Wire rope deflection

http://en.wikipedia.org/wiki/Catenary

Thank you, but I'm not sure how the catenary formulas would apply here. My cable is secured in a vertical position. It is pulled as tight as I can reasonably expect to get it by using a turnbuckle. And I am applying force to the cable at a single point. I am trying to find out how much deflection will result to this 1/4" wire rope, thru stretching and whatever else, as various amounts of force are applied perpendicular to the wire rope at one point.

Unless I'm missing something here, you'll need to know the cable tension to calculate. If you cannot measure directly, you may be able to calculate (approximately) by measuring the distance you're stretching the cable through tensioning with the turn-buckle. Otherwise, you may just have to rig the system up and measure some experimental values.

Thank you. I am currently contacting various turnbuckle manufacturers and trying to find out how much tension I can reasonably expect to attain thru a turnbuckle for a 1/4" dia wire rope. Will that be enough additional information to calculate my potential perpendicular deflection?

Or does anyone know the tension attainable thru the use of a turnbuckle, before the threads deform? Or before standard cable loop hardware gives way?

It'll be pretty rough. What a 160 lb guy thinks is reasonably tight will be pretty different from what a 260 lb guy thinks during installation. I would suggest taking up any slack and then either counting turns or using a dial indicator to measure cable stretch. Then you can calculate a pretty good estimate of the cable tension.

One thing to keep in mind. You mentioned being near the deformation limit on the turnbuckle. On a tensioned rope, any side force is multiplied many times over at the anchor points. We have often used this principle on vehicles stuck in the mud. We'll winch a cable tight from the stuck vehicle to an anchor, and then use a second winch to pull sideways on the cable mid point. Hard on the cable, and you don't get much travel on the stuck vehicle, but you create a lever that far exceeds the winch's actual pulling capacity. Try for yourself. It only takes a few ounces of finger pressure to deflect a cable with several thousand pounds of tension in it. This is a classic statics exercise.

That's good information. Thank you CSM.

Here is the bottom line, if it makes any difference. I will have two of these assemblies, parallel to each other, each 115 feet tall on the side of a building. And 20 feet apart. A 1200 ft² banner will be stretched between them. Around mid point.

My goal is to keep the wind from billowing out the banner out away from the wall because of cable stretch. So I have captured the two cables by partially encircling each of them within a channel. The legs of the channel I've chosen are 5". The open faces of the channels point toward each other.

I am trying to confirm that 5" is enough (or too much) to prevent the wind from allowing the banner to bow the two cables into an hourglass shape to the extent where the center will pop out of their confinement and allow the banner to bulge at it's vertical center.

I feel that it will work. But mathematical confirmation is always a good thing. I'm just not experienced with wire rope characteristics.

These Loos tension gauges might be helpful. If you know a sailor of a boat around 30 feet long, he might let you borrow one.

You may need fairly long turnbuckles to be able to get a lot of tension on a 1/4 inch cable 110 feet long. If it hasn't been pre stretched, there may be the need to take up come "constructional stretch" before the steel wires are really put into elastic tension.

In general (very roughly) 1/4 inch wire rope can have a nominal strength of about 4000 lb -- but you'd need to check the wire type and construction.

I'm not sure I am visualizing this right, but it sounds like the banner is 20 feet wide, 60 feet long, and hung vertically, with these tensioned cables at each side. These cables are 2" away from the building. The force against the banner from wind blowing toward the building will definitely plaster the banner to the building -- the deflection in the center of the banner could easily be a couple feet, but in this direction the building will restrain the deflection.

If the wind direction is such that the banner starts to generate lift away from the building, then the forces on 1200 sq ft can get quite high.

If you had a feel for the side load on the banner from wind more or less parallel to the banner face, you could calculate a caternary, using the drag force as if it were gravity.

Given the elastic modulus of the cable, you could simplify the stretch calculation to a triangle. If the cable is initially at 1000 lb, you could pretty easily pull it out from behind the channel without a lot of force: hand force would easily do it.

