# Linear expansion of solid

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.

Is it 1.79m?

Mentor

## 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 ?

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Mentor
That looks better!

chawki
Wow, my answer is correct?!

Mentor
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 ?

Mentor
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!