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Research, not a design tool.
The example
Four fixed-base columns, 3 m high on a 4 × 3 m plan. Each roof node carries 5 t in X. Roof rotations and Y/Z translations are restrained; equal-X constraints join each transverse pair. Two axial roof ties couple the two remaining coordinates. This is our illustration of the method, not the paper’s original building.
Closed-form reference
The reduced matrices are M = diag(10, 10) t and K = [[1020, −20], [−20, 1230]] kN/m. Solve det(K − ω²M) = 0; normalize each mode to unit modal mass. For Sa = 1 m/s², the modal base shears are Γ²Sa. SRSS discards cross terms; CQC retains their equal-damping correlation at ξ = 5%.
ρ(r, ξ) = 8ξ²(1+r)r³ᐟ² / [(1−r²)² + 4ξ²r(1+r)²], r = ω₂/ω₁.
The paper proposes CQC to reduce modal-combination errors and recovers SRSS for well-separated frequencies. Here SRSS is lower than CQC for base shear. This difference is relative to the CQC estimate, not a measured error against an earthquake record.
Relative tolerance: 1 × 10⁻⁸ for frequencies, base shear and roof displacement. Reference agreement is not engineering certification.
Not yet
- Original paper building and published numerical tables.
- Time-history envelope and record-specific accuracy.
- Torsional response, multi-storey models and parameter sweeps.
- Independent reviews or design certification.
Cite this
Stabileo Research, “Closely spaced modes: SRSS vs CQC”, reproduction of E. L. Wilson, A. Der Kiureghian, E. P. Bayo (1981), doi:10.1002/eqe.4290090207. Implementation: research/benchmarks/cqc-1981 at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.