Linear Expansion of Steel Girder Due to Temperature Change

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Homework Help Overview

The discussion revolves around the linear expansion of a steel girder due to a temperature increase. The original poster presents a scenario involving a steel girder with a specified length and a temperature change, seeking to determine the height the girder rises at its midpoint when fixed at both ends.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore calculations related to linear expansion and question the validity of their results. There is a discussion about the application of the Pythagorean theorem in this context, with some participants expressing uncertainty about the appropriateness of its use given the small changes in length.

Discussion Status

The conversation reflects a mix of attempts at calculation and verification of results. Some participants express surprise at their findings, while others question the assumptions made regarding the geometry involved in the problem. There is no clear consensus on the correctness of the approaches taken.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information available for discussion. The original poster's confidence in their solution appears to fluctuate, indicating a potential impact of peer feedback on their understanding.

chawki
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Homework Statement


A girder made of steel. The length of the girder is 3.77 m. In the middle of the girder there is a fracture. The temperature rises 32° C.

Homework Equations


Find the height that the girder rises from the middle, if it is fixed at both ends. The linear expansion coefficient for steel is 12*10^-6 /C.


The Attempt at a Solution


Is it 1.79m?
 
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chawki said:

The Attempt at a Solution


Is it 1.79m?

Seems a bit unlikely. Show your work.
 
L-L0 = 1.2 E-5 * 3.77 * 32 = 0.00144m
L=3.77+0.00144 = 3.77144

3.77144/2= 1.88572
3.77/2= 1.885

1.885722 =x2 + 1.8852
x=0.052m ?
 

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That looks better!
 
Wow, my answer is correct?!
 
You sound surprised.:smile:
 
yes iam. i lost some self-confidence
 
gneill said:
You sound surprised.:smile:

I think it doesn't look correct...because the the difference between L and L0 is tooooo small to allow the use Pythagorean theorem, don't you think ?
 
I don't know of any reason why Pythagoras would fail to work no matter how small the difference was; a triangle is still a triangle if it has three sides!
 

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