How Does Thermal Expansion Affect Stress in a Bar?

[heloo]

Hi, I have been asked to determine the stress in a bar which has a diameter of 50mm when the temperature changes from 20 C to 50C. That's the first part.

Secondly, I need to then answer whether or not the stress will be sufficient enough to raise a constraining load of 40 tonnes.

Young's Modulus is 70Gpa.

I think i need to use (1+alpha delta T), to work out the change in length. But that's as far as I've got.

Can anyone give me a pointer in the right direction as i totally confused myself.
Thanks

Homework Statement

Yes

Homework Equations

Unsure of what equations are relevant

The Attempt at a Solution

None

 

[LawrenceC]

OK, you have the equation to determine the change in length were it not constrained. So how much force does it take to compress it back to its original length? Do you know what equations to use?

 

[heloo]

I am unsure of what equations to use, i assume i need to work out the thermal expansion but i don't know how to calculate how much force is needed to force it back to its original length.

 

[LawrenceC]

You should have seen the following equation by now in your studies:

S = e * E

where S is stress, e is strain, and E is Young's Modulus. Given the definition of stress as force per unit area, you can solve it from this point onward.

 

[DeeNos]

Hi there,

Thermal expansion is a common phenomenon in materials, where their dimensions change in response to temperature changes. To determine the stress in a bar with a diameter of 50mm when the temperature changes from 20°C to 50°C, you will need to use the equation for thermal expansion:

ΔL = αLΔT

Where ΔL is the change in length, α is the coefficient of thermal expansion, L is the original length, and ΔT is the change in temperature. This equation assumes that the material is uniform and the change in temperature is small.

To find the stress, you will then use the equation for stress:

σ = Eε

Where σ is the stress, E is Young's modulus, and ε is the strain. To find ε, you can use the equation:

ε = ΔL/L

Once you have calculated the stress, you can compare it to the constraining load of 40 tonnes to determine if it is sufficient enough to raise the load.

I hope this helps guide you in the right direction. If you need further assistance, don't hesitate to ask for clarification.