Endless bridge around the equator and gravity

[Drat]

TL;DR

Do structural engineers understand how gravity works?

Hi, I’ve got a question.
it seems that engineers, structural mainly, don’t seem to understand how gravity works regarding an endless stationary (steel) ring/bridge around the equator.

Many if not all have said that such a ring would be modeled as two half circles pushing into each other. So the ring would need to be thousands of times stronger than the material...

I say, and many non-structural engineers agree, that the above assumption is wrong.

it is easily demonstrated with the following example...

Place a tube in a tray of water and attach strings through a funnel in the centre. Add equal self weigh of the tube and nothing will happen. Regular grade 350 steel will take almost 4,000 times it’s own weight.

One reply was that the ring “wouldn’t be floating on water anyway”... Another sent me the maths on how much weigh the tube would hold before it sank into the water... I had to explain that the water only represents lateral stability which is easily controlled and that the ring would be held in place with ground anchored cables. Hovering above the earth.

Because structural engineers are so knowledgeable about land bridges, is it possible that they cannot visualise how gravity would effect such a structure?

I have asked many to explain why they think that their model is right but they refuse to reply... Is this a common phenomenon/mind blockage amongst engineers?

Interested to hear your thoughts.
David

Here’s a link that pretty well confirms my analogy... surely they know what they’re talking about!

 

[PeroK]

What about the Moon's tidal gravity?

 

[Drat]

What about it?

 

[PeroK]

What about it?

It'll pull your bridge about a bit!

 

[Drat]

It'll pull your bridge about a bit!

Nah

 

[PeroK]

Nah

A bridge sustained by the force of chutzpah!

 

[Baluncore]

Many if not all have said that such a ring would be modeled as two half circles pushing into each other. So the ring would need to be thousands of times stronger than the material...

If what you are suggesting was possible, it should also be possible to cross a valley with a segment of the same bridge, pressing against the valley sides.

Using real materials, the radius of curvature would need to be much less than that of the Earth's surface. As a guide look at the vertical curvature of existing arch bridges that use available real materials in compression.

 

[Drat]

Nah

Same with heat expansion and contraction, wind and seismic... can you answer the question, ignoring all other factors, or you’re not sure? Two half circles pressing into each other or the table model?

If what you are suggesting was possible, it should also be possible to cross a valley with a segment of the same bridge, pressing against the valley sides.

Using real materials, the radius of curvature would need to be much less than that of the Earth's surface. As a guide look at the vertical curvature of existing arch bridges that use available real materials in compression.

No, land bridges touch the ground whereas an endless bridge does not. Bridges are limited on land to around 7km maximum using regular steel before they will crush axially from self weight.

 

[Drat]

Same with heat expansion and contraction, wind and seismic... can you answer the question, ignoring all other factors, or you’re not sure? Two half circles pressing into each other or the table model?

No, land bridges touch the ground whereas an endless bridge does not. Bridges are limited on land to around 7km maximum using regular steel before they will crush axially from self weight.

Same with heat expansion and contraction, wind and seismic... can you answer the question, ignoring all other factors, or you’re not sure? Two half circles pressing into each other or the table model?

No, land bridges touch the ground whereas an endless bridge does not. Bridges are limited on land to around 7km maximum using regular steel before they will crush axially from self weight.

but yes a section of the same bridge could easily cross a valley

 

[Nugatory]

No, land bridges touch the ground whereas an endless bridge does not.

In your design the ends of any given curved segment are held in place by the ends of the adjacent segments while the ends of a bridge crossing a valley are held in place by the ground. However, the forces within that segment are the same no matter what’s happening at the ends, so if a segment can’t cross a a valley a hoop of the same curvature won’t be able to go around the earth.

 

[Nugatory]

Many if not all have said that such a ring would be modeled as two half circles pushing into each other. So the ring would need to be thousands of times stronger than the material...

”Many if not all have said” is not an acceptable citation; without knowing what you actually heard, we don’t know whether it’s wrong or whether you’ve misunderstood. So where did you hear this and who said it?

 

[Drat]

Same with heat expansion and contraction, wind and seismic... can you answer the question, ignoring all other factors, or you’re not sure? Two half circles pressing into each other or the table model?

No, land bridges touch the ground whereas an endless bridge does not. Bridges are limited on land to around 7km maximum using regular steel before they will crush axially from self weight.

