cylindrical pipe holding up a screen (real world project)

rollingstein

Quote by Q_Goest

If you need to reduce the deflection of the span further and make it essentially flat, you could use one of the equations above and make a beam that’s bent to that curve, fix the ends as per the equation and then when it’s loaded, it will flatten out.* Of course, if this bent bar were to rotate, it would be horrible, so you would want to keep the bar steady and have some way of having the screen rotate on the bar such that the bar doesn’t need to rotate.

One last option would be to take a pipe/tube and deflect the ends slightly so that you put a moment on the ends of the bar so as to help reduce the sag in the middle. The bar could then rotate if you wish, unlike the other option above. In other words, imagine holding a thin plastic bar horizontally out in front of you and watching it sag in the middle, then twist your hands so the sag comes out of it. You could do the same here and allow the pipe/tube to rotate on bearings but the bearings would be canted slightly so the sag is reduced. Not sure if that would completely eliminate the deflection, I'd have to think about the equations, but that's another possibility.

@Q_Goest

What's the difference between your two ideas? I like them, but they somehow seemed very similar to me. Is it just the difference between elastic and permanent strain?

Q_Goest

Quote by rollingstein

@Q_Goest

What's the difference between your two ideas? I like them, but they somehow seemed very similar to me. Is it just the difference between elastic and permanent strain?

Thanks. It's kinda hard to explain without pictures. But with the first one, you don't allow the bar to rotate and instead you have the screen rotate around the bar. The bar would be bent prior to installation and then when under load it would straighten out, kinda like a flatbed truck.

For the other idea, you have a straight bar that you allow to rotate but you tweak the ends slightly to help eliminate the sag. So you actually put a moment on the ends of the bar which helps to cancel the moment created in the bar by the linearly distributed load. The stresses would never exceed yield so the bar would be straight if you removed it from the installation and laid it on the ground for example.

rollingstein

Quote by Q_Goest

Thanks. It's kinda hard to explain without pictures. But with the first one, you don't allow the bar to rotate and instead you have the screen rotate around the bar. The bar would be bent prior to installation and then when under load it would straighten out, kinda like a flatbed truck.

If the inner bar won't rotate it may be more cost-efficient to go for an I beam / box or some similar non symmetric section?

You only need a high MI to resist deflection along the direction gravity acts. A cylinder might be wastefully exuberant.

AlephZero

Quote by rollingstein

A cylinder might be wastefully exuberant.

If you need a cylinder to roll the screen around, you might as well use it to provide stiffness as well.

The bottom line is that I for a thin cylinder is approximately ##\pi r^3 t## but the mass is proportional to ##rt##. Also the deflection is proportional to w/I.

So ignoring the weight of the screen compared with the cylinder, changing the thickness will not reduce the deflection (w/I stays the same) but the deflection is proportional to ##1/r^2##.

So what you need is a large radius cylinder.

If you try to make an internal non-rotating support, it will need to have a significant depth to get the stiffness, so you will still need a big cylinder radius to fit around it.

If you could split the screen into two parts with the two rollers at a shallow angle, so the two screens overlap when they are unrolled, you could have a central support, and halve the length of each roller, which would make a big difference.

massta

Quote by Q_Goest

For the other idea, you have a straight bar that you allow to rotate but you tweak the ends slightly to help eliminate the sag. So you actually put a moment on the ends of the bar which helps to cancel the moment created in the bar by the linearly distributed load. The stresses would never exceed yield so the bar would be straight if you removed it from the installation and laid it on the ground for example.

This idea is great. By deflecting the ends with a special bracket, it will put an opposite deflection in the beam. When the beam has a load it will straighten out. Only problem is the beam will bow when the screen is unrolled, so better to make it as stiff as possible.

Going through the numbers again for a simple supported beam:

Pipe/beam:
OD: 2in
ID: 1.87in
Length between simple supports: 258in
Total weight/load: approx 80lbs (includes all materials) or 0.2899lb/in
L = Length (258in between supports)
E = Young's modulus for steel material (30,000,000 psi)
I = pi/64 * (OD^4 - ID^4); I = 0.18514in^4

Deflection: d = w * OD^4 / (384 * E * I)
d = 0.2899lb/in * (2^4) / (384 * 30,000,000 * 0.18514in^4)
d = an incredibly small number!

making a mistake somewhere....ugh
so deflection has nothing to do with Stress or Moment?