For example: a 6" deflection only elongates the cable .001' (.012"). That tiny stretch would take very little force even along the length of the cable, and perpendicular to it, ounces or a couple lbs would do it (depending on modulus).

Gut feeling is that 1/4 inch cable is too small for such a long span: you couldn't get enough tension on it to make is resistant enough to side load to keep the banner from flapping around.

Could you anchor the cable to the building every 10'? Or could the cables be pre hour glassed, ala suspension bridge? Or could the channel be the anchoring method, with holes every 4' to which the banner is tied? Or could the banner edge have a rope enclosed in it, with that rope fed into a "sail track", the sail track attached to the building?

Here are some modulus figures for stainless rope.

That's quite a bit of help Ken. Thank you. Yes you visualized the set-up correctly.

Well, I might try going up to 3/8" cable to lessen that stretch factor. Do you think that would make an appreciable difference? I believe there are some types of cable that stretch less than others, at the cost of flexibility. I'll have to look into that also. A couple feet of deflection at the center is going to be unacceptable. I'll have to work on that challenge. I will have a turnbuckle at each end, though. Or perhaps two adjacent to each other at the bottom, for easier access. Your example assumed a 1000 lb tension. I still don't have a feel for what kinds of tensions could be achieved with turnbuckles though. I guess given enough of them ...

As far as attaching the cable to the wall at intervals... no, it can only be attached at the ends, as I need it free to slide d-rings along the full length. And for similar reasons, I can't pre-hourglass it. Sail track is cost prohibitive. The function of a sail-track is what I'm trying to mimic.

With a 5 inch deep channel, the ends of the cable will obviously stay within the channel, as it is mounted 2" away. But that will only be true till about a quarter of the way down. So ... if I attach spreader bars to the back of the banner, the ends of which extend beyond the channel at both ends ... that might work.

You've given me a good feel for some of the variables that I wasn't fully familiar with. These considerations should make my prototype much better. Less debugging. I'll have to put some more thought into a few of these issues.

Achieving high tension seems to be the key. I'll have to work on proper anchors too.

And to GUEST who offered the caternary chart earlier, I apologize. I see the application of it now.

Ken, I just realized what you may have meant about stretching cables like a suspension bridge.

If instead of tying off the cables at each end anchor, I had a complete loop between each pair of eyebolt anchors, I could achieve sufficient tension by pulling the loops together in the center, across the 20' that separates the two loops. Much more slack taken up than would be achievable by turnbuckles alone.

Hmmm ...

Ken, your Loos gauge led me to this: http://www.loosco.com/

It's got a downloadable wire rope Stretch Calculator program! Perfect!

I LOVE this site!

The relationship between the stretch and the strain in the rope is needed to proceed. It sounds as though a right-angled triangle of force vectors is involved here, something that Pythagoras' Theorem might be usefully applied to, perhaps?

With the objective defined, a cable does not appear to be the correct means to create a rail straight anchor point for the banner. I would use a I or H beam with web of the proper height to minimize deflection at 90 degrees and also at 180 and 270 expecting the banner can swing thru a 270 degree arc fastened to the side of a structure.

I'm not sure I'm visualizing what you mean Cameraman. Currently I have d-rings thru grommets in the banner, that also clip around the cable to slide freely the entire length. I cant put a frame around the banner because I need the top of the 60 foot banner to collapse to the ground when in the down position. Are you suggesting I get two 110 foot long channels and mount them at the top and bottom, and loop my rings around that?

If you are able to anchor the beams to the wall,

then put beam trolleys onto the D rings,

the banner can no longer pull the cables together,

or billow out as far in the wind.

It also of course depends upon how permanent this is?

and how big the budget is.

Hmmm... beam trolleys. Yes I see where you're going. Interesting ....

Yes -- good solution.

