NCEES Practice Exam MD&M #112 question

[katiejune]

This problem appears in the 2011 version of NCEES Practice Exam as #520 and appears in the 2016 version as #112.

It is about a steel bar expanding under a temperature increase. The bar is mounted against a spring, the system is horizontal. The system is mounted between two walls.

It is asking for the increase in force produced by the thermal expansion of the bar.

I've tried this problem a few times and I keep getting 648lb instead of their answer of 624. So I'm just looking for some guidance on how they are solving this one, mainly how they are coming up with the main equation they are using, or the logic?

Thanks so much!

 

[katiejune]

http://www.chegg.com/homework-help/problems-section-statically-indeterminate-problems-involve-t-chapter-3.6-problem-7p-solution-9780470912003-exc

similar problem

 

[J_MEC]

Katie, I think you are neglecting the deformation of the material/bar. There will be deformation in the material, not just the spring. So they actual change in length of the spring is the thermal expansion minus the deformation of the material  [ FL/(AE) ].

See my solution at the link below. Delta_S is deformation of the bar, Delta_t is the thermal expansion. I solved using the fx-115es equation solver since I am lazy when it comes to algebra. 

https://www.dropbox.com/s/7zvjkw3ccoas4rb/20170413_215903.jpg?dl=0

 

[katiejune]

Thank you so much for the lead. Are you saying that the elastic deformation is the force of the spring acting on the bar? So as the bar expands, there is a force the spring is pushing back on the bar, thus reducing the compression of the spring? This is how I understand this and I just want to make sure. Thank you!!

 

[J_MEC]

Yes, you have it right. As the bar expands due to thermal expansion and compresses the spring, the spring will exert a force on the bar which will cause elastic deformation of the bar and compress the bar.

 

[katiejune]

Thank you! I am about to post a question on #121.