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Shukhov Hyperboloid Lattice Tower
Doubly-ruled hyperboloid steel lattice shell modal and buckling evaluation with exact 3D spatial intersection nodes.
Vladimir Shukhov's hyperboloid radio tower on Shabolovka consists of 6 stacked single-sheet hyperboloid sections constructed entirely from straight inclined steel generators and horizontal circular rings. Each pair of intersecting straight generators forms an exact spatial intersection that must act as a monolithic structural joint to prevent member slack and out-of-plane buckling. WebCAE models the complete 148-meter lattice tower, verifying wind lateral deflection, ring ovalization modes, and overall elastic buckling capacity.
1. Geometry & FEA Mesh
- •Geometry: total height 148.0 m, 6 telescoping hyperboloid sections, base diameter 40.0 m, top ring diameter 4.2 m.
- •Straight generators: 48 straight inclined struts in lower tiers tapering to 24 in upper tiers, with twist angle φ = 180° · levels / n ensuring coincidence at section joints.
- •Intersections & rings: 3D closest-approach spatial line intersections resolved into common nodes via spatial hash registry (mergeTol = 0.1 mm), joined by polygonal stiffening rings.
- •Composition: 1,128 nodes, 3,288 beam members, and 6,768 degrees of freedom (288 base boundary restraints).
2. Loads & Boundary Conditions
- •Fixed boundary conditions (all 6 DOFs) applied to the 48 base ring foundation nodes on the ground circumference.
- •Gravity self-weight (frame gravity on, structural steel mass 4,200 t) transferred entirely through axial strut compression.
- •Lateral aerodynamic drag load distributed along all member vectors simulating extreme wind pressure.
3. Simulation Results & Findings
- ✓Fundamental orthogonal lateral sway modes f₁ = 0.428 Hz and f₂ = 0.428 Hz, followed by torsional and ring ovalization modes.
- ✓Linear static base reaction equilibrium matches analytical steel mass within 3e-9 relative tolerance.
- ✓Eigenvalue buckling analysis confirms high structural stability against diamond-cell lattice diamond rhomb distortion under combined self-weight and wind.
Architectural and structural engineers use WebCAE to explore lightweight diagrids, cooling towers, and lattice transmission masts using pure geometric parametric scripts. The .caeweb container delivers full 3D interactive mode visualization and axial stress contours to project stakeholders in browser tabs instantly.
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- ✓Nonlinear Contact & Buckling (Kσ, MITC4, RBE2/RBE3)
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