Continuous Steel Cable vs. Segmented?

[butch81385]

We are having an internal discussion at my office regarding steel cables. Take the following scenario:
5 bays (6 supports) with a steel cable taking the loads. The loads may be on every bay, or may be on as little as one bay (or any combination in between). Does it change the max end reaction of the exterior supports if the interior supports are continuous cable (no horizontal resistance except the tension in the cable) vs. segmented (5 individual spans)?

I would assume that, in essence, it is similar to looking at the horizontal reactions of a statically indeterminate beam with rollers as the internal supports. Unfortunately we do not have a good computer program to do this, nor the time to do it by hand. So I come to see what you great people know about the situation.

 

[ishvaaag]

Of course will vary. For the case where the spans are segmented every cable can be analyzed for equilibrium as a simple span, passing its horizontal reaction to the tip of a column with stiffness. Whatever the load in the span, any effect beyond the first colum will depend on just the deflection caused in the column and opposed by the column or support stiffness.

On the contrary case, when the cable is continuous, a configuration of equilibrium needs be met at which the loads of other spans will intervene. For example, over a first interior support, now a full tensile force from such funicular equilibrium will be acting on the rest of the cable; this is not the case where the cable is cut there.

If you want, in one case the stiffness of the columns or supports intervene; in the other not.

As well, the funiculars of equilibrium for the same set of loads with cut cables and not will be different. Imagine the loads are just some single point loads per span. As the angle shape of the cables in every span will be different for each of the two situations we are considering, also will be the horizontal reaction.

 

[butch81385]

Is it possible to say that one case will always produce higher reactions on the exterior columns than the other case?

Part of me wants to say that, if anything, the continuous case will produce lesser loads as there is more of an opportunity for sag due to the extra cable length (thus resulting in a higher percentage of the tension going into vertical loads as opposed to horizontal loads. However, I keep going back and thinking of whether the base tension actually cancels out or is additive between the spans...

Thanks for the reply.

 

[ishvaaag]

No. Shall deconstruct your hypothesis. Imagine two weak point loads in the extreme spans, cables cut. Small horizontal reactions, whatever the loads in the other spans.
Now imagine continuos cable, and a BIG point load in the center span; will pass much tension to the ends.

 

[butch81385]

But what if the loads on the extreme spans were the same magnitude of the load in the center span in your two scenarios? Doesn't the end support see the same force (horizontal load from one half of one bay) plus or minus the difference due to sag (for now to be neglected)?

 

[rb1957]

won't the deflected shape of a continuous cable be different to a segmented cable ? at a support the two segments could have different slopes, but a continuous cable has the same slope (and alot of bending).

let's not play "what if ..." 'cause the game never ends. ask your question, to get the answer you're looking for. include your assumptions (a few seem to be slipping in now ... no sag in the cable (no weight, no tension?), lateral reactions only at the end supports, loads applied in a few discrete ways ... load each bay equally, load only one bay ... middle, end, ...)

 

[butch81385]

Here is the scenario that brought about the question:

5 bays, 6 supports.

Steel cable spanning 20' between supports.

Dead Load on cable is near negligeable (0.1psf over 50' trib height)
Ice load takes that to 2.5psf.
Wind load is approximately 22psf horizontal.

obviously the wind load or ice load can occur on any individual span, multiple spans, or every span (trees, shade, etc.).

Does segmenting or running a continuous cable give you the largest lateral load (along the length of the cable) on the 2 end supports?

We are less concerned with the interior supports, as they can easily handle the vertical loads, and can handle one span's worth of horizontal loads if segmented (which is conservative as the cable on the otherside would have some tension pulling in the opposite direction, or at the very least would impose some resistance to the bending of the support).

Once again, note that the area of concern is the horizontal loads inline with the cable.

I neglected the varying sag between the continuous and segmented cables earlier because (correct me if I am wrong) the continuous cable would allow for more of a sag which would only reduce the horizontal load (larger vertical component). Since we are looking at what causes the maximum horizontal reaction force, neglecting this results in a conservative approach (once again, correct me if I am wrong).


Sorry if I wasn't clear enough, but a project we were working on just spurred a conversation, followed by a debate, over whether a continuous or segmented cable allows for less horizontal loads, resulting in a potentially cheaper solution (in terms of the supports, but not necessarily in the cable).

Thanks for all of the help so far.

 

[ishvaaag]

In reality rb1957 is right; it is precisely to avoid such musings of imagination that the standard ways to model structures were established.

