Structural dynamics / tutorial
A damper retrofit
Size a damper, place it by modal drift, and say what it added.
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesAn existing building cannot have its foundations strengthened, so added bracing is ruled out — a brace would shorten the period and raise the force delivered to a foundation that cannot take it. Viscous dampers add damping without adding stiffness. Size a scheme.
- First mode: ω₁ = 5.1 rad/s, modal mass 800 tonnes
- Candidate damper C = 1.5 MN·s/m, linear (α = 1), braced at 35° to the horizontal
- Relative first-mode displacement across the chosen storey: 0.30
- Peak relative velocity across the damper in the design event: 0.40 m/s
Practice
What fraction of a horizontal damper's effectiveness does the 35° brace retain?
Practice
What axial force does the damper deliver at 0.40 m/s, in kN?
Practice
What damping ratio does one such damper add to the first mode, as a percentage?
Practice
In harmonic motion of 25 mm amplitude at ω = 5.1 rad/s, how much energy does the damper dissipate per cycle, in kJ?
Ten dampers of this size, all well placed, would add about 11% — a credible scheme reaching 13% total. The decision was made from the mode shape in a few minutes, before any time-history analysis. That is the right order: place by modal drift, size by the force the device must deliver, then spend the analysis budget confirming the layout rather than searching for one.