Engineering - Stress and Buckling Load problems

[Plasma2]

Hello,
I am in an engineering summer camp, but since this is a condensed course and it seems the professors assumed the class already had some background in the subject, I am slowly getting lost. They gave us practice tests from previous years, and I was wondering if someone could show me how to complete a few problems. Though I know you wonderful people will explain your answers, could you also tell what conversions you use as well since that is likely what we will have to apply ourselves? Thanks in advance!

1)

You have two samples of the same material. These samples have different lengths and diameters.

• Sample 1: 10 cm long and 1.0 mm diameter -- Buckling load at failure: 10kN
• Sample 2: 20 cm long and 1.0 mm diameter

What is the buckling load that would cause Sample 2 to fail? (report answer in kN)

2)

A circular rod with a diameter of 10 mm experiences a tensile force of 100 kN. What is the stress in the rod in MPa?

3)

A wire that is 1.0 mm in diameter is stretched from 10.6 cm to 10.9 cm by a force of 150 N. Assuming the elastic limit is not exceeded, what is the force required to stretch the wire from 10.6 cm to 11.1 cm?

 

[I like Serena]

Hello,
I am in an engineering summer camp, but since this is a condensed course and it seems the professors assumed the class already had some background in the subject, I am slowly getting lost. They gave us practice tests from previous years, and I was wondering if someone could show me how to complete a few problems. Though I know you wonderful people will explain your answers, could you also tell what conversions you use as well since that is likely what we will have to apply ourselves? Thanks in advance!

Hi again Plasma! ;)

To be honest, I'd rather not just give fully worked answers.
I believe that's ultimately not very useful to you, and no fun for me either.
Anyway, let's see what we can do.

1)

You have two samples of the same material. These samples have different lengths and diameters.

• Sample 1: 10 cm long and 1.0 mm diameter -- Buckling load at failure: 10kN
• Sample 2: 20 cm long and 1.0 mm diameter

What is the buckling load that would cause Sample 2 to fail? (report answer in kN)

Do you have a formula for the stress in a material of a certain length and diameter?
We should be able to tell what the answer is from that formula.

On a different note, do you have a sense of what's going on?
We have a sample that is twice as long. What do you think about its buckling strength when the same load is applied?

2)

A circular rod with a diameter of 10 mm experiences a tensile force of 100 kN. What is the stress in the rod in MPa?

Again we're looking for a formula. Do you have one?

Okay. Let me help you a bit here.
The definition of stress $\sigma$ is:
$$\sigma = \frac F A$$
where $F$ is the tensile force, and $A$ is the area of a cross section.

Does it look familiar? Can you find the stress from that?

3)

A wire that is 1.0 mm in diameter is stretched from 10.6 cm to 10.9 cm by a force of 150 N. Assuming the elastic limit is not exceeded, what is the force required to stretch the wire from 10.6 cm to 11.1 cm?

This is where Hooke's Law comes into play. Did you see it in your notes?
Do you have a formula for the force when stretching a wire by a certain amount?

Hooke's Law says that the force is linear with the distance it is stretched - if there is no permanent elastic deformation.
So stretching it twice as far means the force is twice as big.
Can we find the force from that?

 

[Plasma2]

To be honest, I'd rather not just give fully worked answers.

Seems fair.

Do you have a formula for the stress in a material of a certain length and diameter?

Found it, 1/4 the strength.

Okay. Let me help you a bit here.
The definition of stress $\sigma$ is:
$$\sigma = \frac F A$$
where $F$ is the tensile force, and $A$ is the area of a cross section.
Does it look familiar? Can you find the stress from that?

I knew that part, I didn't know how to convert between Newtons and Pascals

This is where Hooke's Law comes into play. Did you see it in your notes?

Not in my notes, but online yes. Thanks for the pointer.

Sorry for the long delay, but thanks for encouraging me to get it. After all said and done, these were not the parts of the quiz I lost points on. If you want I can show you the final result that will come of all these and other calculations once my group and I build our spaghetti bridge. Anyway, off topic. Thanks for the help.