Cumulative tutorial 11
SRSS or CQC
When modal periods are close, the independence SRSS assumes is not there.
Two modes of a torsionally coupled building have nearly the same period. That happens whenever a plan is close to symmetric: the translational and torsional modes converge, and a small eccentricity is enough to couple them.
Their individual contributions to the force in a corner column are known. Decide how to combine them, and see what the wrong choice costs — then repeat the exercise for a building whose modes are well separated, to see when the choice stops mattering.
What you are given
- Mode i contributes 1 200 kN; mode j contributes 800 kN
- Case A: ωi = 19.9 rad/s, ωj = 20.9 rad/s — close
- Case B: ωi = 19.9 rad/s, ωj = 55.0 rad/s — well separated
- Damping 5% in both modes
Tutorial 11
Work the problem
4 questions
Question 1
What is the SRSS combination, in kN? (It is the same in both cases.)
Question 2
What is the correlation coefficient ρij for case A, the close modes?
Question 3
What is the CQC combination for case A, in kN?
Question 4
What is the CQC combination for case B, the well-separated modes, in kN?
What this establishes
The decision rule people carry — 'use CQC if the periods are within 10%' — is a reasonable heuristic and an unnecessary one. CQC reduces to SRSS automatically when the modes are independent, so there is no case where SRSS is right and CQC is not.