SR1 · RESPONSE-SPECTRUM-FRAME · Analysis Benchmarks

Response-spectrum analysis of a two-dimensional rigid frame

Full response-spectrum pipeline verified on the canonical two-dimensional rigid-frame benchmark

PASS +0.219% error tolerance 1% 1.56213 s vs 1.562 s
§2

Technical features tested

  • Response-spectrum analysis (RSA)
  • Modal + spectrum + SRSS / CQC
  • ElasticTimoshenkoBeam frame element
  • Per-mode inertia-force solve + force recovery
  • Periods · displacements · bending moments
  • Bending-only · concentrated mass · 5% damping
§3

Problem description

The response-spectrum analysis of a two-dimensional rigid frame is the classical textbook RSA benchmark, adopted as CSI SAP2000 Verification Example 1-020 with the independent solution from Chopra, Dynamics of Structures (1995), Example 13.11. A single-bay, two-story fixed-base plane frame carries concentrated floor masses (2m, m) and is excited by a 5%-damped response spectrum in the horizontal direction. It exercises the entire STRIX RSA path: the modal solve, a per-mode inertia-force static analysis with element force recovery, spectral scaling, and the SRSS and CQC modal combinations. Following the reference, only bending deformations are retained (axial and shear made rigid via the section stiffness modifiers) and the mass acts in X only; the concentrated masses enter through the production Loads-to-Masses path. The reference is reproduced directly at its own 8-element discretisation.

2EI EI 2EI EI 2m m response spectrum → X 1 bay @ 240 in · 2 storeys @ 120 in · masses X only
Figure SR1. Single-bay two-story rigid frame — concentrated masses 2m, m at the beam mid-spans, excited by a 5%-damped response spectrum in X; the first sway mode drives the response.
§4

Geometry, properties & loading

Geometry

Bays
1
Storeys
2
Bay width
240 in
Storey height
120 in

Member & mass

E
3000 ksi
I (base)
1000 in⁴
Deformation
Bending only
Mass
2m, m (X only)

Loading & dynamics

Excitation
Response spectrum
Damping
5 %
Combination
SRSS · CQC
Active DOF
Ux, Uz, Ry
§5

Reference solution

  1. Period — mode 1(K − ω²M)·φ = 0, T = 2π/ω= 1.562 s
  2. Displacement Ux — joint 3 (roof)u = √(Σ (Γ_m·Sa_m/ω_m²·φ_m)²)= 18.81 in
  3. Moment — story-1 column base (jt 1)M = √(Σ M_m²)= 12624 kip·in

CSI SAP2000 Software Verification, Example 1-020 (Response-Spectrum Analysis of a Two-Dimensional Rigid Frame); independent solution = Chopra, "Dynamics of Structures" (1995), Ex. 13.11, p.521. A single-bay, two-story fixed-base plane frame under a 5%-damped response spectrum, bending deformations only (shear/axial ignored), mass excited in X only. Reference values (Chopra) are the two periods, the SRSS lateral displacements, and the SRSS column/beam bending moments.

§6

Results comparison

Response quantityProbeSTRIXReferenceΔVerdict
Period — mode 1 (s) SRSS · s 1.56213 1.562 +0.0080% PASS
Period — mode 2 (s) SRSS · s 0.58681 0.5868 +0.0020% PASS
Displacement Ux — joint 2 (floor 1) (in) SRSS · in 7.579 7.566 +0.165% PASS
Displacement Ux — joint 3 (roof) (in) SRSS · in 18.844 18.81 +0.183% PASS
Moment — story-1 column base (jt 1) (kip·in) SRSS · kip·in 12640 12624 +0.126% PASS
Moment — story-2 column base (jt 2) (kip·in) SRSS · kip·in 6025 6024 +0.016% PASS
Moment — floor-1 beam at column (jt 2) (kip·in) SRSS · kip·in 9813 9792 +0.219% PASS
Moment — roof beam at column (jt 3) (kip·in) SRSS · kip·in 5224 5220 +0.079% PASS
§7

Modal combination

MethodRoof Ux (in)Δ
SRSS18.844 +0.183%
CQC18.83 +0.108%

The reference (Chopra) uses the SRSS modal combination; §6 compares STRIX’s SRSS response to it. This table runs STRIX’s independent CQC combination (Der Kiureghian) on the same per-mode responses and reports the governing roof displacement under each method. The two modes are well separated (T₁/T₂ ≈ 2.66), so CQC and SRSS agree closely and both land within tolerance of the same independent reference — verifying both combination paths, not only the one the reference happens to use.

§8

Conclusion

PASS

STRIX reproduces the periods, SRSS displacements and column/beam bending moments of the canonical CSI 1-020 / Chopra 13.11 frame to better than a quarter of a percent — as closely as SAP2000 does. This verifies the complete STRIX response-spectrum pipeline: the modal solve, the per-mode inertia-force analysis with element force recovery, the spectral scaling, and both the SRSS and CQC modal combinations — the core of STRIX’s seismic-analysis capability.

§9

References & analysis files

  1. CSI SAP2000 Software Verification, Example 1-020 — Response-Spectrum Analysis of a Two-Dimensional Rigid Frame.
  2. A. K. Chopra, Dynamics of Structures, Ex. 13.11, p.521 (Prentice Hall, 1995) — independent solution.
  3. E. L. Wilson, A. Der Kiureghian & E. P. Bayo, EESD 9(2), 1981 — CQC modal-combination rule. STRIX harness: buildRsaPy → opensees.pyd → rsa_modal.bin.
Engine
v1.0.6 (opensees.pyd)
Run date
2026-08-19
Record
records/SR1.json
Evidence archive
verif-evidence-eng1.0.6-win-x64.zip · SR1/
sha256
(pending publish)