Unfortunately, I have had a banner, which I did not design or have the liberty to pre-engineer; blow off a wall during the Super Show in Atlanta, GA, ten years ago.

We rig building signs and banners here in NYC. The buildings are full of these types of advertisements. As such, there is much to know about safely rigging these, so the advertising value is insurable. The clients don't like it much when the banner fly's down the street and causes an accident on the local city streets or highway. They also don't like to pay incompetent riggers for the lost advertising. Unfortunately, these same advertising folks often cheap out when they have the banner manufactured, leaving the rigger with a dilemma.

I have personally watched the wind, fill sail and lift four 600lb. dead-man boxes of concrete and stretch the 1/4" Crosby Clips so they would not un-screw from the stretched wire rope; when a banner measuring 80' x 40' was filled from behind with air. (Yes, we had air relief cuts within the banner). The vortices's were more than anyone "thought" would ocure.

We used steel wire rope and rated hardware. We crisscrossed the banner in every direction possible, using pipes through the sleeves, top and bottom and cables from roof to the pavement. (That is all we had to work with).

It did not matter. The process used to edge the materials we were FORCED to fly, were poorly designed and caused catastrophic failure during the event when 40 mph winds swept through the concourse level across from Turner Broadcasting.

The banner this size, is capable of unbelievable stretch and up-lift. The concrete blocks walked 4-6 feet from where we dropped them with pallet jacks. People were scrambling through the storm all around this disaster.

Consideration by the designer / manufacture of the binding materials at the edges of the banner and within the fabric, are critical. We now, often use a welt seam system with a 1/2 inch rope or a synthetic solid core of polyethylene solid tubing, Thermo-welded into the sides of the banner, so the exterior wires can be fastened through the fabric around the rope which is continuous around the edges. These high quality welts are formed during TENT fabric manufacture for massive portable tents, as well.

I suggest you do not use turn buckles, as the length of the rope you are planning is not within the rated use of most manufacturers. The wire rope is wound, which means at extended lengths, it tries to un-wind. The more you turn the buckle, the more you create winding energy from the lay of the rope, as a force on the turnbuckle. Eventually, you will tighten the buckle to the limit and the wire will start to unwind your turn buckles as torsion overcomes the friction of the buckles and threads.

NO, TIE WIRE OR ZIP TIES WILL NOT SUFFICE TO ELIMINATE THIS ACTION. Control, maybe... Fail; absolutely, unless the tension is controlled at every minute of the use of the banner.

The rigging of theatrical overhead pipes in new theaters is often rigged by inexperienced, low budget companies using turn buckles. They fail to maintain the load at longer length wires and they un-wind causing deadly uneven load conditions. Worse yet, regular turn buckles do not have lock nuts. They are not intended for these uses, even though the manufacturer does not dis-allow them from such use. The only rating they will discuss is load rating not UN-WIND caused by long wires and torsion failure of the turnbuckle. They are well within their liability to avoid direct questions about such mis-use. It is up to you, the installer, to adjust proper working conditions and intended usage.

Trucking companies use levers and chain to tension slings during driving conditions, quite effectively. I would crimp eyes into the wire and convert to chain and use chain tensioner's to tighten the slack. You can easily adjust to the next link if the rope stretches. Then use tie wire or zip ties to prevent the chain lever from opening.

If you are serious about learning more, contact Crosby and take the rigging training course on materials safety and design specification. All the tools and wire rope standards are taught, as if you were an instructor, which by completing the home work assignments, you may achieve.

The valuable calculators you seek are part of the training course and shall not be handed out for free, unless you attend the course and accrue certification. (As per our agreement with Crosby, as trainers).

Your best resource for quality banners for increased performance and with proper liability insurance in case of failure may be to contact one of the many professional sign companies in Manhattan or a major tent supplier. I am almost certain, by the nature of the questions you are asking; the amount of quality required to properly rig this banner is well beyond the poorly designed sheet you are considering hanging.

These questions would not exists, otherwise.

