Response Spectrum Concept Questions and Answers

Answer: C

Pseudo-acceleration is the spectral displacement multiplied by the square of the circular frequency, so it is exactly the quantity that gives the elastic force in the spring. For small damping it is very close to the true peak acceleration.

Answer: D

Correct answer: pseudo-acceleration

The elastic force is the mass times the pseudo-acceleration, \( F = m\,S_a \), which is why that ordinate is the one design codes tabulate. It is called pseudo because it is defined as \( \omega^2 S_d \) rather than measured as a true acceleration, but for the light damping found in structures the two are almost identical, and the force relation is exact by construction.

Answer: A

A response spectrum for one record is jagged, and its peaks and valleys are accidents of that motion. Design spectra are smoothed envelopes drawn from many records so that a small change in period does not change the demand abruptly.

Answer: B

Correct answer: the exact period of a structure is never known precisely

A recorded spectrum is jagged, with sharp peaks and troughs whose positions depend on the particular record. A real building’s period is uncertain by a substantial margin - non-structural stiffness, cracking and the actual mass all shift it - so designing on a sharp trough would be unsafe. Smoothing and enveloping ensure the design ordinate is adequate wherever the true period turns out to lie.

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the construction. A design spectrum is built by computing spectra for many records appropriate to the site, then enveloping and smoothing them. It therefore has no single earthquake behind it, and no future earthquake will reproduce it - it is a design envelope, chosen so that the structure is adequate whichever of the plausible motions occurs.

Answer: D

Correct answer: Sa/g

In IS 1893 the design horizontal seismic coefficient is \[ A_h = \frac{Z}{2}\cdot\frac{I}{R}\cdot\frac{S_a}{g}, \] where \( S_a/g \) is the spectral acceleration coefficient read from the spectrum for the structure’s period and the site soil. \( Z \), \( I \) and \( R \) are the separate zone, importance and response reduction factors, each accounting for something different.

Answer: A

Correct answer: a range of periods with constant spectral acceleration

The plateau is the band of periods over which the design ordinate is held at its maximum value. It exists because the underlying spectra peak at different periods for different records and soils, so enveloping them produces a flat top rather than a single peak. Structures whose period falls in that band attract the largest acceleration the spectrum offers.

Answer: B

Correct answer: lower than the plateau value

Beyond the plateau the ordinate falls off, typically as \( 1/T \), because a very flexible structure hardly follows the ground at all - its mass stays nearly still while the ground moves beneath it. The force demand therefore drops, but the displacement demand rises, which is the trade at the heart of base isolation.

Answer: C

Softer soils shift energy to longer periods, so the plateau extends further and the ordinates alter, which is why codes publish separate curves for rock, medium and soft soil. Zone and importance are separate multipliers.

Answer: D

Ductile structures are permitted to yield, dissipating energy and surviving a demand greater than their elastic strength, so the design force is reduced accordingly. The price is accepted damage and a requirement for detailing that delivers the assumed ductility.