Discussion
If that same structure has an actual damping coefficient of 20 kN·s/m, its damping ratio is
Answer: A
Correct answer: 5 per cent
The damping ratio is the actual damping over the critical value:
\[ \xi = \frac{c}{c_{cr}} = \frac{20}{400} = 0.05 = 5\% \]
That is a typical figure for a reinforced concrete building, and it is the value codes assume when constructing a design response spectrum. Steel structures are usually taken lower, at 2 to 3 per cent, which raises the spectral demand - the two questions together show how the ratio is arrived at from measurable quantities.
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