Effect of thermal expansion on restraints

In summary, the conversation discusses how to calculate force reactions within fixed restraints when a beam undergoes thermal expansion. The principle of superposition is mentioned, which states that the net response of multiple stimuli is the sum of their individual responses. The formula Delta=PL/AE is used to determine the displacement caused by thermal expansion, and then stress/strain equations are used to calculate the force required to push the beam back into place. The conversation also touches on how the method would change if the beam was made of different materials with varying young's moduli or cross sectional areas.
  • #1
Ry122
565
2
When a beam undergoes thermal expansion and the restrains that support the beam are fixed so that no movement is allowed, how do you calculate the force reactions within the restraints? The restraints are two walls, and before expansion occurs no horizontal reaction forces are present.

Since the amount by which the beam is deflected would be equal to the amount by which the beam thermally expands could it be determined with the deflection formula Delta=PL/AE?
 
Engineering news on Phys.org
  • #2
Hint: think superposition

Assume that there is intially only one wall, and then a force that pushes the beam back "into place".
 
  • #3
ok but do I use the formula i mentioned above to determine the Force that does that?
 
  • #4
Yes, assume that the loading happens in two steps. The principle of superposition states that
The net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.

In layman's terms, it means that you can take the effect of each load component and add them up to get the sum. Since your bar is fully constrained, the sum effect is no displacement.

So, use your formula to find the displacement that a certain delta T would cause. Then, using stress/strain equations, determine the force and stress required to "push" the beam back into place. That will be your second loading.
 
  • #5
Delta=PL/AE doesn't have anything to do with delta T though.
Do you mean DeltaTx(Alpha)x(L)=Displacement?
So I don't use Delta=PL/AE at all?

For the stress strain equation would i just use
y=mx
where m = young's modulus
x=percentage strain
and y=stress?

How would the method for doing this change if the first 1/3 of the Beam was made of a material with E=100,000 and the next 2/3 were made of a material with E=200,000?
 
Last edited:
  • #6
I didn't check your equations, I was simply saying that the thermal expansion causes a change in length.
[tex]
\Delta x = l \alpha \Delta T[/tex]
The constraints will then exert a force back on the beam with the magnitude that negates expansion. I'm not going to do it for you, but your PL/AE equation may come in handy.
 
  • #7
Would the method for doing this change if the first 1/3 was made of brass of a different cross sectional area to the 2/3 of the beam which is made of steel?
 
  • #8
The method is going to stay the same, but the implementation would be a little trickier.
 

Related to Effect of thermal expansion on restraints

What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract when subjected to changes in temperature.

How does thermal expansion affect restraints?

When a restrained material is heated, it will expand and exert a force on the restraints. This force can cause stress and potentially damage the restraints if they are not designed to withstand the expansion.

What materials are most affected by thermal expansion?

Thermal expansion affects all materials to some degree, but it is most noticeable in materials with high coefficients of thermal expansion, such as metals and plastics.

How do engineers account for thermal expansion in restraints?

Engineers must carefully consider the material properties and potential temperature changes when designing restraints. They may use materials with lower coefficients of thermal expansion or incorporate features that allow for expansion without causing damage.

Can thermal expansion cause restraints to fail?

In extreme cases, thermal expansion can cause restraints to fail if they are not designed to handle the forces exerted by the expanding material. This is why it is important for engineers to carefully consider thermal expansion when designing restraints.

Similar threads

A How are the thermal expansion of a solid and the stress tensor related?
Replies
3
Views
2K
Thermal Expansion of a Triangular Frame
Replies
2
Views
1K
B Loschmidt's paradox and free gas expansion
Replies
5
Views
1K
Thermal Physics: Reversible processes
Replies
19
Views
2K
Thermal Expansion, Young's Modulus
Replies
5
Views
7K
Thermal Physics Expansion Coefficient Problem
Replies
13
Views
20K
Thermal expansion of an aluminum bar
Replies
1
Views
2K
Free Thermal Expansion and Stress
Replies
8
Views
10K
Entropy-Isobaric Expansion of a gas to thermal equilibrium
Replies
4
Views
5K
B Beware of "truthiness" in astronomy in seemingly reliable websites
Replies
21
Views
2K

Hot Threads

Recent Insights

Back
Top