Cantilever shell strip with eccentric rectangular rib (Steiner theorem)

Cantilever plate strip stiffened by an eccentric rectangular rib: composite section bending stiffness verified against the Steiner parallel axis theorem and flush-in/flush-out sign invariance.

Tolerance:

5%

Problem statement

Geometry

Cantilever strip L = 2.0 m, width b = 0.2 m, thickness t = 0.01 m. Stiffening rib: rectangular cross-section w = 0.01 m, h = 0.03 m on common mesh nodes along the strip centerline (j = 2).

Material

Structural steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³.

Boundary conditions

Fully clamped at root i = 0 (all 6 DOFs). Transverse tip load P = 100 N distributed across tip nodes at x = 2.0 m.

Measured quantity

Vertical tip deflection w at x = 2.0 m. Analytical Steiner composite section: w_ref = 9.2775 mm (I = 1.4351e-7 m⁴). Compare flush=outer (w = 9.2840 mm, 0.07% error), flush=inner invariance (0.00% difference), and concentric rib without eccentricity ecc=0 (w = 33.88 mm vs 33.72 mm, 0.48%).

WebCAE Terminal

units m
material E=2e11 nu=0.3 density=7850
frame up=z
frame patch geom=quad p00=0,0,0 p10=2,0,0 p11=2,0.2,0 p01=0,0.2,0 nu=40 nv=4 t=0.01
frame stiffen patch=1 j=2 section=rect w=0.01 h=0.03 flush=outer
frame support patch=1 side=i0 dofs=all
frame load node=41 force=0,0,-12.5
frame load node=82 force=0,0,-25
frame load node=123 force=0,0,-25
frame load node=164 force=0,0,-25
frame load node=205 force=0,0,-12.5
frame solve static
frame probe disp node=123 comp=uz id="tip"

Results comparison

Updated: 2026-10-19 · WebCAE solver