cylindrical pipe holding up a screen (real world project)


by massta
Tags: cylindrical, holding, pipe, project, real, screen, world
Q_Goest
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#19
Feb3-13, 11:37 AM
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Quote Quote by rollingstein View Post
@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
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Feb3-13, 01:13 PM
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Quote Quote by Q_Goest View Post
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
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Feb3-13, 05:02 PM
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Quote Quote by rollingstein View Post
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
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Feb3-13, 06:07 PM
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Quote Quote by Q_Goest View Post
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
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Feb3-13, 07:22 PM
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Quote Quote by massta View Post
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 Do instead of L in the deflection equation. I've edited the post. You should get a deflection of 0.8967"
massta
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#24
Feb3-13, 07:54 PM
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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
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Feb3-13, 08:06 PM
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Quote Quote by massta View Post
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
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Feb3-13, 08:55 PM
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Quote Quote by massta View Post
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
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Feb4-13, 08:42 PM
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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
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Feb5-13, 10:16 AM
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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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