Q_Goest

Quote by massta

This idea is great. By deflecting the ends with a special bracket, it will put an opposite deflection in the beam. When the beam has a load it will straighten out. Only problem is the beam will bow when the screen is unrolled, so better to make it as stiff as possible.

Going through the numbers again for a simple supported beam:

Pipe/beam:
OD: 2in
ID: 1.87in
Length between simple supports: 258in
Total weight/load: approx 80lbs (includes all materials) or 0.2899lb/in
L = Length (258in between supports)
E = Young's modulus for steel material (30,000,000 psi)
I = pi/64 * (OD^4 - ID^4); I = 0.18514in^4

Deflection: d = w * OD^4 / (384 * E * I)
d = 0.2899lb/in * (2^4) / (384 * 30,000,000 * 0.18514in^4)
d = an incredibly small number!

making a mistake somewhere....ugh
so deflection has nothing to do with Stress or Moment?

Sorry, my bad. I had D_o instead of L in the deflection equation. I've edited the post. You should get a deflection of 0.8967"

massta

Pipe/beam:
OD: 2in
ID: 1.87in
Length between simple supports: 258in
Total weight/load: approx 80lbs (includes all materials) or 0.2899lb/in
L = Length (258in between supports)
E = Young's modulus for steel material (30,000,000 psi)
I = pi/64 * (OD^4 - ID^4); I = 0.18514in^4

Deflection: d = w * L^4 / (384 * E * I)
d = 0.2899lb/in * (258in^4) / (384 * 30,000,000psi * 0.18514in^4)
d = 94.9 in

How did you get 0.8967?
hmmm...

I was using this eq. in my original math:
D = (F x L^3) / (3 x E x I)

Q_Goest

Quote by massta

Deflection: d = w * L^4 / (384 * E * I)
d = 0.2899lb/in * (258in^4) / (384 * 30,000,000psi * 0.18514in^4)

Check again. You should get 0.6022. I accidentally input 285" in length and got .8967".

The Superbowl is being distracting! lol

Oh... and when deflecting the ends of the beam you would maintain a moment on the ends of the beam so that as it rotates it remains relatively straight. You might imagine a couple of rolling element bearings on the end of the beam so that they tend to point the beam upwards toward the center. Those bearings would simply maintain a moment on the end of the beam tending to flatten the curvature. The beam wouldn't change shape as it rotates so the sag in the beam wouldn't change as it turns. Think about it...

Q_Goest

Quote by massta

Deflection: d = w * L^4 / (384 * E * I)
d = 0.2899lb/in * (258in^4) / (384 * 30,000,000psi * 0.18514in^4)
d = 94.9 in

How did you get 0.8967?
hmmm...

I see what you did. You raised the moment of inertia (0.1851 in⁴) to the 4'th power. Those are just units. Understand?

nvn

massta: You would want to keep the design as simple as possible. Therefore, you would want to use just a simply-supported beam, which is just your steel pipe. Roll your screen directly onto your steel pipe. Rotate the pipe faster, to obtain the same effect.

Therefore, for your current given data, the simply-supported beam midspan deflection would be, y = 76.49 mm, which is fine. This is not a huge deflection, and is OK. If you want the deflection to be less, then simply use a larger-diameter SAE 4130 steel pipe. If you choose a larger-diameter steel pipe, then give us the pipe OD and ID, and we can check your simply-supported deflection calculation.

nvn

massta: You perhaps could run a tight string line (or strong thread) across the room, then loosen it until it sags 76 mm. Then see if this amount of sag is noticeable or acceptable to you. If not acceptable, gradually tighten the string line, until you determine the maximum amount of sag (deflection) you find acceptable. Next, find what SAE 4130 steel pipe/tube sizes are available to you, then compute the deflection, to see if it exceeds your maximum allowable deflection. In this way, you can determine the minimum steel pipe/tube size (OD and ID) required.

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