Response spectrum: single-degree-of-freedom oscillator under the SP 14.13330 spectrum

Response spectrum analysisPASS · 0.07%

A massless cantilever with a tip point mass is a single-degree-of-freedom oscillator. Its period, spectral displacement u = Sa(T)/ω² and base shear V = m·Sa(T) under the SP 14.13330.2018 design spectrum (site intensity 8, soil category II) are checked against… show full text

Tolerance:: 5%

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Problem statement

Geometry: Massless cantilever L = 3 m, square section 100 × 100 mm (beam elements), point mass 1000 kg at the free end.
Material: Steel: E = 200 GPa, ν = 0.3 (the beam itself carries no mass).
Boundary conditions: Fully fixed at the root. SP 14.13330 spectrum: site intensity 8, soil category II (K0 = K1 = Kψ = 1), base excitation along z, CQC (the square section makes the y/z modes degenerate: CQC treats them as fully correlated), missing-mass correction off.
Measured quantity: Period T = 2π√(m/k), tip displacement u = Sa(T)/ω², base shear V = m·Sa(T) and the mass coverage 100 %. The reference Sa(T) is taken from the SP 14 spectrum builder at the analytic period, so the card verifies the oscillator physics and the wiring, not the norm tables.

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
beam length=3000 section=rect w=100 h=100 n=8 scheme=cantilever P=1
mass node=3000,0,0 m=1000
solve spectrum code=sp14 intensity=8 soil=II dir=y combine=cqc nmodes=3 missingmass=off
probe spectrum_displacement id="u"
probe spectrum_base_shear dir=y id="V"
probe spectrum_cumulative_mass dir=y id="cum"
probe frequency mode=1 id="f1"

Results comparison

Reference value	T = 0.461718 s, Sa = 4.65384 m/s², u = 25.1307 mm, V = 4653.84 N
Our result	T = 0.461918 s, u = 25.1471 mm, V = 4652.83 N, coverage 100 %
Deviation	0.07%
Tolerance	5%
Status	PASS · 0.07%
Element family	Beam element
Mesh details	8 Euler–Bernoulli beam elements (massless) + point mass 1000 kg at the tip, 54; modal: webcae_solve (native)

Updated: 2026-10-21 · WebCAE solver