# Calculating Sag & Tension for 2 Wires: 5000 lbs Horizontal Tension

• epena
In summary, the conversation discusses how to calculate the sag and tension of a wire hanging between two objects. The equation used is Sag = (W*L^2)/(8*T), where W is the weight of the wire, L is the span between two supports, and T is the horizontal tension. The conversation also mentions adding a heavier wire and how to calculate the new sag and tension for the combination. The solution involves using the average density of the two wires and treating them as one wire. A resource for further understanding is also provided.

#### epena

I'm trying to figure out the sag of a wire hanging between two objects. If I string a wire between two structures and tension the wire 5000 lbs in the horizontal direction, I can estimate the shape of the wire to be parabolic and use the equation: Sag = (W*L^2)/(8*T), where W=Weight of wire, L=Span between two supports, and T=Horizontal Tension to calculate the sag. If now I add a much heavier wire to the first wire, how can I arrive at the new Sag and Tension for the two wire combination? I am assuming the same temperature for both installations (60 degrees F). The first wire is .65 lbs/ft; the second wire is 7.8 lbs/ft. I am trying to solve the problem without neglecting the initial wire's weight.

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Have a look at this

http://mathworld.wolfram.com/Catenary.html

If two different wires hang in the same curve they must be joined along their length, so you can pretend it's one wire with the average density (?)

To calculate the sag and tension for the two wire combination, we can use the same equation, but we must account for the weight of both wires. The weight of the first wire is given as 0.65 lbs/ft, so we can calculate the total weight of the first wire by multiplying it by the span length between the two supports. Let's say the span length is 100 ft, then the total weight of the first wire is 65 lbs.

For the second wire, we are given its weight as 7.8 lbs/ft. So, the total weight of the second wire would be 780 lbs (7.8 lbs/ft x 100 ft).

To calculate the new sag and tension, we can use the same equation but with the total weight of both wires (845 lbs) and the same span length of 100 ft. So the new sag would be:

Sag = (845 lbs * (100 ft)^2)/(8 * 5000 lbs) = 168.9 ft

To find the new tension, we can rearrange the equation to solve for T:

T = (W * L^2)/(8 * Sag)

Plugging in the values, we get:

T = (845 lbs * (100 ft)^2)/(8 * 168.9 ft) = 5002.4 lbs

Therefore, the new tension for the two wire combination would be approximately 5002.4 lbs.

It is important to note that this calculation assumes the wires are perfectly parallel and have the same temperature. In real-world situations, there may be slight variations in temperature and the wires may not be perfectly parallel, which could affect the sag and tension calculations. Additionally, if the span length or weight of the wires were to change, the sag and tension would also change.

## 1. How do you calculate sag and tension for 2 wires?

To calculate the sag and tension for 2 wires, you will need to know the horizontal tension of the wires, the length of the span between the two poles, and the weight per unit length of the wires. You will also need to use mathematical equations and formulas, such as the catenary equation, to determine the sag and tension values.

## 2. What is the purpose of calculating sag and tension for 2 wires?

The purpose of calculating sag and tension for 2 wires is to ensure that the wires are able to support the intended load without breaking or sagging too much. This is important in various industries, such as telecommunications and power transmission, where the wires must be able to withstand high levels of tension and maintain a certain level of sag to prevent damage to the wires and maintain efficient transmission.

## 3. How does the horizontal tension affect the sag and tension of 2 wires?

The horizontal tension, also known as the line tension, is a major factor in determining the sag and tension of 2 wires. The higher the horizontal tension, the lower the sag will be between the poles. Additionally, a higher horizontal tension will also result in a higher tension in the wires, which can affect the overall strength and stability of the wires.

## 4. What are some factors that can affect the sag and tension of 2 wires?

Aside from the horizontal tension, other factors that can affect the sag and tension of 2 wires include the weight per unit length of the wires, the temperature, wind speed, and ice buildup on the wires. These factors can cause the wires to expand or contract, leading to changes in sag and tension.

## 5. Are there any safety precautions to consider when calculating sag and tension for 2 wires?

Yes, it is important to follow safety precautions when calculating sag and tension for 2 wires. This includes wearing appropriate protective gear and using proper equipment when working with high tension wires. It is also important to follow industry standards and guidelines to ensure the safety of both the workers and the general public.