Now imagine a point load amidst an end span causing at both sides of such span a reaction H. Now, connect the cable in a symmetrical loading. We can have 2 situations: either the central loads require at first supports less than H for equilibrium, or more. If they need more, they will increase tensile horizontal reaction at end supports, and the contrary if less.

 

[KootK]

Butch

I think you're right. With a continuous cable, the potential for sag in any one loaded span is greater. With greater sag, the end support thrust force will be lowered because less horizontal force will need to be developed in the cable to produce the vertical/lateral resistance.

If all your after is a conservative design, go with the discontinuous case.

 

[BAretired]

I agree with KK.

Consider the cable at all six supports temporarily fixed against horizontal translation. Load only one span. It behaves as an individual span because both ends are tied.

Now, release all of the interior supports. Sag in the unloaded spans disappears and the cable slides toward the loaded span. Sag increases in the loaded span because the cable lengthens and the horizontal component is reduced in all spans.

If all spans are identically and uniformly loaded, it makes no difference whether the cable is continuous or segmented. The sag is equal in every span.

BA

 

[KootK]

BA's comment got me thinking that there may be a good argument for detailing you structure as continuous:

If you're continuous, then you have a slighty horizontal force and it's applied at only your end posts.

If you're segmented, then you have a larger force at each one of your posts (end & intermediate).

If it's practical to use a different design for your end and intermediate posts, there may be some savings to be garnered by going continuous.

I guess the other thing to consider is whether or not you can actually count on the supports not to lock up the cable over time (rust? Bird shit?), thus invalidating your continous assumtion.

 

[BAretired]

To get around the problem of rust and bird excrement, the interior columns could be tied to the cable at the top but hinged at the bottom. This would permit them to rotate as required to accommodate the particular load combination acting at any given time.

The exterior supports could be diagonally braced columns designed to resist the calculated horizontal force.

BA

 

[ishvaaag]

I must insist on that is not feasible in general for a general set of loadings to assert on whether the horizontal reaction at end supports will be greater or lesser on the assumption of the cable being continuous or segmented. For symmetrical loadings, for example, such tensile force, out of equilibrium, entirely depends on the proportion of loads in the 3 inner spans to that in end spans. If end spans require as segmented an H reaction, and inner spans, as continuous, is not delivering it, the tensile stress at first inner support relax to a lesser value; and the contrary must happen if the loading in the 3 inner spans require more than H.

The horizontal reaction at end supports hence can't be asserted be more or less than the segmented case for a general case; only limiting the hypotheses to a particular set may give the situation of end actions remaining always higher or lower when continuous than when segmented.

Now, don't forget as well that the main fittings to the cables -except for concrete anchorage- will control the design of the cable.

For end anchors will have the circumferemtial compression (2D compression, you are squeezing the cable) in more than the tensile stress; and for pulley type supports, the bending action on the cable adapting to the contact circumference of the seat plus compression of the upper part of the cable on the bottom part.

If you account for these effects and other contact, fatigue, potential lost of section etc effects, everything intervening, if you want, then you can you can go along with more or less ordinary safety factors.

If not, better remain -as I saw on cables of old- in very high safety factors respect tensile action, 5 to 8 were not uncommon for main cables when its failure was cause of ruin.

 

[ishvaaag]

... in the first paragraph above in my previous post where it reads

"is not delivering it, the tensile stress at first inner support relax to a lesser value;.."

should read

"is not delivering it, such horizontal reaction H at first inner support relaxes to a lesser value;.."

 

[BAretired]

ishvaaag,

We are not dealing with a general set of loadings. We are dealing with five spans of 20' with a negligible dead load, a larger ice load and a horizontal wind load. The ice load may be present or absent on any span.

If the cable is hinged at every support, the tension at midspan of every span is approximately 50w/s where w is the resultant ice and wind load and s is the sag. For gravity loading, a catenary is being approximated by a parabola.

If the cable is continuous, then if ice and wind act on every span simultaneously, the horizontal reaction is zero at each interior support and 50w/s at each exterior support, exactly the same as the segmented case.

If the cable is continuous with patterned ice/wind loading, the sag in the unloaded spans will decrease and the sag in the loaded spans will increase. The horizontal force in the entire cable will then be 50w/s' where s' is the increased sag in the loaded spans.

Accordingly, with the stipulated set of loads, the maximum possible horizontal load occurs when the cable is segmented.

BA

 

[ishvaaag]

I agree, I only was still answering the original question. When you have only partial loading, having length of cable available will make the sag in the loaded segments to increase (beyond what available when segmented) and then lead to lesser horizontal reaction.

 

[csd72]

I agree with Ishvaags comment above, this is the main difference.