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Aug 18, 2022
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How tall could you build a skyscraper?

How tall could you build a skyscraper?

The sky is literally the limit. This is the Jeddah Tower and it will be the tallest building in the world. A record that will likely hold for some time. Its height will be more than 1000 meters. Historically, it is not uncommon for owners to keep the final figure a secret until completion. So that some other builder does not try to outdo them and “steal the crown”.

Built in 1931, the Empire State Building is 381 meters above the ground. In 1973, this record was broken by the World Trade Center building at 417 m. And by 2004, the tallest building was the Taipei Tower at 448 meters.

This is the Jeddah Tower and it will be the tallest building in the world.  A record that will likely hold for some time.  Its height will be more than 1000 meters.

The height of the buildings has grown by 67 since 1931. And then the Burj Khalifa in Dubai, at 739.44 meters. That’s over 300 meters taller than the new tower. And almost as much higher than the previous record holder.

As the Saudis began work on an even taller building, it’s worth wondering just how high you could get. If your only limits were ego and strength of materials.

Utility problems

Have you ever tried to make a sand tower? It is very easy to make a small crumb. This will be enough to stand. But if you try to build a really big castle, it will flatten like a pancake.

The same thing happens with buildings. The buildings we build are strong, but we couldn’t make one that goes into space, otherwise the top would crush the bottom.

We can make buildings quite tall. The tallest buildings are almost 1 kilometer high. And we could probably make buildings 2 or even 3 kilometers tall if we wanted to. And they could still stand under their own weight. Above this can be tricky.

But besides weight, a tall building would have other problems.

The height of the buildings has grown by 67 since 1931.  And then the Burj Khalifa in Dubai, at 739.44 meters. That's over 300 meters taller than the new tower.  And almost as much higher than the previous record holder.

One of the problems will be the wind. The wind is very strong at the top, and the buildings must be very strong to withstand the wind.

Another big problem, oddly enough, is the elevators. Tall buildings need elevators, as no one wants to climb hundreds of flights of stairs. If your building has many floors, you need many different elevators. Because there will be so many people trying to come and go at the same time.

If you make a building too tall, it will all be taken up by the elevators and there won’t be room for regular rooms. The absolute true height limit of buildings is not constructive. This is a vertical transport. As long as we have to bring people down to and from ground level, we’re going to be devoting an obscene amount of floor space to the equipment that allows us to do this.

Elevators and wind are big problems, but the biggest problem will be money.

To make a building really tall, someone has to spend a lot of money. And nobody wants a really tall building to be tall enough to pay for it. A building many kilometers high will cost billions of dollars.

We can make buildings quite tall.  The tallest buildings are almost 1 kilometer high.  And we could probably make buildings 2 or even 3 kilometers tall if we wanted to.  And they could still stand under their own weight.  Above this can be tricky.

Fresh air

Another thing to consider is air. In other words, you can’t open a window for fresh air, it has to be pumped in. Can you imagine how scary it would be to open a window on the 150th floor?

In any case, you will need mechanical devices to draw in fresh air. But that means you need vertical ducting space and a LOT. Because you will be moving a lot of air. Thus, even more space is taken out of your structure for transporting air, and not people.

In short, the efficiency of buildings decreases significantly as they get taller. In terms of usable floor space, not in terms of land use, efficiency increases in this case. Due to the need for vertical movement of both people and “utilities”.

Is there a limit?

Another thing to consider is air.  In other words, you can't open a window for fresh air, it has to be pumped in.  Can you imagine how scary it would be to open a window on the 150th floor?

However, the question of the maximum height of a skyscraper seems like a logical next step. At first glance, this may seem like a simple calculation based on mathematics.

We would make the structure out of the strongest conventional material: T1 low carbon vanadium steel. And they would determine the height by comparing the tensile strength of the material with its density.

If we compare these numbers, we get the height: 8.96 kilometers. But this is the maximum only for a certain design, a wide T1 steel flagpole in the absence of wind.

