Response Spectrum Concept Questions and Answers

Answer: A

Correct answer: reduce the acceleration demand from the spectrum

Isolators lengthen the period to two or three seconds, well beyond the plateau, so the structure sits far down the descending branch of the spectrum and attracts much smaller accelerations. The superstructure then moves nearly as a rigid body above the isolators. The price is a large displacement across the isolation plane, which the bearings and the surrounding moat must accommodate.

Answer: B

Correct answer: determine the natural periods and mode shapes

Everything else depends on them: the spectral ordinate is read at each modal period, the modal forces follow from the mode shapes and participation factors, and the combination rule needs the periods to judge how correlated the modes are. Scaling accelerograms belongs to time-history analysis, and member strengths are checked after the demands are known.

Answer: C

Correct answer: 3, 2, 1

The sequence is fixed by what each step needs. Periods and mode shapes come from the mass and stiffness matrices alone. The spectral ordinate for each mode can then be read at its own period. Finally the modal responses, each a separate maximum, are combined statistically - by the square root of the sum of squares if the periods are well separated, or the complete quadratic combination if not.

Answer: D

Correct answer: one ground motion and one damping ratio

Both qualifiers matter. A different record gives a different spectrum, and the same record gives a different curve at each damping value, which is why spectra are published as families of curves labelled by damping. A design spectrum is a generalisation across many records, but it too is drawn for a stated damping ratio, conventionally five per cent.

Answer: A

Displaced and released, a structure oscillates at its own period, which depends on its mass and stiffness alone. It is the single most important dynamic property, because the demand is read from the spectrum at that period.

Answer: B

Correct answer: longer natural period

Height brings flexibility, and \( T = 2\pi\sqrt{m/k} \) lengthens as stiffness falls. A useful consequence is that a tall building sits further down the descending branch of the spectrum and attracts a lower acceleration coefficient than a squat stiff one at the same site - but its displacements and its sensitivity to long-period motion are correspondingly greater.

Answer: C

Correct answer: decay in amplitude with time

Damping removes energy from the system in each cycle, so successive peaks of free vibration are smaller and the motion dies away. The rate of decay is what defines the damping ratio, and measuring it from the logarithmic decrement of a recorded free vibration is the standard experimental method of determining it.

Answer: D

Correct answer: just prevents oscillation from occurring

Critical damping is the smallest amount that returns a displaced system to rest without overshoot, so at that value the motion is no longer oscillatory. It serves as the reference against which real damping is expressed - five per cent damping means five per cent of critical - and it makes the damping ratio a dimensionless number comparable between structures.

Answer: A

Correct answer: 5 per cent

Five per cent of critical is the conventional design value for reinforced concrete, and design spectra in codes are drawn for it. Steel structures are usually taken at two per cent, and the code supplies multiplying factors to adjust the ordinates. The figure represents the aggregate of many dissipation mechanisms - cracking, friction at joints, non-structural elements - rather than any one measurable effect.

Answer: B

Correct answer: is close to the predominant period of the motion

This is resonance. When the structure’s natural period matches the period at which the ground motion has most of its energy, each cycle of the input reinforces the response and the amplitude builds up over many cycles, limited only by damping. It is why soft soil sites, which filter the motion towards longer periods, are particularly damaging to buildings of matching period.