If what you are suggesting was possible, it should also be possible to cross a valley with a segment of the same bridge, pressing against the valley sides.

Using real materials, the radius of curvature would need to be much less than that of the Earth's surface. As a guide look at the vertical curvature of existing arch bridges that use available real

In your design the ends of any given curved segment are held in place by the ends of the adjacent segments while the ends of a bridge crossing a valley are held in place by the ground. However, the forces within that segment are the same no matter what’s happening at the ends, so if a segment can’t cross a a valley a hoop of the same curvature won’t be able to go around the earth.

a segment on the ground can go to a maximum of around 7km using regular steel. There are no ends on a ring though so the weight is evenly distributed around the ring... ground is the problem as it is a vertical force. With a ring there are no vertical forces, just the rings own self weight

 

[PeroK]

I wonder whether this bridge would gravitationally collapse even without the Earth? Given it's made from some known material.

 

[Baluncore]

No, land bridges touch the ground whereas an endless bridge does not. Bridges are limited on land to around 7km maximum using regular steel before they will crush axially from self weight.

As I understand it, the Earth has a circumference of more than 7 km. Surely the mass of any section of the ring must be supported by it's curvature and axial compression. What makes you think there is something special about bridges that do not touch the ground?

 

[PeroK]

As I understand it, the Earth has a circumference of more than 7 km. Surely the mass of any section of the ring must be supported by it's curvature and axial compression. What makes you think there is something special about bridges that do not touch the ground?

This is the blessing bestowed upon those who never studied engineering formally:

He has had no training in engineering, which he says is the reason he can think ‘outside the box’ and was a blessing in disguise.

 

[Frodo]

The engineers are correct. Let's do a simple calculation.

Imagine, for simplicity, the bridge is a footbridge and it is 1m wide and 1m deep and made of concrete.

Concrete weighs about 2,500 kg/m^3 so a 1 metre length of the bridge will weigh 2,500kg.

See the diagram below where the angles are exaggerated to show the effect.

The weight acts downwards and the compressive force P acts circumferentially.

Now the vertical components of the two circumferential compressive forces must be equal to the weight of the section so 2 x Pvert = 2,500kg, or Pvert = 1,250kg.

We now know Pvert - all we need to do is calculate P.

The angle theta to the Earth's centre is 1/6,366,000 radians or (1/6,366,000) x 2pi/360 degrees

Looking at the right we see that Pvert = P sin (theta/2) kg

So we have Pvert = 1,250kg = P sin (theta/2) kg

So P = 1,250/sin(theta/2) kg

Sin(theta/2) is sin(0.5/6,366,000) = 0.0000000789 which is very small.

So P = 1,250 / 0.0000000789 kg = 15,840,000,000 kg, or 15.8 million tonnes, which is very big.

Calculate the stress on the face. The face is 1m x 1m so it is 15,840,000,000 kg/m^2.

The maximum stress concrete can withstand is about 16,000 lb/in^2 which is about 16,000 x 39.37 x 39.37 / 2.2 kg/m^2, or 11,272,704 kg/m^2, or 11 thousand tonnes/m^2.

So, concrete can withstand 11 thousand tonnes per square metre and you are stressing it at 16 million tonnes per square metre.

It breaks long before the moon has any chance to affect things.

You can save yourself a lot of hard work by realising this problem is identical to a pressure vessel where every student remembers the formula Stress in wall = PD/2t (Pressure x Diameter/(2 x wall thickness)). Just plug in the numbers.

Engineers would have used this formula to calculate, in their heads, why no known material can build such a bridge - it doesn't even need pencil and paper.

So, in answer to your question: Do structural engineers understand how gravity works? The answer is yes they do ... even if you don't!

...

 

[Baluncore]

I have asked many to explain why they think that their model is right but they refuse to reply... Is this a common phenomenon/mind blockage amongst engineers?

No.
The problem is with people who are so convinced that they are right that they cannot, or will not, try to understand the mathematical theory behind structures. That is the real mind blockage.
https://en.wikipedia.org/wiki/Dunning–Kruger_effect

 

[Nugatory]

This seems like a good time to close the thread. As with all thread closures, you can PM me or any other mentor to ask that it be reopened to add more to the discussion - but we will not reopen it just to allow the same arguments to be repeated.