A more realistic height suggests a building with half its volume being empty space. Used for living and other purposes. And where there is a significant amount of self-weight from floors, windows, people, furniture, etc. Applying these numbers, we get the maximum height, but only for a cylindrical building without a safety margin and without taking into account the wind.

about 7 kilometers

This is more than ten times more than the Burj Khalifa. But this probably underestimates the maximum value for a steel or even concrete building. Because the cylinder is not the optimal shape for maximum height.

Huge Pyramid

If the towers had been built conical or pyramidal, the height could have been much greater: three times as much.  Because the volume of the cone, and hence its weight, is 1/3 of the weight of the cylinder, given the same base and height.

If the towers had been built conical or pyramidal, the height could have been much greater: three times as much. Because the volume of the cone, and hence its weight, is 1/3 of the weight of the cylinder, given the same base and height.

The tapered shape is better for a very tall tower. And this shape is chosen for “The Shard”, the second tallest building in Europe. But it’s not the ideal shape. The ideal is like the Eiffel Tower.

Made of glass and concrete

But before talking about this form, it is worth talking about building materials. At the heights we are discussing, it becomes quite ridiculous to talk about a steel and glass building.

Tall steel buildings have serious vibration problems. Even at the heights, long before they are destroyed by wind and vibration, people at the top will begin to experience severe seasickness. Because of this, the tallest buildings were constructed from concrete and glass.

Concrete is not suitable for bridges as concrete does not stretch well. But concrete can be quite strong in compression. It’s also much cheaper than steel when you consider the simplicity of the design.

The Trump Tower in New York and Chicago was the first major building to be built in this way. This and the second building in Chicago were considered aesthetic marvels until Trump became president.

Like the Trump Tower, the Burj Khalifa is made of concrete and glass. And from now on, let’s start from this construction.

Concrete is not suitable for bridges as concrete does not stretch well.  But concrete can be quite strong in compression.  It's also much cheaper than steel when you consider the simplicity of the design.  The Trump Tower in New York and Chicago was the first major building to be built in this way.

H’ max-cone-concrete = 3 x H’ max-cylinder-concrete = 13.7 kilometers.

That this is a reasonable number can be seen from the height of Everest. Everest is an uneven cone with a height of 8.84 kilometers. This is not much less than what we calculated above.

To achieve this height with a wind-resistant building, you must make the base fairly wide. As in the case of Everest. In the absence of wind, the base of the cone could be much narrower. But the maximum height would be the same. But the shape of the cone is not optimal for a very tall building.

Because there is no real limit to how big the bottom can be. There is hardly a limit to how tall a tower can be. However, aesthetics impose limitations even in the absence of wind.

Calculations show that stability requires that the area of ​​the tower doubles for almost every 3 kilometers of height. But the area expansion rate also continues to increase as the tower gets heavier.

And it can be assumed that due to the artistic ego, no builder will want a tower with an inclination of more than 45 °. The Eiffel Tower has an inclination of 51°.

Thus we get the height = 69 kilometers.

This is eight times the height of Everest.

To achieve this height with a wind-resistant building, you must make the base fairly wide.  As in the case of Everest.  In the absence of wind, the base of the cone could be much narrower.  But the maximum height would be the same.  But the shape of the cone is not optimal for a very tall building.

tower of babel

From the foregoing, it is clear that our current buildings are far from the maximum achievable, even for building with conventional materials. We should be able to build buildings several times higher than Everest. Such Buildings are worthy of Nimrod, the builder of the Tower of Babel, for several reasons.

Not only because of the lack of a safety margin, but also because the height is much higher than the height of the highest mountain. Also, as with the construction in Babylon, there is probably a social problem.

Suppose the floors are 5 meters apart. The first 3 kilometers of the tower will have 600 floors. Each of which will be the size of Rostov-on-Don. Assume that the population per floor will be about 1 million.

From the foregoing, it is clear that our current buildings are far from the maximum achievable, even for building with conventional materials.  We should be able to build buildings several times higher than Everest.  Such Buildings are worthy of Nimrod, the builder of the Tower of Babel, for several reasons.

Thus, it can be assumed that the tower will accommodate 1.28 billion people. With a population of this size, the tower will develop different cultures and begin to speak different languages.

They may well go to war – a real problem in a confined space. There is probably a moral here somewhere, for example, too much unity is not good. It is possible that 1.28 billion is too much even for one country.

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