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Willis Tower: 442 m Bundled Tube Skyscraper (Sears Tower)
Fazlur Khan 3×3 bundled tube concept, 4 stepped setback tiers, framed tube perimeter, and twin broadcast spires.
Verify the structural efficiency of the bundled-tube concept in minimizing shear lag across diaphragms, resisting lakefront storm winds, and ensuring stability across all 4 setback tiers.
1. Geometry & FEA Mesh
- •9 structural steel framed tubes in a 3×3 matrix (each tube 22.5×22.5 m, total base 67.5×67.5 m)
- •Tier 1 (z = 0 to 200 m, level 50): All 9 tubes rise together as a rigid composite bundled tube
- •Tier 2 (z = 200 to 260 m, level 66): 2 diagonally opposite corner tubes terminate, leaving 7 active tubes
- •Tier 3 (z = 260 to 360 m, level 90): 2 more corner tubes drop off, creating an iconic cruciform 5-tube tower
- •Tier 4 (z = 360 to 442 m, roof): 3 more tubes terminate, leaving central 2-tube core rising to roof
- •Twin broadcast spires rising from the central tube cores from z = 442 m to 520 m
- •Framed tube columns and deep spandrel beams with diaphragm caps at each setback level
2. Loads & Boundary Conditions
- •Base column nodes fixed in 6 DOFs across all 16 column lines at ground z = 0
- •Self-weight gravity with floor and mechanical equipment dead loads
- •Chicago lakefront lateral wind pressure along +X with atmospheric boundary layer gradient
3. Simulation Results & Findings
- ✓Bundled tube design exhibits minimal shear lag with uniform axial stress across perimeter column lines
- ✓Smooth drift curve up to 442 m validates the aerodynamic and structural logic of progressive setbacks
- ✓Fundamental sway frequency f₁ and torsional modes reflect the shifting center of rigidity across tiers
Validates historical benchmark tall-building structural systems in modern cloud FEA, providing immediate educational and professional insight into tube mechanics.
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