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

[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.

 

[PhanthomJay]

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?