Concentrated load and uniform load on a cable 2

[StrP88]

Dear colleagues:
I am trying to figure out when a cable is under both concentrated loads and uniform load, then how the T max = Maximum tension can be calculated?
All the static text books deal with uniform load on cable separately and don't tell you when you have both uniform load and point loads then what method has to be used to determine the tension in cable?

I appreciate a direction or if any source has a practical example, I appreciate for it

 

[jayrod12]

I don't know if I've got an example but,

You can calculate the stretch in the cable due to only self weight. The point load also causes stretching which can be calculated as well. The point load causes the cable to go from a catenary curve to a triangle. You'll know the vertical reactions, and the applied loads. The rest is just geometry.

 

[BAretired]

The loaded cable adopts the same configuration as the bending moment of a beam with the same span irrespective of the type of loading.

Under uniform load, the cable configuration is parabolic. Under a concentrated load, the cable configuration is a straight line between each support and the load. Under a combination of uniform load and one or more concentrated loads, the cable adopts the same shape as the bending moment diagram found by statics. Note that cable dead load is a uniform load per unit length of cable, but is not uniform per unit length of span.

Unless there are horizontal forces applied within the span, the horizontal component of cable tension H is constant from end to end and may be found as M[sub]x[/sub]/S[sub]x[/sub] where M denotes bending moment, S denotes sag and x is the horizontal distance to the point under consideration.

Cable tension can be found as T[sub]x[/sub] = H/cosθ[sub]x[/sub] where θ[sub]x[/sub] is the slope of the cable at point x. T is maximum at the supports because the slope is maximum at the supports.


BA

 

[StrP88]

Can I calculate them separately and then add them up?

 

[XR250]

The loaded cable adopts the same configuration as the bending moment of a beam with the same span irrespective of the type of loading.

Fascinating - I did not know that

 

[BAretired]

Can I calculate them separately and then add them up?

No, that would not yield the correct solution because the sag would be inconsistent with each type of load considered separately.

For example, a concentrated load at midspan would result in a sag which could be calculated based on the initial length of cable plus elongation. Adding a uniform load over the entire span would decrease the sag at midspan, so the calculation of cable tension due to concentrated load would have been too low, having been based on a sag which was too large.

BA

 

[dhengr]

BA:
Very nicely done. You must actually own a real old text book or two and have learned the hard way, by studying over time. Remember when the internet, Google and E-Tips used to be..., going to the Uni. engineering library, and start digging, until you found that golden nugget which gave you some ideas and direction? I’ve got nothing else to add.

 

[StrP88]

BAretired (Structural)
Since I am defining the sag, is it alright adding the max Tension in cable for two cases, one point load at midspan with 18" sag and then distributed load with 18" sag assumption.

Can I add the max tensions in each case since now I defined same sag at mid span for both cases?
If not then how do I deal with it and how do I calculate the max tension in cable under both point load at mid sapn and uniform load with 18" sag at mid span?

Any examples, excel sheets or help?

Thanks

 

[BAretired]

StrP88,
If you are defining the maximum sag S in span L, then with uniform load W and point load P at midspan:
M = WL/8 + PL/4
H = M/S (the horizontal component of cable tension)
T[sub]max[/sub] = H/cosθ
T[sub]max[/sub] occurs at each support (assuming they are both at the same elevation) and you need the angle θ in order to calculate T[sub]max[/sub]. If S is small compared with L, T[sub]max[/sub] is only slightly greater than H but the geometry is not too difficult, so it is best to calculate it properly.

The principle of superposition, in this instance, works for H but it does not work for T[sub]max[/sub] because the wrong values of θ would be used in the calculation.


BA

 

[BAretired]

dhengr:
Thanks. I do have some fairly old text books lurking about.

BA

 

[BAretired]

StrP88,

Taking a uniform load and a concentrated load at midspan is a symmetrical load case where maximum sag occurs in the same location for both load types. In a general case where loads may be unsymmetrical, the maximum sag can occur in different locations for each type of load. In the general case, superposition cannot be used to calculate H, nor is there any practical advantage in using it.

BA

 

[StrP88]

BAretired (Structural)

Thank you for your help.
Do you have by the chance a text book or a hand book example dealing with it or solving an example that you can attach it here
I know I may ask too much and may be trouble for you but I would really appreciate it. Seems you are the only one that have good information.
I am really sourceless and not much people know or deal with cables.

I also was looking a book or hand book teach you the design of cables and how you size them and select them? if you know any text book or hand book I appreciate that as well

Have a good weekend

 

[BAretired]

I have not been involved with cable design in recent years. I have a very old copy of "Blue Strand Wire Rope Catalogue" (Canadian publication) which I used in the selection of some steel cables; that was about 1980. There are a couple of examples of engineering calculations in it but I have never referred to them because the statics and geometry of a cable are elementary. There are several Wire Rope Handbooks available on the internet including one by the US Navy. I don't know how useful these would be in your case.

You can use the "Search" function of Eng-Tips to find other useful stuff. I searched for "wire rope" and came up with 125 references. A search for "steel cables" yielded even more. You may find something useful there.

If you want catenary equations, these can also be found on the internet. Personally, I have never used them, preferring instead to use simple approximations.



BA

 

[Denial]

StrP88. If you want to understand what is going on, you won't do better than BA's experience, discussion and material. If you want a spreadsheet that solves the problem of a cable under combined uniform load and one point load, you will find one on my website (rmniall.com). However the method used by the spreadsheet is totally different from BA's.

 

[desertfox]

Hi StrP88

You might find this site helpful

http://nptel.ac.in/courses/Webcourse-contents/IIT Kharagpur/Structural Analysis/pdf/m5l31.pdf

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[StrP88]

Denial (Structural):
Thank you so very much. Impresive website. I will get back to you on your spread sheets during the week. Just is Sunday here.

desertfox (Mechanical)
Thank you for the link, however the examples donot explain the loads on the same time