Calculate the size of the cross section relating to tension

[joe465]

Homework Statement

A medium carbon annealed steel rod has a rectangular cross section and must cope with a tension of 3 tonnes. The thickness of the rod is 15mm. Calculate the size of the cross section.

Tension limit = 3 tonnes
Thickness = 15mm
Cross Section = ?

Homework Equations

o = P/A or P = Ao

P = total external force in Newtons
A = area of cross section in square millimetres
o = stress in Newtons per square millimetre

The Attempt at a Solution

I do not have clue where to start since I'm given a tension limit in tonnes. Tension is when two forces act in opposite directions causing the body to elongate. Now if i presumed that the tension needed to act directly downwards then it would be right to assume:

3000 * 9.81 = 29430N

Now I am stuck, am i on the right track?

Any help would be greatly appreciated

Thanks, Joe

 

[anathema]

Dear Joe,

Thank you for your post. You are on the right track with your attempt at a solution.

To find the size of the cross section, we need to use the formula o = P/A or P = Ao, where o is the stress in Newtons per square millimetre, P is the total external force in Newtons, and A is the area of the cross section in square millimetres.

In this problem, we are given the tension limit, which is 3 tonnes or 3000 kilograms. We need to convert this to Newtons by multiplying it by the acceleration due to gravity, which is 9.81 metres per second squared. This gives us a total external force of 29430 Newtons.

Now, we need to find the area of the cross section. We are given the thickness of the rod, which is 15mm. We can use this to find the area by multiplying it by the length of the rod, which is not given in the problem. Let's assume a length of 1 metre for simplicity. This gives us an area of 15 square millimetres.

Now, we can plug in our values into the formula o = P/A or P = Ao to find the stress in Newtons per square millimetre. This is equal to 29430/15 = 1962 Newtons per square millimetre.

Therefore, the size of the cross section is 15mm x 1m, or 15 square millimetres.

I hope this helps. Let me know if you have any further questions.