About this experiment
Place two towers on the same shaking table. One is an unbraced reference; the other uses the bracing and damping you choose. Run the prescribed ground motion, inspect the roof response and compare peak storey drift. A stiffer tower can avoid one resonance while moving closer to another, so appearance alone does not decide the result.
Learning goals
- Separate ground motion from displacement relative to the ground
- Relate mass and stiffness to natural frequency
- Observe resonance and the effect of damping
- Compare the same excitation on two different elastic structures
- Interpret interstorey drift without claiming to predict collapse
How to use it
- 1Shake both towers and inspect the peak response. Explain why their roofs move differently under the same base motion.
- 2Keep the bracing fixed and sweep the shaking frequency across the first natural frequency.
- 3Increase modal damping with the orange handle and compare the maximum roof displacement.
- 4Change floor mass while keeping stiffness fixed. Predict the shift in natural frequency.
- 5Compare bare, diagonal and cross-braced presets, recording both roof displacement and storey drift.
The model
Assumptions
- Each tower has two equal lumped floor masses and two equal linear storey stiffnesses. Floor rotations, torsion, foundation flexibility and soil response are omitted.
- Bracing presets multiply the supplied unbraced storey stiffness by 1, 2.5 or 4. These are declared equivalent-stiffness choices, not a calculation of real brace connections.
- The reference tower always has bare-frame stiffness and 5% modal damping. The adjustable tower uses Rayleigh damping tuned to its two natural modes.
- Ground displacement is a sine wave multiplied by a sin⁴ envelope over 12 seconds. Its exact second derivative drives the equations, followed by 12 seconds of free response.
- RK4 uses a fixed 0.005-second step; plots are stored every 0.05 second. Motion is magnified equally for both towers. Yielding, cracking and collapse are not included.
Try this in class
- Q1Why can increasing stiffness make response worse at one forcing frequency?
- Q2Why does doubling floor mass lower natural frequency?
- Q3What is the difference between roof displacement and maximum storey drift?
- Q4Why must both towers receive the same ground motion for a fair comparison?
Frequently asked questions
Why does the roof move after shaking has stopped?
The elastic structure retains kinetic and strain energy. Damping gradually dissipates that free vibration.
Does a large drift mean the animation predicts collapse?
No. It shows an elastic response. Large drift can exceed the assumptions of that model, and no damage law is included.
Why do bracing lines change stiffness by fixed factors?
The lab compares transparent lumped-parameter models. A real brace stiffness would also require section, geometry, connections and construction details.