Structural dynamics / tutorial
SRSS or CQC
When modal periods are close, the independence SRSS assumes is not there.
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesTwo 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.
- 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
Practice
What is the SRSS combination, in kN? (It is the same in both cases.)
Practice
What is the correlation coefficient ρij for case A, the close modes?
Practice
What is the CQC combination for case A, in kN?
Practice
What is the CQC combination for case B, the well-separated modes, in kN?
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.