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Félix Candela 8-Lobed Hypar Groin Shell Vault
Thin-shell reinforced concrete groin vault (Ø 44 m, H = 13.5 m, t = 60 mm) formed by 8 intersecting hyperbolic paraboloid lobes on 8 inclined V-piers.
Félix Candela pioneered ultra-thin reinforced concrete shells by exploiting the doubly-ruled geometry of hyperbolic paraboloids (hypars), allowing straight timber formwork to generate anti-clastic curved surfaces with pure membrane compression and virtually zero bending moments. This 44 m diameter octagonal umbrella vault (inspired by the Los Manantiales restaurant in Xochimilco) combines 8 saddle hypar lobes intersecting along diagonal groin arches, supported by 8 peripheral inclined V-piers. WebCAE proves the extreme efficiency of the 60 mm thick shell, calculating membrane stresses, groin arch compression, vibration modes, and buckling factors.
1. Geometry & FEA Mesh
- •Geometry: 8 symmetric hyperbolic paraboloid shell sectors spanning Ø 44.0 m with a central apex elevation of 13.5 m, supported on 8 perimeter V-shaped concrete piers at R = 22 m.
- •Shell discretization: 512 MITC4 quad shell elements with ultra-thin concrete thickness t = 60 mm (1/730th of the span diameter).
- •Groin arches & free edges: 280 frame beam elements modeling the 8 intersecting valley groin arches (0.35 × 0.25 m) and cantilevered parabolic free perimeter eaves.
- •System size: 576 nodes, 280 beam members, 512 shell quads, 3,408 DOFs with validated edge matching between adjacent hypar leaves.
2. Loads & Boundary Conditions
- •Pinned and fixed base supports (6 DOFs constrained) at the 8 perimeter pier foundation pads (z = 0).
- •Structural self-weight of micro-concrete (E = 28 GPa, ν = 0.20, ρ = 2,400 kg/m³) distributed over the hypar surface.
- •Uniform live roof snow load (-1.0 kPa) acting vertically on the 8 hypar sectors.
3. Simulation Results & Findings
- ✓Extremely low maximum static deflection |u| = 9.83 mm at the outer scalloped crests under combined self-weight and live load.
- ✓Fundamental natural frequency f₁ = 3.77 Hz corresponds to an octagonal breathing and twisting mode of the 8 groin arches.
- ✓Critical eigenvalue buckling factor λ₁ = 87.7 demonstrates the incredible geometric stiffness of anti-clastic hypar curvature against oil-canning.
WebCAE showcases how parametric shell modeling validates thin-concrete shell concepts, proving that optimal geometric form drastically reduces material consumption while maintaining high buckling margins.
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