SCENARIO
Structure & ground motion 5 floors · 0.20 g synthetic input
DOUBLE MASSEDITABLE
T₁—s
Undamped natural periods
Peak roof |u|— mm
500 t / floor · 100 MN/m · 5% damping
0 s20 s · excitation ends30 s
Double the mass. Lengthen the period.
At fixed stiffness, natural periods scale with √m.
Roof displacement mm
Relative to groundReference 0.0Modified 0.0
Roof acceleration g
AbsoluteReference 0.000Modified 0.000Ground 0.000
Click or drag either chart to inspect the same instant in both buildings.
Peak response comparison
Full 30 s analysisNatural period T₁
——
Undamped eigenperiod
Peak roof displacement
——
Maximum absolute relative displacement
Peak interstorey drift
——
Storey displacement difference / 3 m
Peak roof acceleration
——
Absolute acceleration · includes ground
Values describe the modified building. Changes are relative to the reference under the current input.
Mode shape comparison
ReferenceModified
Shapes are normalized to a maximum magnitude of 1. They are not response displacements.
Modified building · all modes
All modes contribute to the time response.
| Mode | T s | Td s | f Hz | Eff. mass % |
|---|
Inside the model Equations, assumptions & references
One horizontal degree of freedom per floor
Rigid floor masses are connected by linear storey springs. Floor displacements are measured relative to the moving ground. Storey height is 3 m; the reference has uniform 250 t floor masses, 100 MN/m storey stiffness and 5% modal damping. Floor count and excitation are shared.
M ü + C u̇ + K u = −M 1 ag(t)
Eigenmodes solve Kφ = ω²Mφ. The same damping ratio is assigned to every mode. The first-storey stiffness setting only changes the modified building.
Tr = 2π / ωr · Td,r = Tr / √(1 − ζ²)
How the response is calculated
The calculation retains every mode and integrates each modal equation with the Newmark average-acceleration method (β = ¼, γ = ½). Output is sampled every 0.005 s; the internal integration step resolves the shortest natural period with at least 600 steps.
The synthetic earthquake is a deterministic sum of 24 frequency components, normalized to the selected PGA. Both inputs ramp in and out, end at 20 s, and are followed by 10 s of free response. This is not a recorded earthquake.
Scope: an educational, linear elastic model. No yielding, failure, torsion, soil–structure interaction or code compliance assessment is included. A common displacement scale fits both buildings into the diagrams; its multiplier is shown above them.