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Cylindrical pipe holding up a screen (real world project) 
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#19
Feb313, 11:37 AM

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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. 


#20
Feb313, 01:13 PM

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


#21
Feb313, 05:02 PM

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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 nonrotating 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. 


#22
Feb313, 06:07 PM

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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? 


#23
Feb313, 07:22 PM

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#24
Feb313, 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) 


#25
Feb313, 08:06 PM

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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... 


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Feb313, 08:55 PM

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#27
Feb413, 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 simplysupported 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 simplysupported 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 largerdiameter SAE 4130 steel pipe. If you choose a largerdiameter steel pipe, then give us the pipe OD and ID, and we can check your simplysupported deflection calculation. 


#28
Feb513, 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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