What’s the technology that made buildings of sky-scraping heights possible? Building
higher brings up unique challenges that if left unchecked could have disastrous consequences.
In this video, we explore the technologies that rendered skyscrapers possible. Specifically,
we focus on Taipei 101 and its ability to resist wind loads that exceed 200km/hr.
In the early days, the design of high-rise structures did not consider any wind loads.
The weight of the construction materials was so high that made the self-weight of the building
the most critical load to be resisted. As materials improved, the strength-to-weight
ratio increased which allowed for relatively more flexible and taller structures.
As structures became taller, the wind became the predominant force that engineers needed to deal
with. The wind usually becomes the governing load for structures above 40 storeys high. The
reason for this is three-fold. The wind speed tends to increase with the increase in height.
The open space at higher altitudes allows for higher wind speeds due to the fewer obstructions
that could slow down the wind. The second, and more obvious reason is the
increase of the surface area of the building which provides a larger platform for the wind to push
against. And the third and most important reason is related to the sway of the building. According
to Bennet’s book on skyscrapers, the sway is usually limited to 1/500 of the building’s height.
This means that for a 500m tall building the maximum allowed sway of the top floor should be no
more than 1 meter. One meter may sound like a lot, but this limit becomes increasingly hard to meet
as the height of the building increases. With the increase in height, structures become much more
flexible and easier to sway by the wind forces. In fact, the tip displacement increases according to
the fourth power of the height of the building. To limit this displacement,
engineers apply a variety of techniques. To reduce the aerodynamic loads on skyscrapers,
designers implement modifications that change the flow pattern around the building
or break up the wind affecting the building façade. Common modifications are setbacks such as the ones
seen on Burj Khalifa or an inward-tapering façade such as the Transamerica Pyramid. Aerodynamic tops
can also release a big part of the wind pressure that builds upon the building’s façade. An example
of an aerodynamic top is the Shanghai World Financial Center which has its aerodynamic feature cleverly disguised
in the architectural aesthetic of the building. Taipei 101 implements all of these aerodynamic
modifications that effectively reduce the aerodynamic loads by 25%. However, due to
its geographic location and exposure to Typhoons with extreme wind speeds exceeding 150km/h,
these modifications are not enough to limit the sway of the building. To illustrate
how insane these wind speeds are, remember that it takes a wind speed of about 100km/h
to derail a freight train which is 50% less than the wind gusts expected to hit Taipei 101.
The most effective way to counteract these wind loads is to increase the stiffness of
the building. This is achieved by introducing additional braces or in general increasing the
sizes of the beams and columns. This would shift the building’s oscillations away from the critical
period zone that matches the period of the wind gusts and avoids possible resonant behavior.
This can be illustrated on the wind spectral density plot. We won’t go into detail about
the generation of this plot, for now, the only important thing is to know that the
peak of the curve shows the frequencies for which the wind carries the most power.
We want the frequency of our structure to be as far away from this peak as possible.
In simple terms, this means that we want our structure to oscillate at a different rate
than the blowing of the wind. This rate at which the structure oscillates is called the natural
period of vibration and is dependent only on the building itself for example the height,
size of members, materials used, and so on. Making the structure more flexible and “bendy”
moves the building to the left side of this spectrum since flexible structures
oscillate much slower. In contrast, making the structure stiffer moves the
building to the right side of the spectrum. The region all the way on the left side of the
graph is not available to us since there is no construction material that could achieve
that level of flexibility and yet still be stiff enough to carry the self-weight of the structure.
The obvious alternative is to make the structure stiff and move to the right side of the spectrum.
This is what is usually done in practice; however, Taipei is located in a seismically active zone
whose density spectrum falls right into the right side of the plot. So now the engineers
have two peaks to avoid. Moving all the way to the right would require columns the size of a room
which is economically not feasible. The only available space is to place
the structure somewhere between these two peaks meaning the structure would need to have just
enough stiffness to be away from syncing in with the wind loads but not stiff enough to
be too affected by earthquake loads. This makes Taipei 101 the ultimate “catch22” scenario.
This is where the ingenious solution comes into play. This solution had been known for
a long time however this is one of the first implementations on this scale.
The engineers designed the building such that its natural period of vibration
is about 6.7 seconds [4]. This places the building within the wind susceptible range and produces
high wind sways. However, the engineers also added a giant hanging ball within the structure
that would sway opposite of the sway of the building and in that way pull the building back to
its equilibrium position. This ball hangs in the form of a pendulum from the 92nd down to the 87th
floor. Its mass is about 730 tons. The ball is also known as a Tuned Mass Damper is so heavy that
there was no crane that could lift it into place. Instead, the pieces had to be brought up to the
top of the building and then assembled there. The key idea of the mass-tuned damper is that
it always opposes the sway of the building. The massive pendulum is also equipped with
dampers that convert its kinetic energy from the sway into heat. This way, the Mass Tuned Damper
removes energy from the building that would have otherwise resulted in 40% larger sways. Keep
in mind that the explanations presented in this video are simplified to avoid technical details
that the non-engineering audience might find boring. However, there are many more details
that have to be considered in the design of a skyscraper. For example, torsional motion induced
by wind forces is extremely destructive and could be a great threat if left unchecked. Additionally,
flexible structures could exhibit vortex-induced motions that cause cross-wind displacements that
in many cases govern the design of skyscrapers. But these topics require deeper explanations
and will be left for another time. Thanks for watching, let us know in the
comments how much of this video you managed to understand. We always strive towards making simple
yet informative videos that are easily understandable for the general public,
though sometimes we do end up deep into technicalities that could confuse the audience.
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