How Does Thermal Expansion Affect Stress in a Bar?

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Discussion Overview

The discussion revolves around determining the stress in a bar due to thermal expansion when subjected to a temperature change. Participants explore the relevant equations and concepts necessary to calculate the stress and whether it can support a specific load, with a focus on the implications of thermal expansion and material properties.

Discussion Character

  • Homework-related, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving a bar with a specified diameter and temperature change, seeking guidance on how to calculate the resulting stress.
  • Another participant suggests using the equation for change in length due to thermal expansion and questions how to determine the force required to return the bar to its original length.
  • A third participant expresses uncertainty about the equations needed for calculating the force and thermal expansion.
  • A later reply introduces the relationship between stress, strain, and Young's Modulus, providing a formula to connect these concepts.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing uncertainty about the appropriate equations and methods to use for the calculations. No consensus has been reached on how to proceed with the problem.

Contextual Notes

Participants have not specified certain assumptions, such as the value of the coefficient of thermal expansion or the constraints on the bar, which may affect the calculations. There is also a lack of clarity regarding the specific equations that should be applied in this context.

heloo
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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
 
Last edited:
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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?
 
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.
 
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.
 

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