Suspending Cable under own weight

In summary: But because the cable is not uniform, the nodes of the bar solutions will be displaced and the approximation will be less good. For more information and examples, see: http://en.wikipedia.org/wiki/Catenary_%28mathematics%29 In summary, the teacher is trying to solve a problem where the nodes are displaced and the approximation is less good.
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Kronustor
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Homework Statement



In this project, the methodology of Finite Elements and convergence of numerical solution is explored.

A cable has the following properties:

weight per unit length of wo = 5 N /m
length l= 24.2m

The cable is suspended with its two ends a distance of L = 20 m apart, as shown below.


The analytical solution for this type of problem is presented in an example in Chapter 7 of your textbook. The middle of the cable would drop a distance of h’ = 6 m vertically from its two ends, and the cable tension force has a maximum of Tmax = 75.9 N which occur at its two ends.

Procedure:
Part 1. You are now using the finite element approach to solve this problem. The approach is to divide the cable into equal sections. The number of sections N will be 2, 3, 4, 5 respectively. Consider each section as a rigid rod which is then pined to the next section. Lump the weight of each section to concentrated forces on the section ends. Then solve for the forces in each section and the positions of the section ends. From your solution, determine the drop of the middle point of the cable from the ends in the vertical direction hN, and the cable tension force at the ends TN, where the subscript N denotes the number of sections considered. Make sure that you take fall advantage of the symmetry in the problem. After your solutions for 2, 3, 4, 5 sections are achieved, group hN and TN into a table, and plot them versus N . Compare your plot with the follow plot of numerical solution convergence patterns. Answer what type of convergence it is for the solution of h, and what type of convergence it is for the solution of T.

Homework Equations



ƩFx=0
ƩFy=0
ƩMo=0

The Attempt at a Solution


I have done the first permutations from the problem. Where there 2 rods instead of the cable and where there are 3 rods intead of the cable. What i am having problems with is in the third and fourth permutations. I can't figure out how to solve the angles. I am sure if i could find one angle i for both of the last permutations i could finish the rest on my own.
The teacher has stressed that we use the symmetry in the problem but i can't figure out how to do it.
In the part where we use 4 rods i know each rod has a length of 6.05 and there is 3 suspended weights of 40.333. i have tried projecting the 4 rods over the length of 20m to form an octagon but that didnt work. I also thought of using isosceles triangles but didnt know where to go from there. Can someone point me in the right direction?
 

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  • #2
Your work is upside down.
 
  • #3
If the suspended cable were uniform, the shape would be a cosh function (catenary) for which a parabola is a good approximation when the span is (say) greater than 8 times the dip. The nodes of the rigid bar solutions should also lie on a catenary (or parabola).
 

1. How much weight can a cable safely suspend on its own?

There is no one answer to this question as it depends on various factors such as the type and material of the cable, its diameter, and the conditions under which it is suspended. It is always best to consult a structural engineer to determine the maximum weight a cable can safely support.

2. Can a cable be suspended vertically?

Yes, a cable can be suspended vertically as long as it is properly anchored at both ends and can withstand the weight it is supporting. However, it is important to note that vertical suspension can put more strain on the cable and may require additional support.

3. What is the best material for suspending a cable?

The best material for suspending a cable depends on the specific application and the weight it needs to support. Some common materials used for cable suspension include steel, aluminum, and synthetic materials like nylon or polyester. It is important to choose a material that is strong enough for the job and can withstand any environmental factors.

4. Is it safe to suspend a cable over a long distance?

It is generally safe to suspend a cable over a long distance, but it is important to consider the weight it will be supporting and any external factors that may affect the cable's strength. It is also important to regularly inspect and maintain the cable to ensure its integrity and safety.

5. Can a cable be suspended without any additional support?

The answer to this question depends on the weight and distance the cable is supporting. In some cases, a cable can be suspended on its own without additional support, but it is always best to consult a professional to determine the safest and most effective way to suspend a cable.

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