Linear Expansion of Steel Girder Due to Temperature Change

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SUMMARY

The discussion centers on calculating the height that a steel girder rises due to a temperature increase of 32°C, given its length of 3.77 m and a linear expansion coefficient of 12 x 10-6 /°C. The correct calculation involves using the formula for linear expansion, resulting in a height rise of approximately 0.052 m. Participants debated the validity of using the Pythagorean theorem for small differences, ultimately confirming its applicability in this scenario.

PREREQUISITES
  • Understanding of linear expansion principles
  • Familiarity with the linear expansion coefficient
  • Basic knowledge of the Pythagorean theorem
  • Ability to perform unit conversions and calculations
NEXT STEPS
  • Study the concept of thermal expansion in materials
  • Learn about the applications of the Pythagorean theorem in engineering
  • Explore the properties of steel and its behavior under temperature changes
  • Investigate real-world examples of structural expansion in civil engineering
USEFUL FOR

Students in engineering or physics, civil engineers, and anyone interested in the effects of temperature on material properties and structural integrity.

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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