Module 14
Response-spectrum analysis
One curve that summarises what an earthquake does to every possible structure — what it contains, what it deliberately throws away, and why that discarded information has to be replaced by a combination rule.
What this module covers
- Construct a response spectrum from a ground motion by solving many oscillators
- Relate spectral displacement, pseudo-velocity and pseudo-acceleration, and say why 'pseudo'
- State the two asymptotes every spectrum must satisfy and use them as checks
- Carry out a modal response-spectrum analysis and recover base shear and storey forces
- Explain why modal peaks are combined by SRSS or CQC and never added
- Distinguish a response spectrum from a design spectrum
Lessons
Solve one oscillator, record its peak, change the period, repeat. The definition is the algorithm, and the two ends of the curve are fixed by physics.
Start lesson →Each mode's peak is known and the instants at which they occur are not — so they cannot be added. What replaces addition, and when the simpler rule stops working.
Start lesson →
Module checkpoint
Check what you have taken in
5 questions
Question 1
An oscillator of period 0.8 s has a spectral displacement of 65 mm. What is its pseudo-acceleration, in m/s²?
Question 2
Modal base shears are 6.0, 2.5, 1.2 and 0.8 MN. What is the SRSS combination, in MN?
Question 3
A response-spectrum analysis reports a base shear coefficient V/W of 2.8. What should be concluded?
Question 4
Two modes have a frequency ratio r = 0.90 and 5% damping each. What is the CQC correlation coefficient?
Question 5
What information does a response spectrum deliberately discard?