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Eiffel Tower 3D Space Truss
Full-scale 3D latticed space truss modal analysis and extreme wind pressure verification with analytical X-brace intersections.
The 300-meter Eiffel Tower is a landmark example of an exponentially tapered 3D latticed space truss designed to optimize wind resistance and gravity axial loads. The engineering model features four 4-chord box legs converging into a single vertical shaft, 4 intermediate platforms, ground-level arches, and an upper spire. WebCAE computes unconstrained orthogonal vibration mode pairs, self-weight static settling, and wind drift across 93k+ discretized beam degrees of freedom.
1. Geometry & FEA Mesh
- •Geometry: base footprint 125 × 125 m, top platform elevation 300 m, mast tip 320 m, with exponential silhouette profile b(z) = 2.5 + 60·(e^(-4z/300) - e^(-4))/(1 - e^(-4)).
- •Legs & shaft: 4 box legs with X-bracing (analytical trapezoid diagonal intersections with shared nodes), merging into a square shaft above the 115 m platform.
- •Platforms & arches: platforms at 57, 115, 276, and 300 m; four double elliptical arches with intermediate hangers structurally coupled to leg chords.
- •Member categorization: 18 distinct structural cross-sections (chords, diagonals, rings, arches) totaling 1,040 principal joints, 2,959 members, and 93,852 FE DOFs under multi-element discretization.
2. Loads & Boundary Conditions
- •Fixed supports (all 6 DOFs) across 16 lower chord base nodes (4 legs × 4 chords) anchored to massive concrete footings.
- •Gravitational self-weight (frame gravity on, total steel mass 6,171 t) with vertical settlement check.
- •Distributed transverse wind pressure (40 m/s gale) applied along all member projections, delivering global overturning shear.
3. Simulation Results & Findings
- ✓Fundamental orthogonal bending mode pair f₁ = 0.3050 Hz and f₂ = 0.3050 Hz (exact C4 symmetry match within 3e-13, with 86% kinetic energy concentrated in the shaft).
- ✓Second bending modes f₁₃ = 1.0417 Hz and f₁₄ = 1.0728 Hz coupled with mast tip deflection; torsional mode f₃ = 0.6347 Hz.
- ✓Top platform lateral deflection under 40 m/s storm wind reaches 371 mm (H/810 drift ratio), while self-weight buckling safety factor reaches λ₁ = 15.57.
Structural engineers and heritage restoration teams use WebCAE to assess space truss behavior, evaluate wind gust responses, and inspect member force utilization directly in the browser. The lightweight .caeweb container packages complete 3D axial force diagrams and mode animations for instant client presentations without CAD overhead.
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- ✓Up to 1.5M+ DOFs (direct sparse solver)
- ✓Native Windows & macOS Apps (100% offline)
- ✓Nonlinear Contact & Buckling (Kσ, MITC4, RBE2/RBE3)
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