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

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Discussion Overview

The discussion revolves around calculating thermal stresses in a steel cube placed inside a larger steel cube, with both cubes supported by steel bars and in contact with fluids at different temperatures. Participants explore methodologies for this calculation, including mathematical approaches and finite element analysis (FEA), while considering the complexities of the geometry and heat transfer involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a methodology for calculating thermal stresses, suggesting conventional formulas like E*A*T but expressing a preference for mathematical approaches.
  • Another participant suggests using a finite element analysis package, but the original poster indicates a lack of proficiency in FEA and a desire for a mathematical solution.
  • Clarifications are requested regarding the geometry of the setup, including the connection of the internal cube to the external one and the arrangement of the fluids.
  • Some participants propose simplifying assumptions, such as treating the internal cube as uniformly at 70°C and the external one at 30°C, while noting potential complications from heat transfer and bending stresses.
  • Discussion includes considerations of the stiffness of the plates and how it affects stress calculations, with suggestions for treating the bars as pin-jointed or assuming rigid bending.
  • Participants highlight the importance of understanding the cross-section of the bars and its impact on mechanical stresses.
  • One participant mentions the need for a comprehensive approach that may require extensive calculations and references to textbooks, while another suggests that finding the temperature distribution is a crucial first step.

Areas of Agreement / Disagreement

Participants express a range of views on the complexity of the problem, with some agreeing on the need for simplifications while others emphasize the difficulty of achieving a comprehensive solution. There is no consensus on a single methodology or approach to the problem.

Contextual Notes

Participants note that the problem may require numerous simplifying assumptions and that the geometry and boundary conditions significantly affect the analysis. The discussion also highlights the potential for bending stresses and the importance of understanding heat transfer mechanisms.

chetanladha
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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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Any cheap finite element analysis package can do this.
 


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..
 


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.
 


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,...
 


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

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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.
 


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
 


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?
 

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