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High-Rise Shear Core Wall (3D Buckling)
Rigorous 3D shell geometric stiffness matrix K_σ benchmark verifying cantilever core wall buckling and shear deformation against Euler-Greenhill theory.
The central elevator and service core serves as the primary lateral-load resisting spine for high-rise towers. In standard FEA formulations, evaluating the eigenvalue buckling multiplier λ₁ of a 3D box tube under distributed self-weight requires capturing both in-plane and out-of-plane membrane geometric stiffness K_σ across orthogonal walls. WebCAE validates core cantilevering deflection, natural bending frequencies, and Greenhill heavy-column critical buckling load within 0.52% of analytical closed-form solutions.
1. Geometry & FEA Mesh
- •Core geometry: height 288.0 m (72 stories × 4.0 m), cross-section 13.5 × 13.5 m with two internal dividing shear walls at x = ±2.25 m.
- •Material properties: reinforced concrete with E = 40.0 GPa, ν = 0.20, ρ = 2,500 kg/m³, wall thickness t = 0.6 m (total mass 35,000 t, distributed weight 121.5 t/m).
- •Section properties: area A = 48.6 m², moments of inertia I_x = 1.0671 m⁴, I_y = 1.2307 m⁴, shear area A_s,x = 16.2 m².
- •Mesh: 3,888 quad shell elements (mesh 9 × 72 per wall), 3,796 nodes, and 22,776 system degrees of freedom.
2. Loads & Boundary Conditions
- •Continuous 6-DOF clamped constraint at foundation level (z = 0) along all exterior and interior wall footprints.
- •Uniform lateral pressure p = 1,000 Pa applied to western and eastern walls (total lateral force 7.776 MN, overturning moment 1,119.7 MN·m).
- •Self-weight gravity load generating axial compression σ_z = 6.82 MPa at base elevation for geometric stiffness K_σ construction.
3. Simulation Results & Findings
- ✓Critical self-weight buckling multiplier λ₁ = 11.811 matches the Greenhill analytical solution (11.749) within 0.52% error.
- ✓Top lateral wind deflection u_top = 0.5408 m matches the combined Euler-Bernoulli flexure and Timoshenko shear solution (0.5481 m) within 1.34%.
- ✓Fundamental vibration frequency f₁ = 0.1267 Hz agrees with Dunkerley shear-corrected beam theory (0.1259 Hz) within 0.64%.
Design bureaus evaluate shear core wall dimensions and verify geometric stability margins under gravity loads before running multi-hour commercial FEA models. The pre-calculated .caeweb container delivers full 3D stress distributions and buckling mode shapes for structural peer review directly in modern web browsers.
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