Calculation of Thermal stress in a steel cube put inside another bigger steel cube

In summary, the thermal stresses in the system are related to the temperature gradient and the bending stiffness of the bars.
  • #1
chetanladha
59
0
Hi.
I am trying to calculate the thermal stresses in a steel cube which is placed inside another steel cube of bigger dimensions, supported by steel bars at the base and sides.
Both the cubes are in contact with fluids at different temperatures.
Can someone please suggest the methodology as i can't think of anything except using the conventional formulae ( E*A*T).

For marine engineers, i am trying to do it for ship's double bottom.

Thanks in advance
 
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  • #2


Any cheap finite element analysis package can do this.
 
  • #3


Unrest said:
Any cheap finite element analysis package can do this.

Hii..
I am not very good in FEA..
Thats the reason i want to do it mathematically..

Any ideas in there..
 
  • #4


chetanladha said:
Thats the reason i want to do it mathematically..

Can you describe the geometry a bit more clearly? Maybe with a sketch.

Is the internal cube connected to the external one with the bars? It seems like there are 3 cavities, inside the internal cube, between the cubes, and outside the bigger cube. Where are the fluids?

Are you only interested in the steady state of temperature, after it has been assembled with the same temperature throughout, then the different temperatures are applied and allowed to stabilize?

I'm hoping the problem reduces to finding the longitudinal stresses in the bars and then doing some conventional stress analysis to find the stresses in the cubes caused by the forces that the bars apply to them.
 
  • #5


Unrest said:
Can you describe the geometry a bit more clearly? Maybe with a sketch.

Is the internal cube connected to the external one with the bars? It seems like there are 3 cavities, inside the internal cube, between the cubes, and outside the bigger cube. Where are the fluids?

Are you only interested in the steady state of temperature, after it has been assembled with the same temperature throughout, then the different temperatures are applied and allowed to stabilize?

I'm hoping the problem reduces to finding the longitudinal stresses in the bars and then doing some conventional stress analysis to find the stresses in the cubes caused by the forces that the bars apply to them.

Hi.
All the members in diagrAm are steel bars. The figure is a cross section of a model.
The temperatures of two fluids remain the same (70 & 30 C) throughout the process, and heat is continuously being transferred from oil to water..

Now with this kind of heat transfer, and temperature distribution, i want to find out the thermal stresses that will be generated..

Am i being clear?? or should i explain furthermore..

Thanks,...
 
  • #6


Hey!
Sorry the file was too big to upload..
i have changed the format..
 

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  • #7


This is quite complicated. To do it by hand you'll have to make a lot of simplifying assumptions.

Can you assume the inside container is all at 70deg and the outside container at 30? This might not be valid if there's heat transfer across the space between them and might lead to bending stresses in the plates due to the temperature differences though their thicknesses.

Maybe you can treat the bars as being pin-jointed at their ends. Then you don't have any stress caused by bending of the bars.

There's also a complication caused by the stiffness of the plates. Two ways you could simplify it:

1) Assume the plates are rigid in bending. Find the stresses in the bars. Assuming a linear temperature gradient, calculate the longitudinal thermal stress using the average temperature (50deg). You'll also need to know the initial temperature when there's no thermal stress.

2) Assume the plates have zero bending stiffness. The bars will have zero thermal stress and you can calculate their thermal strain in a similar way. Then you know the deflection of the plates and can calculate the stresses in them from their deflections. Again you'll need to know the initial temperature where the plates have no stress caused by thermal strain in the bars.

If you don't make any such simplifications then you don't need to know the initial temperature.

You need to pay some attention to how the plates are supported at the top. Are the sides free to bend in/out? I guess they're fixed together by something. If they're free to move vertically wrt each other then there may be no stress due to the bottom bars because the inside container can freely move upward on the thermal expansion of the bottom bars.
 
  • #8


also, it looks like the actual cross section of the bars will have an effect if you are talking about mechanical stresses... like, an i-beam will flex differently to a rectangular bar, for instance
 
  • #9


carmatic said:
also, it looks like the actual cross section of the bars will have an effect if you are talking about mechanical stresses... like, an i-beam will flex differently to a rectangular bar, for instance

Hi Carmatic.
You can consider the system as a cube filled with water placed in another cube and supported by a lot of steel bars. (steel bars are solid cuboid)
What i have shown in the figure is a cross section..

Like UNREST has said that it's complicated, and i'll need to consider the bending stresses in the bars too..
 
  • #10
You might want to check out the following reference:

TEMPERATURE-INDUCED STRESSES IN BEAMS AND SHIPS
NORMAN H. JASPER

Journal of the American Society for Naval Engineers

Volume 68, Issue 3, pages 485–497, August 1956

This article is available thru:
Wiley Interscience

http://onlinelibrary.wiley.com/doi/10.1111/j.1559-3584.1956.tb05265.x/abstract
 
  • #11


chetanladha said:
You can consider the system as a cube filled with water placed in another cube and supported

You mentioned they are cubes several times. Is is actually symmetric? With bars on the top as well? Seems unlikely, but that could make it a bit simpler.
 
  • #12


It doesn't have the bars on top..

Any more ideas??
 
  • #13


I don't think there's really a comprehensive answer that can be described on a forum. You'd need to go through a few textbooks and do piles of calculations. Break it down into individual members and find equations for all their moments and forces. Write up a big system of equations and solve. But by the time you've done that you might as well have spent a week learning to use FEA.

If you explain the application in more detail, that might show ways it can be simplified. For example, is your diagram showing the cross-sections of the bars or their side view? What happens in the direction into the page? The end conditions will probably be significant, and may introduce twisting in the plates, do you expect that? Are you comfortable doing hand calcs for plates? Are the plates really homogeneous without other stiffening members? If you get a partial result which shows the design won't work, is that sufficient? Do you need to be able to modify it until it does work? Are you able to change things like connections between the parts? Is there a significant difference in scale between the plates and the bars?

But I think first, you should find the temperature distribution. What kind of heat transfer is occurring in the cavity between the inside and outside?
 

1. How is thermal stress calculated in a steel cube?

Thermal stress in a steel cube is calculated by determining the difference in temperature between the inner and outer surfaces of the cube, the material properties of the steel, and the dimensions of the cube. This information is then used to calculate the thermal strain, which is then multiplied by the modulus of elasticity to determine the thermal stress.

2. What factors affect the thermal stress in a steel cube?

The thermal stress in a steel cube is affected by several factors, including the temperature difference between the inner and outer surfaces, the material properties of the steel, the dimensions and geometry of the cube, and the boundary conditions of the cube (such as whether it is fixed or free to expand).

3. How does the thermal stress in a steel cube affect its structural integrity?

If the thermal stress in a steel cube exceeds the yield strength of the material, it can cause permanent deformation or even failure of the cube. However, if the stress is within the elastic limit of the steel, the cube may experience temporary deformation but will return to its original shape once the temperature difference is removed.

4. Can the thermal stress in a steel cube be reduced?

Yes, the thermal stress in a steel cube can be reduced by either decreasing the temperature difference between the inner and outer surfaces, or by using a steel with a higher yield strength. Additionally, incorporating design features such as expansion joints can also help to reduce thermal stress.

5. How is thermal stress in a steel cube typically managed in engineering applications?

In engineering applications, thermal stress in a steel cube is typically managed by carefully considering the material properties, dimensions, and boundary conditions during the design phase. Additionally, thermal stress can be reduced through proper insulation and ventilation of the cube, as well as incorporating expansion joints and other design features to accommodate for thermal expansion and contraction.

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