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Analysis of Cable Balustrade
2

Analysis of Cable Balustrade

Analysis of Cable Balustrade

(OP)
Hello, has anyone had to calculate the tensile stress on a cable balustrade which has UDL applied along its length?

Looking from guidance online most calculations seem to be based on an initial sag, which we don't know and for horizontal loads it will probably be 0mm.

We know the tensile capacity of the cable from the manufacturer but that's all, we are back checking something which has already been constructed on site to keen to keep this as a cable balustrade.

Thanks

RE: Analysis of Cable Balustrade

These kinds of calculations are fairly straight-forward, but it can be a bit of a challenge to wrap your head around the concept first.

Quote (BD26)

calculations seem to be based on an initial sag, which we don't know and for horizontal loads it will probably be 0mm

You must specify the initial sag as part of your design. Alternatively, you can specify the initial tension. Your calculation starts with either assuming an initial sag and then calculating the initial tension, or vice versa. Note that your initial sag cannot be 0mm - as your initial sag is reduced, the initial tension increases...in order to get 0mm you would technically need an infinite tension (for short spans and light cable you can get to very near zero sag, but there is still some).

I don't have time write the full procedure, but the basics are this:

- Use your install conditions to define initial sag/tension (you have an existing condition, measure the sag)
- Use this to determine your initial cable length
- With a UDL, you can use the same equations you've used to calculate initial tension/sag but this time use the UDL instead of the cable-weight. In this calculation, use your initial cable length/sag.
- This will give you a larger tension than you had in the self-weight condition, thus a larger strain and an increase in cable length. Calculate the increase in cable length.
- With the slightly longer cable, you'll have more sag and less tension - and less strain. This is where you need to start iterating for a solution

That is the basis of the procedure. If you have a long stretch of cable you also need to consider large temperature swings as that can have a big impact on the sag/tension.

RE: Analysis of Cable Balustrade

There is a procedure in AASHTO sign spec (Standard and LRFD) as Appendix A for span wire structures.

For a cable guardrail/fence structure, the allowable deflection with the applied point live loading on the cable typically dominates the stress and force calculations. The selfweight of the cable can typically be ignored in situations where a live load is applied.

If it doesn't have to support any loading other than the initial applied, then the solution becomes incredibly simple - just pull the cable to an initial tension within the allowable stress. Unless it's spanning an incredibly long distance, the sag will be virtually imperceptible.

RE: Analysis of Cable Balustrade

Is this a hand rail in a building or a guard for vehicles? I remember coming across a calculation for a handrail by a manufacturer, where they essentially limited the final sag such that the code prescribed maximum gap between wires was still met.

RE: Analysis of Cable Balustrade

(OP)
It's a barrier around a raised platform (raised 600mm) within a gym environment, there is basically posts with 3 cables running between them so spacing between cables must be about 300mm vertically. They have wrapped these cables in foam to make it look like a boxing ring, although the area will only be used for fitness classes.

Don't know what building control will think of it but we are trying to prove structurally the cables are fine for people leaning against them etc.

RE: Analysis of Cable Balustrade

"a raised platform (raised 600mm) ... with 3 cables ... spacing between cables must be about 300mm vertically."

Is the spacing (300mm) connected with the raised height (600mm) ? Is this meant to look like a boxing ring ? (I guess so, since you say that !?)

If I had 3 cables spaced 300mm apart, I'd get 900mm height (you wouldn't have one cable on the floor). The problem I see with this is that it isn't very high, and easy for people to overbalance … 900mm is only about 36". I'd expect at least 5' to have people leaning against it.

Spacing between cables is probably limited by code. 300mm (12") sounds a little large ?

Your original post says "UDL" … does someone leaning on your cable model well as a UDL ? (and not as a point load ?)

another day in paradise, or is paradise one day closer ?

RE: Analysis of Cable Balustrade

(OP)
Please see the attachment, it only looks like vertical spacing is a requirement where there may be children present. The architect may argue that there will be no children present in the gym to get around this regulation.

The 300mm spacing was an estimate as I dont have the project infront of me right now. Normally barriers in UK are designed to a height of 1100mm.

I am trying to design for both a UDL and a point load. When designing balustrades according to eurocodes and document pd6688 there are two load values given for this occupancy class, a PL(0.5kN in this instance) and a UDl (0.74kN/m in this instance) so I would be checking both and designing to the worst case as per code.

RE: Analysis of Cable Balustrade

BD26:
You better make sure that your lateral load on the one or two top cables is at least equivalent to two heavy guys running across the ring and crashing into the cable. Sooner or later, you can bet that some jokers will make that happen in a gym setting. I’ll bet the wire rope spacing is more like 200, 200 & 200mm. And, as soon as you start the problem, you will see that the biggest issue is going to be anchoring the four corner posts (as cantilevers), so that they don’t just buckle over under the cable loading. How are the wire ropes fixed at the corner posts? You will see that a 100lb. lateral load on the wire rope leads to a wire rope tension of many hundreds of pounds, and thus, a mighty high lateral load on the corner posts. Look for some ref. books on wire rope tension structures for how to approach the wire rope problem.

