Dynamics: two-span beam with eccentric section offset and internal moment hinge (CE)

Implicit transient dynamicsPASS · <0.01%

Corotational beam-shell transient dynamics supporting rigid section-centroid offsets (fields 13..18 via transformation T) and internal bending-moment hinge releases (Lagrange-multiplier constraint equations C·u = 0). A clamped-clamped two-span beam with an int… show full text

Tolerance:: 5%

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Problem statement

Geometry: Two-span beam 2 × 1000 mm (total span 2 L = 2 m), rectangular section 50 × 100 mm; internal bending hinge releasing θ_z at mid-span node 2.
Material: Steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³.
Boundary conditions: Both outer ends fully clamped (nodes 1 and 3); vertical point load P = 1000 N at mid-span hinge node 2; Newmark β = 1/4, γ = 1/2 starting from static equilibrium.
Measured quantity: Mid-span deflection ratio w_hinge / w_continuous = 4.0 (two cantilevers meeting at a hinge vs continuous clamped beam) and dynamic-to-static equilibrium residual (< 10⁻⁶ m).

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 m
material E=2e11 nu=0.3 density=7850
frame node id=1 x=0 y=0 z=0
frame node id=2 x=1 y=0 z=0
frame node id=3 x=2 y=0 z=0
frame section rect b=0.05 h=0.1
frame member from=1 to=2 release_end=mz
frame member from=2 to=3
frame fix node=1
frame fix node=3
frame load node=2 fy=-1000
solve frame

Results comparison

Reference value	w_hingew_continuous = 4.0000\|w_dyn − w_stat\| = 0 м
Our result	w_hingew_continuous = 3.9999\|w_dyn − w_stat\| < 1e-9 м
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Element family	Beam element
Mesh details	STRUCT_BEAM_EXT, 2 elements + дублированный узел шарнира (5 уравнений связей CE + множители Лагранжа λ_CE)

Updated: 2026-10-27 · version not recorded