Home / Games / Seismic Diagrid Tower
🏙️ Seismic Diagrid Tower
In a diagrid there are no columns — the diagonals do everything. That's the problem: resisting shear wants shallow diagonals (35°), resisting bending wants steep ones (toward vertical), and you only get one angle. Which one wins depends on how slender the tower is. Change the aspect ratio and watch the optimum move.
Tower
Your Diagrid
Live Result
—
Optimal Angle for This Tower
—
Drift Penalty vs Optimum
Shear stiffness contribution (∝ sinθcos²θ)—
Bending stiffness contribution (∝ sin³θ)—
🎯 Goal: land within 2° of the optimum. Then slide the aspect ratio from 1 to 10 and watch the optimum climb from ~51° to ~74°.
The stiffness relationships here were derived from
first principles (unit-displacement work on an inclined axial member) rather
than quoted, so they're checkable: shear ∝ sinθcos²θ, maximized at exactly
arctan(1/√2) = 35.264°, confirmed both analytically and by numerical sweep.
The optimum is found by minimizing total drift, not by maximizing a
weighted sum of stiffnesses — during derivation the weighted-sum approach was
found to degenerate toward θ→90° (vertical columns, zero shear capacity),
which is physically absurd. That degeneracy is pinned by a regression test so
the reasoning stays visible (
engine/diagrid.js). For typical tall
buildings (H/B 4–7) this gives 66–71°, consistent with the 60–70° range
reported by Moon et al.Method
Moon et al. (2007)"Diagrid Structural Systems for Tall Buildings" — diagonals carry both shear and bending; optimal angle depends on aspect ratio.
ScopeRelative drift comparison at fixed member area — a design-intuition model, not an absolute deflection calculation or a substitute for full analysis.