Response Spectrum Concept Questions and Answers

Answer: A

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

Both are true and the reason gives the justification. The period of a real building is uncertain by a wide margin because of cracking, non-structural stiffness and mass estimates, so it could fall anywhere within a band. Designing on a jagged spectrum would risk landing in a trough that the real structure does not occupy, so the curve is smoothed and enveloped.

Answer: B

Correct answer: the 0.3 s building, being on the plateau

With the plateau running from 0.1 to 0.5 s, the 0.3 s building sits at the maximum ordinate the spectrum offers, while the 1.2 s building is well down the descending branch. Being taller or more flexible does not raise the coefficient - it lowers it. What the flexible building does attract is a larger displacement.

Answer: C

Correct answer: two-thirds

Vertical spectra are commonly taken as two-thirds of the horizontal, a ratio that has held reasonably well in recorded motions away from the immediate vicinity of the fault. Close to the source the vertical component can approach or exceed the horizontal, which is why near-fault design is treated separately. Vertical motion matters most for long cantilevers and prestressed members.

Answer: D

Correct answer: the centre of mass and centre of stiffness may not coincide

When the two centres are offset, the inertia force acting through the centre of mass produces a moment about the centre of stiffness, so the building twists as well as translates. The twist adds displacement at the perimeter, where it is most damaging. Codes also require an accidental eccentricity to be included even when the calculated centres coincide.

Answer: A

An open ground storey has far less stiffness than those above, so the drift demand piles up in it and its columns must survive almost all the deformation. Codes penalise the configuration or require the columns to be designed for magnified forces.

Answer: B

Correct answer: Repainting the exterior finishes

Paint changes neither mass nor stiffness in any meaningful degree, so the period is unaltered and the ordinate read is the same. Each of the others does change it: a softer soil classification changes the spectrum itself, a roof-level water tank adds mass and lengthens the period, and shear walls add stiffness and shorten it.

Answer: C

Correct answer: the duration and frequency content of the motion

Peak ground acceleration is a single number from a single instant, and two records sharing it can do quite different damage. A brief spike does little; sustained shaking of the same amplitude accumulates cycles of inelastic demand. And motion concentrated near a structure’s own period is far more damaging than the same peak spread across other frequencies.

Answer: D

Correct answer: gives the response at every instant rather than only the maximum

A response spectrum retains only each oscillator’s peak, discarding sign and timing, which is why modal responses must afterwards be combined by a statistical rule. A time-history analysis integrates the equations of motion step by step, so the responses of all modes are correctly in phase at each instant - and it can accommodate non-linear behaviour, which a spectrum cannot.

Answer: A

Correct answer: the sign and the timing of the peak responses

The computation of every ordinate takes the maximum absolute value and throws away when and in which direction it occurred. That is precisely why modal maxima cannot simply be added, and why a combination rule is needed. The maxima themselves, and the base shear derived from them, are exactly what the spectrum does provide.

Answer: B

Past the corner the curve descends, typically in proportion to \( 1/T \) and then to \( 1/T^2 \), reflecting the shift from velocity-controlled to displacement-controlled response. Nothing about the spectrum stays flat for ever.