Cantilever shell strip with eccentric tee rib (Steiner theorem)

Bending of a cantilever shell strip stiffened by a tee stringer with its flange flush to the skin: centroid offset and composite section inertia verified against analytical Steiner formulation and concentric baseline.

Tolerance:

5%

Problem statement

Geometry

Cantilever plate strip L = 2.0 m, b = 0.2 m, t = 0.01 m. Tee stringer: total height h = 0.04 m, flange width bf = 0.03 m, web thickness tw = 0.004 m, flange thickness tf = 0.006 m, attached flush=outer (flange contacting skin).

Material

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

Boundary conditions

Fully clamped at root side i = 0 (all 6 DOFs). Tip vertical force P = 100 N distributed across tip nodes.

Measured quantity

Tip deflection w at centerline tip node. Composite section Steiner reference w_ref = 9.7462 mm, FE computed w_FE = 9.7550 mm (0.09% deviation); concentric baseline ecc=0 gives w_ref = 33.72 mm, w_FE = 33.88 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=tee d1=0.04 d2=0.03 d3=0.004 d4=0.006 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