Response Spectrum Concept Questions and Answers

Answer: A

For one ground motion and one damping value, a family of oscillators of differing period is solved and the maximum response of each is plotted. Reading the curve at a structure's own period gives the demand on it directly.

Answer: B

Correct answer: mass, stiffness and damping

These three properties determine everything about how the system responds: mass and stiffness fix the natural period through \( T = 2\pi\sqrt{m/k} \), and damping fixes how quickly free vibration decays and how large the resonant response becomes. Strength and ductility govern what happens once the response is known, but they do not enter the dynamics of a linear system.

Answer: C

Correct answer: increasing mass

From \( T = 2\pi\sqrt{m/k} \), the period grows with the square root of the mass and falls with the square root of the stiffness. Damping alters the amplitude of the response but has almost no effect on the period at the small ratios found in buildings, and the ground acceleration is the input rather than a property of the system.

Answer: D

Correct answer: halves

\[ T = 2\pi\sqrt{\frac{m}{k}} \quad\Rightarrow\quad T \propto \frac{1}{\sqrt{k}}, \] so quadrupling \( k \) divides the period by \( \sqrt{4} = 2 \). Stiffening a building therefore shortens its period, which usually moves it towards the plateau of the spectrum and increases the acceleration it attracts - a trade the designer must make deliberately.

Answer: A

The natural frequency is the square root of 1 600 000 divided by 4000, which is 20 rad/s, and the period is 2 pi over 20, about 0.31 seconds. Forgetting the factor of 2 pi gives roughly 0.05, and confusing frequency with period gives the others.

Answer: B

Critical damping is the value that just prevents oscillation, and real structures are a small fraction of it, commonly 5 per cent for reinforced concrete. Expressing it as a ratio makes it independent of the size of the structure.

Answer: C

Correct answer: reduces the spectral ordinates

Damping dissipates energy in each cycle, so the peak response to the same ground motion is smaller. The effect is largest near the peaks of the spectrum, where the response is built up over many cycles, and smallest at very short and very long periods where the ordinates are governed by the peak ground acceleration and displacement instead.

Answer: D

A very stiff system moves with the ground, so its peak acceleration is the ground's own. At the other extreme a very flexible system stays still while the ground moves beneath it, and its peak displacement approaches the peak ground displacement.

Answer: A

A very flexible system barely follows the base, so the relative displacement between mass and base tends to the ground displacement itself. The two ends of the spectrum are anchored to ground motion parameters in this way.

Answer: B

Correct answer: displacement, velocity and acceleration on one chart

For a given period the three peak quantities are related by \( S_a \approx \omega S_v \approx \omega^2 S_d \), so on logarithmic axes each becomes a set of straight lines. The tripartite plot exploits this by drawing displacement and acceleration as two families of diagonal grid lines over a velocity plot, letting all three be read from one curve.