Cable loads in horizontal fall restraint system 2

[LSAnderson]

Hi All, I am busy designing a horizontal cable fall restraint system which goes around 3 platforms. The geometry of the fall restraint is in the attached picture, which shows a top view of the system. The cable has a diameter of 15 mm. The applied loads are in the horizontal plane and are according to guidelines for a fall restraint - which say that a minimum load of 3 kN at the midspan should be used per person and we are assuming 2 people per platform as a conservative first pass.

If I ignore self weight of the system (I think the vertical sag will be negligible compared to the deflection caused by the applied loads) how can I calculate the maximum deflection per span as well as the reaction loads at each anchor point? I have seen an equation that states theta = (W/EA)^1/3 which can then be used to calculate deflection and as a result the reaction loads. Would this equation be applicable in this case? And if so I just want to clarify the units of theta - is this in radians?

It should be noted that the cable is able to slide freely through the 4 intermediary anchor points and it only fully fixed at the two terminations. I am not sure if this will influence the results or not.

 

[LSAnderson]

 

[human909]

There is alot to consider here. Might be better to go the the guys who do this every day.

Some things to consider
-you will some initial tension on the line.
-a longer line require more tension to achieve the same deflection requirements
-how close is this to an edge? A fall restraint system can readily become a fall arrest system if it is close to an edge. Given you mention platforms it seem like this might need to be rated for fall arresting.

But if you really insist on doing this then an iterative approach can work. Start with a given deflection deflection and load and work backwards with the known cable stiffness. If you don't know the elasticity of the cable you plan on using, then find out! That is a good start.

 

[LSAnderson]

Thanks for your response. Yeah I will have an initial tension on the cable (I still need to determine how much tension). The closest edge is about 1.3m from the cable and the operator harnesses are 1m so I have about 300mm to play with before it becomes a fall arrest (which I am hoping to avoid as it increases the design load by 5x).

Thanks I will try an iterative approach as you have described and see what I can come up with.

 

[klaus.]

usually the cables have no pre-tension ...they are hanging 'lose'
also usually the manufacturer of the fall arrest system will define what forces you need to apply to the support points especially the end points.

 

[human909]

usually the cables have no pre-tension ...they are hanging 'lose'
also usually the manufacturer of the fall arrest system will define what forces you need to apply to the support points especially the end points.

It would really depend on the cirucmstances. A long cable will have a hell of alot of slack if hung "loose". Even nominally taught it might still have too much slack as soon as a load is put on it. There is a reason why tensioners exist for this purpose.

(Disclaimer: I have zero experience in engineering these systems. But I've dealt with plenty of fall restraint and fall arrest system for recreation.)

Yeah I will have an initial tension on the cable (I still need to determine how much tension).

If you have the load and the maximum deflection then that will give you then tension and total cable stretch. You can then work backwards with the elasticity of the cable to reach the require tension.

The closest edge is about 1.3m from the cable and the operator harnesses are 1m so I have about 300mm to play with before it becomes a fall arrest (which I am hoping to avoid as it increases the design load by 5x).

 

[LSAnderson]

If you have the load and the maximum deflection then that will give you then tension and total cable stretch. You can then work backwards with the elasticity of the cable to reach the require tension.

Ah this is a very helpful point. Yes, then I can set the deflection to be the maximum allowable at the design load and then calculate the required tension in the cable. Thanks you, I think this will help me get to the answer I am looking for.

 

[CANPRO]

I have designed many multi-span fall arrest systems like this - they can be a bit tricky to get your head wrapped around the problem, but it boils down to some simple concepts. I only have time for a quick list, but happy to expand on these points later:

[ul]
[li]You can't ignore the self-weight of the cable, you need this value to set-up the unloaded condition of the cable[/li]
[li]In your initial condition you will have some value of sag in each span, the sag will be different for different span lengths[/li]
[li]You can draw a free-body diagram of each half span - you will have the sag, self-weight of the cable, and the initial installation tension. You use this free-body diagram to relate these (3) parameters. You should know the cable-weight, and now you can either specify the initial sag or initial tension (calculate the 3rd parameter using the free-body diagram[/li]
[li]Once you have the initial sag in each span determined for the installation condition, you can estimate your total cable length[/li]
[li]Once the cable is loaded, all of the slack will pull the loaded span - you'll have a straight-line cable in the other spans and a triangle shape in the loaded span[/li]
[li]You can use the shape of triangle to determine the loaded tension in the cable[/li]
[li]Use the loaded tension in the cable to determine the strain in the cable - with the strain calculate a new cable length, with the new cable length calculate the triangle shape....from here you need to iterate until your results converge[/li]
[/ul]

