Forty storeys of a round steel tower, 36 m across, whose floors move out along x and back as it rises: 12 m out half way up, and back over its foot at the roof. Three rings of sixteen columns stand round an open core, with ring and radial beams and a 200 mm slab at every floor. The El Centro earthquake shakes the ground along x, the way it bows.
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 edge of the roof, over the same 20 s.
The model
| Group | What it does |
|---|---|
| 1 - Geometry | The sliders - Columns round it, Radius, Core radius, Storeys, Storey height and Bend - and a Python component that draws the frame from them: three rings of columns, from the core's to the outside's, each floor moved along x by Bend times the sine of its height over the tower's times π, ring and radial beams, a slab mesh round the core at every floor, the columns' feet, and the edge of the roof the charts follow. |
| 2 - Members | S355 from Material Library; box columns 700 × 40 mm, a Rectangle Hollow CS, and IPE600 beams from Steel Section Library, as ForceBeamColumn; 200 mm of concrete, a Plate Fiber Section, as ASD Shells. |
| 3 - Supports | Every column built in at the ground, with a Support. |
| 4 - Ground motion | The El Centro record from a Python component, its first Duration seconds times Ground motion scale; a Path Time Series of it; a Load Pattern of the UniformExcitation type, along the direction it shakes. |
| 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 25 times, its elements' edges and its supports drawn, its colours in iso-surfaces on the slabs over 0 to 240 mm for every step alike, with a Legend. Drag Step to go through the record. |
Its 6 400 elements are past the free limit of 50: it needs a licence. The analysis takes about three minutes 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, 5% 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 sways along x, its roof 236 mm off at the most, 6.4 s in. Bowed, it is a little softer the way it bows - its first period is 2.2 s that way, and 2.0 s across, against 1.9 s both ways with Bend at 0: its columns lean, first out and then back in, and lean columns stiffen a frame less than straight ones.
The moment it moves the most, and the record up to then.
Try
- Bend at 0 for a straight tower, at 25 for one that bows out twice as far.
- Columns round it at 24: more columns, a stiffer tower.
- Core radius larger: a bigger hole, and less floor.