Too many low budget advertiser's and low budget theatrical companies try to force half baked, cheap banners upon the riggers I have worked for and with. It is up to you to say NO and walk away from the job, unless THE CLIENT has designed and supplied an engineered, quality banner. They are very expensive and almost every question you have asked will be designed into the system for you. Otherwise, you should have an indemnification of any and all liability of damages or fault, signed by the banner owner. (My letter would include the intentional advise of possible death, should such a poorly engineered banner be flown. Don't worry, they will NEVER sign such a release).

The largest banners in NYC have stainless eyes every 12" minimum, around the entire banner with wire rope stitched into the Vectran or other Aramaic Fiber reinforced fabric. The elasticity, porosity and windage of this fabric must be ascertained or all the wire rope engineering you employ will be useless.

I quit the Super Show when they would not remove the banner in Atlanta. The wires could have easily broken and slashed anyone of the tens of thousands of bystanders during a critical failure. The company did not want to lose the $15,000.00 ad dollars and chose to risk death and dismemberment, instead of removal of the death banner.

Don't follow in my footsteps. Walk away before the cheapskates try to ruin your reputation. Can you believe the Company tried to tag me with insubordination for insisting we remove this failure of engineering?

If the Interior or especially the EXTERIOR banner is not engineered by a certified design engineering company with known components, DO NOT HANG IT. OSHA will fine YOU should anyone be injured, under OSHA 29CFR 1910, 29CFR 1926 and ASME B30.26, for improper use of rigging. You risk losing your insurance bond, should anyone be killed.

The next ASME Standards and OSHA Rigging classes, specifically pertaining to your situation, are scheduled in Richmond, VA during December and again in Orlando FL Convention Center's; Lighting Dimensions International, (or LDI), taking place next Jan./Feb.

Nearly every calculator you will ever need for assessing materials safety and load lifting will be given to you for free, during the FREE course.

Get Crosby Quality certified and train others against critical rigging failure. The kind folks here on this forum are not always properly trained or experienced to give you other than assumed answers based on book-learned experience. Get the facts from the company who's self insured quality program is good enough for Boeing and GE.

It's taught by engineers and best of all, it's FREE! Attendance is limited and by appointment.

That 2 inch off the wall dimension, is more of a problem than you are ready for with grommets and no intermediary hard points. The wire will break before you can tension it enough to control minor fluctuation's and the gap will increase and catch air under poor conditions.

Have a stand-by team round the clock to drop it fast in case of increased wind.

Dear friend,

You have mentioned in your posting “How do I find the potential deflection at mid point, as various amounts of force are applied perpendicular to the cable? (pulling on it like a bow string)”

Also you have mentioned “Off-set is 2 Inches and total length of rope is 110 Feet”

You have NOT mentioned the pitch of the bolt in the turn buckle. Also you have not mentioned what type of force is applied and its magnitude.

My reply is : 1. Since off-set is 2” and for a length of 110 ‘ the angle ( if imagined in horizontal position) or slope will be tan θ = ((2)/ (110 x 12)) = 0.001515. Therefore θ = 0.08680 Degree, which is negligible.

While tightening the turn buckle, initially the rope will be loose and starts getting pulled at one point the rope is just zero loose and getting pulled further. At this point, note down the thread position in the buckle and once you tightened fully and no more possibility at this juncture the rope is under full tension and the elongation can be found out from the turn buckle threads how much the rope has been pulled to the max limit. Knowing the pitch of the thread and number of thread in both turn buckle bolts the elongation can be measured which can be taken as the strain of the rope

Asper Hook’s law you know that stress is directly proportional to the strain and we can evaluate the stress induced.

In my opinion since the rope is fully tightened it may not undergo any deflection. If you want to calculate the deflection use the formula (W x L^3)/(8 x E x I) and as the rope is steel you know the value of E and I and L is 110 feet and only value of horizontal Load W is to be given by you.

DHAYANANDHAN.S