That covers the basics, here are a few other notes:

[ul]
[li]If you have a really long run of cable you might want to build in an allowance for temperature change between install and active use - I usually check a 20deg C swing in temperature, if it gets warmer after install you'll increase the loaded sag, if you decrease temperature you'll increase your loaded tension[/li]
[li]Its really important to define the use of this cable. How many workers at a time? If one falls, how do they rescue him? If the rescue plan involves the cable you should design for (1) worker hanging from the cable and another impact. You can't just keep designing for additional rescue workers falling, but I've always felt that (1) self weight + (1) impact was reasonable[/li]
[li]Statistically, it is unlikely that all workers will fall and subject the line to impact loads simultaneously - unless they're all on something like a suspended stage that could fail have them all fall at the same time[/li]
[li]The loaded sag is a critical value that must be communicated to the end-user. They need this for their fall distance calculation - if you're aware of hazards close below, this might become a critical design parameter.[/li]
[li]Make sure you're using the effective area of the cable and the effective elastic modulus in your calculations[/li]
[/ul]

 

[klaus.]

It would really depend on the cirucmstances. A long cable will have a hell of alot of slack if hung "loose". Even nominally taught it might still have too much slack as soon as a load is put on it. There is a reason why tensioners exist for this purpose.

Well a cable always has a certain tension ... but I have never used pretensioning cables for fall arrest system on roofs
what should be the purpose of pretension ??? makes no sense to me

 

[CANPRO]

klaus, the biggest reason to pre-tension your cable would be to reduce the loaded sag of the cable. If you have a hazard not far below you might want to control the loaded sag. Another reason is if the cable is close to the roof/floor and is in contact with it, you might get accelerated corrosion in the cable. I've seen this with galvanized cable in fall arrest systems before.

Given no other restraints I agree its best to limit the install tension as it reduces the demand on the system.

 

[Geoff13]

Lots of great advice in CANPRO's posting.

I would highlight that in your sketch the maximum deflection will happen with workers in only one span and no workers in the other spans. Thus all the initial cable slack will pull into that span, allowing the greatest deflection there under load.

A 15 mm cable will be able to handle a large pretension (to minimize the initial slack), but will create large loads on the 2 anchors and 4 corners. And these will increase with the worker loads. In this case all spans loaded will likely create the maximum cable tension and anchor loads. This may be a difficult trade-off between high pretension to minimize slack vs low pretension to minimize anchor forces.

Some aspects of your problem may be simple equations, but others will be trial-and-error. I use Excel's Goalseek tool to handle the trial-and-error when designing fall arrest systems.

 

[LSAnderson]

Thanks everyone for your input. As Geoff13 put it the problem is really a matter of a tradeoff. I can either keep the deflection to a minimum, but then the reaction forces get really high and the anchor fittings have to become very bulky, or I can reduce the reaction loads - in which case the amount of deflection becomes large enough that it defeats the point of the system, which is to constrain the operators from reaching the edge of the platform.

That being said I have decided to simplify the problem by only applying the loading to a single span at a time as applying it to all spans at once constitutes all operators falling simultaneously, which is very unlikely. I have contacted the lead engineer for this project regarding how he wants to proceed and I'm just awaiting feedback from him.

 

[phamENG]

CANPRO is spot on. Once you've read up and done a few trials by hand, here is a great tool:

Link

I validated it with a system I designed last year, but don't take my word for it - make sure you understand the mystery behind the curtain (fortunately they spell out the formulas and it's pretty easy to see where everything comes from).

While anchorage forces can get really high, it's important to remember that the wire rope in these systems stretches a LOT. The iterative approach CANPRO brought up will help you understand the actual deformed shape of the system under load, which significantly reduces the reaction forces over assuming the cable has remained straight. I've calculated anchor reactions near 20kips with the simplified assumptions, but they reduced to something closer to 4.8k after iterating the shape of the cable.