REFERENCEFIXED
T₁—s
Undamped natural periods
Peak roof |u|— mm
250 t / floor · 100 MN/m · 5% damping
Open Frame Explorer: individual members, different heights, N–M–V and frequency comparisons →
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
Recorded ground acceleration · g
A local catalogue of freely downloadable example records. One horizontal component is applied uniformly to both buildings. No automatic filtering, baseline correction or spectrum matching is applied.
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.
Column moments, shear & capacity
Elastic demand / user-defined limitsStorey shear is shared by identical fixed-ended columns. Edit the number and capacity of columns on each storey; values apply to both buildings.
Column assumptions & capacities
The starting capacities are examples. Enter section capacities appropriate to the axial force and detailing of your columns. Changing column count changes load sharing; the total storey stiffness above stays fixed.
| Storey | Identical columns | M limit / column kN·m | V limit / column kN |
|---|
Capacity exceedance is not a collapse prediction. This model does not redistribute forces after yielding. After the first M or V limit is reached, the curves show an elastic extrapolation. Collapse assessment requires nonlinear member behaviour, axial-force interaction, ductility, degradation and P–Δ effects.
Selected column · at cursor
Bending moment kN·m
Shear force kN
| Storey | Peak |M| kN·m | Peak |V| kN | M / limit | V / limit | First M limit s | First V limit s |
|---|
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 editable; 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. Synthetic and harmonic inputs ramp in and out and end at 20 s. Recorded input uses the complete published acceleration array and its own time step, with linear interpolation. All inputs are followed by 10 s of free response; a small free-response amplitude is not guaranteed by this fixed tail. A record starts at t = 0 with zero relative displacement and velocity, and equilibrium-consistent initial acceleration. Acceleration is set to zero after the last record sample.
Vi,col = ki(ui − ui−1) / ni
Mbottom = Vh/2 · Mtop = −Vh/2
Mbottom = Vh/2 · Mtop = −Vh/2
These are internal section forces for columns with both end rotations restrained, constant EI, no distributed lateral member load and an inflection point at midheight. The internal moment diagram is M(z) = V(h/2 − z), z measured upward. Equivalent EI per column = k h³ / (12 n). The entered storey k already represents the whole storey. Modal viscous damping forces are not allocated to column section resistance. Gravity-induced moments and axial-force changes are not calculated.
Capacity times are found on every internal step with linear interpolation to |M|/M limit = 1 or |V|/V limit = 1. The critical input multiplier is 1 / maximum utilization in the full elastic history, with all other inputs held fixed. It is the multiplier for first limit attainment, not a collapse intensity or a design safety factor.
Scope: an educational, linear elastic model. No yielding, failure mechanism, torsion, soil–structure interaction or code compliance assessment is included. Remaining below the entered limits does not establish structural safety. A common displacement scale fits both buildings into the diagrams; its multiplier is shown above them.