Equation: Formula for Calculating a Skycraper's Sway

Mercredi, 08 Décembre 2010 13:00

Equation: Formula for Calculating a Skycraper's Sway

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Photo courtesy: Taipei 101

A skyscraper is a giant tuning fork. Give one a good knock — like with an earthquake or a heavy gust of wind — and it’ll start vibrating at its own natural resonance frequency (about seven octaves below the lowest notes on a piano). If you’re on the top floor of, say, the

1,667-foot-tall Taipei 101, you could find yourself swaying back and forth abruptly, a total of up to 2 feet within five seconds. Highly barfogenic. So Taipei 101’s designers hung a pendulum inside the building — in this case, they used an equation like the one below to determine that the megastructure needed a 730-ton weight with giant shock absorbers bolted to its bottom. It’s called a tuned mass damper, and when the tower starts to bend in the wind, the pendulum swings at the same frequency in the opposite direction, pulling the building upright and damping vibrations. It still sways, but subtly and smoothly. Here are the factors that come into play. <![CDATA[ #skyscraper_cont { display:block; float:left; clear: position:relative; width:660px; margin-top:16px; padding:0px; } .last_cont { } #formula_img { display:block; float:left; margin-right:16px; } .formula_elem { float:left; margin-right:12px; width:130px; border-left-style:solid; border-left-color:#342D7E; border-left-width:5px; padding-left:5px; } .last_cont .formula_elem { width:112px; } .formula_elem.first { clear:right; width:220px; margin-right:0px; } .formula_elem.last { margin-right:0px; } #content #skyscraper_cont p { font-size:1.2em; line-height:1.1em; margin:0px; } .formula_elem img { display:block; float:left; margin:0px 6px 5px 0px; } ]]>