The engineering lab
Explore the relationships behind a skyscraper. These simplified experiments explain behaviour; they do not predict any named building.
When a tower meets the wind
Compare the same tower with 1% damping and your selected damping.
Dashed: 1% damping. Solid: selected damping. Vertical plot scale adjusts to the larger response.
- Peak displacement
- Natural period
- Peak acceleration
| 1% damping amplitude, metres | |
|---|---|
| Selected damping amplitude, metres |
Equations, assumptions and limits
A single mass on a spring under sinusoidal force: amplitude = (F/k) / √((1 − r²)² + (2ζr)²), where r is forcing frequency divided by natural frequency. k = 3EI/H³; EI = 2 × 10¹⁴ N·m²; effective mass = 25% of 250,000 kg per 4 m floor. Wind force amplitude is 10% of ½ρv²CdBH, with ρ = 1.225 kg/m³, Cd = 1.2 and B = 40 m. The curve shows steady-state motion, omitting startup, torsion, nonlinear behaviour and aerodynamic feedback. The damping slider represents equivalent viscous damping, not a detailed tuned-mass-damper design.
MIT engineering dynamics: forced vibration ↗ · Read about structural systems ↗
The morning elevator queue
Send passengers from a lobby to randomly assigned floors for ten minutes.
- Mean lobby wait
- 95th percentile wait
- Passengers served
| Zones | Mean wait | 95th percentile | Round trips |
|---|
Waiting time ends when a car becomes available for boarding. All passengers are eventually served, including queues remaining after the ten-minute arrival window.
How the experiment works
Riders arrive at evenly spaced times. A fixed random seed assigns destination floors uniformly, so comparisons use the same demand. Each zone receives a dedicated share of cars. Cars leave when available with the riders already waiting, up to capacity, visit occupied stops in ascending order, and return empty. Each floor is 4 m; acceleration is 1 m/s²; each stop uses 8 seconds for doors and transfer. No lunch traffic, down passengers, sky-lobby transfers, dispatch optimisation or accessibility boarding variability is modelled. Adding zones can help or hurt because it splits both demand and available cars.
Elevator engineering deep dive ↗