A hexagonal core of concrete walls and three wings round it, each two corridor walls with a hammerhead wall across its end and columns down its faces: the wings buttress the core, and the core holds the wings. The wings step back 9 m at a time, one after another round the tower, until only the core is left at the top of its 160 storeys, 592 m up, where a steel spire goes on for another 220 m. This is the structure of the Burj Khalifa in Dubai. The El Centro earthquake shakes the ground along x.
The first 20 s of El Centro, as they happened, the movement drawn larger than it is. Beside it, the ground's acceleration and the movement along x of the spire's tip and of the roof, over the same 20 s.
The model
| Group | What it does |
|---|---|
| 1 - Geometry | The sliders - Core, Corridor walls apart, Wing width, Module, Modules a wing, Storeys, Storey height and Spire - and a Python component that draws the tower from them: each storey's walls as a mesh of panels, a storey tall and up to two modules long; the columns and beams of the wings; the spire, a mast held at each of the top eight floors by spokes from the core's corners; the feet; each floor's nodes and the one it is driven from, for the diaphragms; each node's share of its floor's mass; and the spire's tip and the roof, which the charts follow. |
| 2 - Members | The walls 800 mm of concrete, a Plate Fiber Section of an nD material, as ASD Shells; Concrete C30/37 from Material Library for columns 1.2 × 1.2 m and beams 0.6 × 1 m, RectangleCS sections; the spire a steel tube 8 m across and 60 mm thick, a CircleCS; all as ForceBeamColumn. |
| 3 - Supports and floors | Every column and wall built in at the ground, with a Support; and every floor a Rigid Diaphragm - its nodes move together in its plane, as a concrete floor makes them - driven from one of its nodes. |
| 4 - Ground motion and masses | The El Centro record, as in the other earthquakes, along x. A Mass Point at every node of every floor: Floor mass kg/m² of the floor's area - its slab, finishes, facade and some of what is in it - shared between its nodes. |
| 5 - Transient analysis | Assemble, with an MPCO Recorder of the displacements alone, which is all the view reads; Damping, Rayleigh's from Damping and its two frequencies; the Newmark Integrator; Analysis Step, a step a sample of the record; Analysis Settings for a transient analysis with the Linear algorithm, one solve a step, as an elastic model needs; and Run Analysis. |
| 6 - Results | A Model View of the analysed model at Step, deformed 20 times, its supports drawn, its colours over 0 to 800 mm for every step alike, with a Legend. Drag Step to go through the record. |
Its 10 100 elements are past the free limit of 50: it needs a licence. The analysis takes about eight minutes, its walls the most of it on a laptop; then each step takes a second or a few to draw as you drag Step.
The ground motion
El Centro, 18 May 1940, the north-south component: 0.32 g at its peak, 2 s in, the first 20 s of it. A Path Time Series of its accelerations shakes the ground under the whole structure through a Load Pattern's UniformExcitation type, and Run Analysis follows it step by step, 0.02 s at a time, a transient analysis with Newmark's average acceleration. Damping is Rayleigh's, 2% of critical at two frequencies that bracket the modes that matter. Ground motion scale makes the record stronger or weaker, Duration takes more or less of it.
What it shows
The tower's walls sway as one, slowly - its first period is 7.5 s - and its roof moves 1.1 m at the most. The spire, thin and light on a heavy tower, whips about on top of it: its tip moves 5.3 m at the most, 19.3 s in, still swinging wider as the 20 s end, far more than the roof under it - and past the top of the colours, which stop at 800 mm so that the tower's own movement shows. It is a model of how the tower's structure works, made from its published shape and sizes, not a model of the tower itself: its members' sizes and its floors' mass are a designer's guesses, it is built in at the ground rather than standing on its foundations, and the real tower has much more in it.
The moment it moves the most, and the record up to then.
Try
- Spire at 0: the tower alone.
- Modules a wing at 4: shorter wings, a slimmer tower that sways further.
- Duration at 31 s, the whole record: it takes half as long again.
