Cable Analysis for a Backstop Net

[KirkGH]

I've read through the posts on cables and gathered that the most appplicable equation to use to analyze the the attached schematic is wL^2/8=TH.
T = tension in cable
H = amount of sag in cable

The attached diagram shows the support for a net suspended over some bleachers. The net spans 6 feet between secondary cables. The secondary cables are attached between yet other cables. I included a sample calculation of the tensions in the cables for a 2.4 psf wind load which shows a 60 kip tension in the primary cable (which is supposed to supported by a 38 foot cantilevered tube). This can't be correct though, it sounds too high. Can anybody offer guidance on analyzing this cable system?

KGH

 

[EngineeringEric]

The wind load is high for this type of structure, may be correct. i just ran your numbers on my spreadsheet and got similar values (i had some self weights and other things so do not use my name)
1ft sag = 2455
2ft sag = 1233
3ft sag = 827

Sorry i don't have a solution other than confirming those loads for the 39.5' spans. I believe your calculation for the attaching cable may be conservative, but not much... Reducing the spacing of the cables and more sag would reduce their tension, which should reduce the load in the attaching cable.... see what max tension you can have in that cable and work backwards to get spacing and sags... Free Body diagrams are your friend with cables sometimes, sometimes they are not :/

 

[KirkGH]

Thanks Eric.

Do you know if I can assume a higher sag condition with for wind loads that at service loads? Let's say I want to keep the sag at 1'-0" for typical conditions but when the wind blows for a 90 mph wind load it can sag for 6 feet. Will the structure have any give to it?

KGH

 

[KirkGH]

For the wind load we're taking the net surface area/gross area to get a percentage of wind (12%). Know of any better way?

KGH

 

[BAretired]

There is a significant error in your calculation of cable forces. The secondary cables will not have a length of 36.9' because the primary cables are sagging 6' in a direction parallel to the slope of the secondary cables. Thus the shortest secondary cable near the midspan of the primary cable will be approximately 25' long.

Also, the load on the primary cables will not be uniform, so the magnitude of the primary cable force would be substantially smaller than you have calculated.

BA

 

[BAretired]

I'm not sure that the system of cables being proposed is a good one, but have not really given the matter sufficient thought. I would be concerned about flutter of the net with sudden changes in wind direction. My current belief is that you should have some hold down cables to contain wind uplift thus adding some control to unpredictable wind flutter.

BA

 

[KirkGH]

"Thus the shortest secondary cable near the midspan of the primary cable will be approximately 25' long."

Good point, that is a significant error. However, wouldn't the length of the secondary cable be closer to 36.9'- 6'=30.9' (not including sag from the primary cable at the north end)?

"so the magnitude of the primary cable force would be substantially smaller than you have calculated"

Yes, I'll need to run the calcs but doubtful the tension force in the primary cable will get down to the 10 kips I need to get down to to keep my 38 foot cantilevered pole to a reasonable size.

I don't think there is room for hold down cables, the ground needs to be free of obstruction.

Thanks for the input, it is very much appreciated. I'm hoping somebody will propose an alternate method of calculating (lower) forces for this structure that is eating my shorts for breakfast.

KGH

 

[BAretired]

If the primary cable at the north end is half the length of the south end cable, its sag would be about 3'. With a net primary cable sag of 6'+3' = 9', the shortest secondary cable would be about 28' in length. Its tension would be about 2.4*6*28²/8*1 = 1411# with one foot sag. Other cables would have more tension even if the sag was proportionately increased, so it seems unlikely that you will be able to reduce cable tension to 10 kips unless you use a lower wind pressure or provide more sag.

Also worth noting is that the secondary cables on each exterior edge will have substantially more tension than the typical secondary cables because they are resisting the tension in the netting material. This will contribute to a larger force on the cantilevered pole.



BA

 

[dhengr]

KirkGH:
I’m not quite as willing to wade through the math as BA is, and he’s very good at it, but he is certainly on the right track with his posts.

One thing I do know is that cables don’t work worth a darn when slack or work too well in compression either. The whole roof (net) system must be shaped in such a way that the cables are always in tension, and shaped with enough sag so you can tolerate the forces. Many times a primary force cable goes over the top of a column, which is then load primarily in compression, but can also move some distance (any direction) at its top to accommodate the cable movement under loading, almost a pinned-pinned strut, and the cable then continues on to a deadman in the ground, or a structure that can take the loads. Trying to cantilever a tube column 38' can probably be done, but it is going to be on heck of a column and foundation.

BA suggested that you need tie downs to keep the cables from fluttering. And, one way to do this is with two cables in tension, tied together with struts or cables, but apposed in their catenary direction. That is, with the top cable (one of your primary cables) concave opening upward, and a second, lower cable concave opening downward, tied to the top cable, and keeping it from fluttering. Your secondary cables kinda do this in one direction for your primary cables, when they are cut to proper length and tensioned during installation.

These cable roof systems are really fairly complex structures. Your primary cables could be light trusses, in the shape of an angle. The vert. truss to carry gravity loads and the horiz. truss to carry the secondary cables and netting. Then, the trusses framing into the columns would form light portal frames w.r.t. lateral loads.

 

[KirkGH]

Ok dhengr and BA, thanks for your time.

KGH

 

[KirkGH]

I think I may have found a book that proposes a method of analyzing cables. Others may find it of use but its math looks to be beyond my capabilities.

Cable Structures by H. Max Irvine.

I found it on

http://www.ScribD.com.

This is my first introduction to the website and it appears to have some value with providing access to various engineering texts among other more general subject matter.

KGH