# Calc. Resultant Increase in Length of 5m Steel Roof Tie Rod Under 80 KN Load

• prettys073
In summary, to calculate the resultant increase in length of a 5m steel roof tie rod, you can use the formula L = F * L0 / A * E, where L is the increase in length, F is the load applied, L0 is the original length, A is the cross-sectional area, and E is the Young's modulus of the steel. The cross-sectional area of a steel roof tie rod can be found by measuring its diameter or width and using the appropriate formula. The Young's modulus of steel is typically around 200 GPa or 29,000,000 psi. The load applied directly affects the resultant increase in length, and other factors such as material properties, temperature, and imperfections can also impact
prettys073
the question is:-

calculate the resultant increase in lenth of a 5m long roof tie rod made of 25mm diameter steel when subject to a tensile load of 80 KN. (assume E=210KM/mm2)

does anybody know how to solve this or what the calculation is that i got to use? help apprecited thanks in advance!

I can provide a response to this question. To solve for the resultant increase in length of the steel roof tie rod, we can use the formula:

ΔL = (F * L) / (E * A)

Where:
ΔL = change in length
F = applied load (in Newtons)
L = original length of the rod (in meters)
E = Young's Modulus of Elasticity (in N/mm^2)
A = cross-sectional area of the rod (in mm^2)

In this case, we are given the values of F (80 KN), L (5m), and E (210 KN/mm^2). However, we still need to determine the cross-sectional area of the rod (A) in order to calculate the change in length.

To find the cross-sectional area, we can use the formula:

A = π * (d/2)^2

Where:
A = cross-sectional area
π = 3.14 (approximate value for pi)
d = diameter of the rod

In this case, the diameter (d) is given as 25mm. Plugging in these values, we get:

A = 3.14 * (25/2)^2 = 490.625 mm^2

Now, we can plug in all the values into the first formula to solve for the change in length:

ΔL = (80 KN * 5m) / (210 KN/mm^2 * 490.625 mm^2)
= 0.190 mm

Therefore, the resultant increase in length of the 5m steel roof tie rod under an 80 KN load is 0.190 mm. It is important to note that this is a small change and may not be noticeable to the naked eye. However, it is important to consider these changes when designing structures to ensure their stability and safety.

## 1. How do I calculate the resultant increase in length of a 5m steel roof tie rod?

To calculate the resultant increase in length of a 5m steel roof tie rod, you will need to use the formula L = F * L0 / A * E, where L is the increase in length, F is the load applied (in this case, 80 KN), L0 is the original length of the rod (5m), A is the cross-sectional area of the rod, and E is the Young's modulus of the steel used. Plug in the values for A and E, and solve for L to get the resultant increase in length.

## 2. What is the cross-sectional area of a steel roof tie rod?

The cross-sectional area of a steel roof tie rod can vary depending on the specific dimensions and type of the rod. To find the cross-sectional area, you will need to measure the diameter or width of the rod and use the formula A = π * (d/2)^2 for a circular rod or A = w * t for a rectangular rod, where d is the diameter, w is the width, and t is the thickness of the rod.

## 3. What is the Young's modulus of steel?

The Young's modulus of steel can also vary depending on the specific type and grade of steel. However, for most commonly used structural steel, the Young's modulus is typically around 200 GPa (Gigapascals) or 29,000,000 psi (pounds per square inch).

## 4. How does the load applied affect the resultant increase in length of a steel roof tie rod?

The load applied directly affects the resultant increase in length of a steel roof tie rod. As the load increases, the rod will experience more stress and will elongate more, resulting in a greater increase in length. This can be seen in the formula L = F * L0 / A * E, where F is a factor in determining the resultant increase in length.

## 5. Are there any other factors that can affect the resultant increase in length of a steel roof tie rod?

Yes, there are other factors that can affect the resultant increase in length of a steel roof tie rod. These include the material properties of the steel, such as its yield strength and ultimate tensile strength, as well as the temperature and environmental conditions in which the rod is being used. Additionally, any imperfections or defects in the rod can also impact its elongation under load.

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