Cumulative tutorial 17
A damper retrofit
Size a damper, place it by modal drift, and say what it added.
An 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.
What you are given
- 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
Tutorial 17
Work the problem
4 questions
Question 1
What fraction of a horizontal damper's effectiveness does the 35° brace retain?
Question 2
What axial force does the damper deliver at 0.40 m/s, in kN?
Question 3
What damping ratio does one such damper add to the first mode, as a percentage?
Question 4
In harmonic motion of 25 mm amplitude at ω = 5.1 rad/s, how much energy does the damper dissipate per cycle, in kJ?
What this establishes
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.