Linear Expansion of Steel Girder Due to Temperature Change

[chawki]

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?

 

[gneill]

The Attempt at a Solution

Is it 1.79m?

Seems a bit unlikely. Show your work.

 

[chawki]

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 ?

 

[gneill]

That looks better!

 

[chawki]

Wow, my answer is correct?!

 

[gneill]

You sound surprised.

 

[chawki]

yes iam. i lost some self-confidence

 

[chawki]

You sound surprised.

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 ?

 

[gneill]

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!