# How Do You Calculate Reaction Forces in a Thermally Stressed Column?

• Xaspire88
In summary, the conversation discusses a problem with a constrained column under thermal stress where the goal is to find the reaction forces at the supporting ends of the column due to its own weight after being heated. The solution attempt involves using an equation for the deformation of the column under its own weight and thermal stress, but there may be an error in the signs of the reaction forces. The conversation also mentions that the class is theoretical and does not use numbers, and the solution may need clarification.
Xaspire88
I have a problem with a constrained column under thermal stress where I am to find the reaction forces at the supporting ends of the column due to its own weight after being heated. Attached is the problem, equations used, and my solution attempt.

I tried to solve for the reaction forces using the equation for the deformation of the column under its own weight and the thermal stress. This class is pretty much all "theory" as the prof. likes to say so we use no #'s.. Is my solution correct? or am I going down the wrong path. Thank you in advance.

Also, if anything I have written is unclear, feel free to ask me about it.

Xaspire88 said:
I have a problem with a constrained column under thermal stress where I am to find the reaction forces at the supporting ends of the column due to its own weight after being heated. Attached is the problem, equations used, and my solution attempt.

I tried to solve for the reaction forces using the equation for the deformation of the column under its own weight and the thermal stress. This class is pretty much all "theory" as the prof. likes to say so we use no #'s.. Is my solution correct? or am I going down the wrong path. Thank you in advance.

Also, if anything I have written is unclear, feel free to ask me about it.
I believe your solution is almost correct. It appears that you have the plus and minus signs, in your F_A and F_B reactions, reversed. When the column heats, the thermal stresses are compressive, so the reaction at A (bottom) from the thermal stresses acts up, and the top reaction at B, from the thermal stresses, points down. For the weight force, the bottom reaction (half the weight) acts up, and the top reaction (half the weight) also points up. So overall, combining both stresses, the bottom reaction would be greater than the top reaction, wouldn't it?

it is important to accurately solve problems and verify solutions. In this case, it is difficult to provide a response without seeing the attached problem, equations, and solution attempt. However, I can provide general guidance on approaching a problem involving a constrained column under thermal stress.

Firstly, it is important to understand the underlying principles and equations governing the behavior of a constrained column under thermal stress. This may involve studying the theory of elasticity, thermal expansion, and structural mechanics. Once you have a solid understanding of these concepts, you can then apply them to your problem.

Secondly, it is crucial to carefully consider all the assumptions and boundary conditions of the problem. This includes the material properties of the column, the temperature change, and the supports at the ends of the column. These assumptions and conditions will influence the equations and solutions you use.

Thirdly, it is important to use the correct equations and ensure they are applied correctly. This may involve algebraic manipulation and substitution to solve for the unknown reaction forces. It is also important to double-check your calculations and ensure they are consistent with the principles and equations you are using.

In summary, it is difficult to determine if your solution is correct without seeing the problem and your solution attempt. However, as a scientist, it is important to have a strong understanding of the underlying principles, carefully consider all assumptions and conditions, and accurately apply the correct equations to solve the problem. If you have any further questions or concerns, do not hesitate to seek guidance from your professor or a fellow scientist.

## 1. What causes thermal stress in a column?

Thermal stress in a column is caused by a difference in temperature between the top and bottom of the column. This difference in temperature causes the column to expand or contract, resulting in stress.

## 2. How does thermal stress affect the strength of a column?

Thermal stress can significantly weaken a column's strength and structural integrity over time. The repeated expansion and contraction can lead to cracks, buckling, and other forms of structural damage.

## 3. Can thermal stress cause a column to fail?

Yes, thermal stress can cause a column to fail if it is not able to withstand the stress and strain caused by the temperature difference. This can result in collapse or other forms of structural failure.

## 4. How can thermal stress be prevented in columns?

Thermal stress in columns can be prevented by using materials with a low coefficient of thermal expansion, ensuring proper insulation and ventilation, and incorporating expansion joints into the column design.

## 5. Are there any safety concerns related to thermal stress in columns?

Yes, there are safety concerns related to thermal stress in columns. If left unchecked, it can lead to structural failure and potential hazards for those in the building. It is important to regularly inspect and maintain columns to prevent any potential safety risks.

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