Response spectrum: CQC for close frequencies (cantilever with a rotated section)
Response spectrum analysisPASS · 0.08%A cantilever whose section is rotated by 30° has two bending families with close frequencies (ratio 1.10) that are BOTH excited by a base motion along one global axis. The CQC base shear and tip displacement (components combined with their signs) are checked against a hand calculation with the Der Kiureghian correlation; SRSS is reported alongside. The base shear differs between the rules by more than 5 %; the tip displacement magnitude does not, because the two families vibrate in orthogonal planes (the card states this rather than hiding it).A cantilever whose section is rotated by 30° has two bending families with close frequencies (ratio 1.10) that are BOTH excited by a base motion along one global axis. The CQC base shear and tip displacement (components combined with their signs) are checked a… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Cantilever L = 2 m, rectangular section 50 × 55 mm rolled by 30° about the beam axis (beam elements, 80 per span).
- Material
- Steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³ (lumped translational mass).
- Boundary conditions
- Fully fixed at the root. Base excitation along the global y axis (dir=y), damping ζ = 5 % in the CQC correlation, missing-mass correction off, 8 modes (4 close pairs).
- Measured quantity
- Base shear V_y and tip displacement |u| from CQC against the hand calculation (all 8 x 8 correlation terms, signed modal contributions); the same quantities from SRSS as a control (the base shear must differ from CQC by more than 5 %).
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units mm
material E=2e11 nu=0.3 density=7850
beam length=2000 section=rect w=50 h=55 n=80 scheme=cantilever P=1 roll=30
solve spectrum code=custom points="0.001,4;0.02,4;0.1,2.5;0.3,1;2,0.3" abscissa=period unit=m/s2 dir=y combine=cqc zeta=0.05 missingmass=off nmodes=8
probe spectrum_base_shear dir=y id="Vcqc"
probe spectrum_displacement id="ucqc"
solve spectrum code=custom points="0.001,4;0.02,4;0.1,2.5;0.3,1;2,0.3" abscissa=period unit=m/s2 dir=y combine=srss zeta=0.05 missingmass=off nmodes=8
probe spectrum_base_shear dir=y id="Vsrss"
probe spectrum_displacement id="usrss"
probe spectrum_cumulative_mass dir=y id="cum"Results comparison
| Reference value | V_y(CQC) = 71.5297 N, |u|(CQC) = 0.883267 mm (ρ₁₂ = 0.523SRSS: 62.6063 N, 0.883296 mm) |
| Our result | V_y(CQC) = 71.5855 N, |u|(CQC) = 0.883738 mm (SRSS: 62.6395 N, 0.883767 mm) |
| Deviation | 0.08% |
| Tolerance | 5% |
| Status | PASS · 0.08% |
| Element family | Beam element |
| Mesh details | 80 Euler–Bernoulli beam elements, section 50×55 mm rolled 30°, 486; modal: webcae_solve (native), 8 modes (4 close pairs, f_b/f_a = 1.10) |
Updated: 2026-10-21 · WebCAE solver