RE: Analysis of Cable Balustrade

(OP)
I can check the pictures when I am in office tomorrow and try to get better idea of the spacing, it was a colleague who visited site.

Yes that's true, we should have a rethink of the load we are looking to apply, bit of engineering judgement.

The posts for the wire rope is 100x100 SHS's. I will need to have a look at the baseplate connections depending on what comes out of this analysis, as some are only fixed into timber.

Product is similar to link at bottomw of this post, same end connections. I will need to check how these are currently being fixed onto the SHS with my colleague tomorrow.

Could you recommend any books? I have been looking everywhere but they all seem to assume an inital sag or have more information before starting the analysis.

Link - https://www.ironmongerydirect.co.uk/product/balust...

RE: Analysis of Cable Balustrade

The key parameter is the max allowable deflection of the cables. At 2% or 3% of the span, you'll be pushing the capacity of a 1/4" or maybe even a 3/8" wire rope, and you'll be putting a huge load on the corner posts. Allowing deflection of 10% of the cable span, the tension in the wire drops dramatically. Superimpose your force vectors on the cable deflected by a 200 lb point load at midspan and you'll see what I mean.

RE: Analysis of Cable Balustrade

Quote (BD26)

I have been looking everywhere but they all seem to assume an inital sag or have more information before starting the analysis.

Did you not see my first reply? First reply to your post. All of the solutions use initial sag because it is a key parameter. And since this is an existing condition, initial sag should be easy to determine.

RE: Analysis of Cable Balustrade

(OP)
CANPRO, sorry for not getting back to original post.

How would there be sag in the horizontal direction, would there not only be sag in the vertical? Or do you mean the sag after the horizontal imposed load has been applied?

RE: Analysis of Cable Balustrade

No, I'm talking vertical direction. You need to define your initial conditions before you can determine what is happening in the loaded condition.

The initial tension and initial sag are linked together, if you know one, you can calculate the other. Once you know the initial sag, you can calculate the initial cable length.

Once you have the initial cable length, you can start looking at your loaded condition. If it is a UDL, as I mentioned above, use the same equations you have for cable under self weight, but replace the self weight with your UDL. If you have a point load, you can assume your loaded cable forms a triangle between the supports and applied load (from there its easy to calculate the cable tension, basic statics). You can now calculate the tension in the cable, the strain in the cable, and the increase in length. With the increase in length, you now have a new loaded geometry and a new tension/strain/cable length - you need to iterate until this converges.

A few other things to looks out for:

- cable properties - they have an effective area and an effective elastic modulus.
- support movements - small movement in the supports will effect your cable tension

RE: Analysis of Cable Balustrade

Most railings of this type have a rigid top rail. As you go through the loading conditions, you should discover why. A 200 lb point load on a cable that is deflected to 5% of the span length by that load creates a horizontal (along the span) force vector of 2000 lb and a wire tension of about 2010 lbs. At 1% deflection under that same load, the horizontal force becomes 10,000 lb, and the tension is 10,002 lb. The tension force must be resisted by the anchorage (post) at the end of the cable. Do you see why the maximum deflection of the cable allowed (as determined by the initial sag and the additional movement in the system under load) is the defining parameter of the system?

RE: Analysis of Cable Balustrade

(OP)
Thanks for your replies everyone.

CANPRO - very good description that made it all alot clearer to me now, initial sag is only really to find your initial tension.

HOTROD - Yeah I have seen various handrails with rigid top rail throughout, although never had to design on. I can understand why now maximum deflection if the cable has such a big influence on the design.

Is there a percentage sag you would normally specify for the initial condition, I don't really know what value seems reasonable. 1 percent of 1500mm span is 15mm deflection (initial sag), I thought that might be slightly high.

RE: Analysis of Cable Balustrade

You will have to calculate (or back calculate) what horizontal deflection under load will keep the horizontal force within the capacity of the posts and cable. From there, you can determine what the initial sag would be. The length of the cable without live load ('initial' length) can be determined as the length with the cable deflected under live load minus movement at the anchorage (post connection) due to the live load minus the stretch in the cable due to live load. The actual sag under uniform gravity loading will be a catenary, but you could approximate it using triangles. If your posts are fairly rigid, the vertical sag will not be much different than the horizontal deflection due to live load, since the stretch in the cable will be fairly small.

Whether the amount of initial sag that keeps the loads on the posts and cable acceptably low, is acceptable to the client is up to you to find out.

RE: Analysis of Cable Balustrade

It uses horizontal or vertical cables in place of spindles, glass, and mesh for infill.
The total minimum height required varies per building codes depending on the area and target use of either residential or commercial
Cable is very strong in tensile strength, with a breaking strength in excess of 1000 lbs for these types of uses, and is a suitable in-fill material for a railing ("guard" in ICC codes). Typical diameters are 1/8", 3/16" for residential and 3/16" and 1/4" for commercial applications.[4] There are many different types cable and strand (also referred to as wire rope).
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