Linear Expansion of Steel Girder Due to Temperature Change

In summary, the problem involves a steel girder with a length of 3.77m and a fracture in the middle. The temperature has risen by 32°C and the task is to find the height of the girder if it is fixed at both ends, using the linear expansion coefficient of steel (12*10^-6 /C). After showing work, it is determined that the girder rises 0.052m from the middle, which is a plausible answer despite initial doubts.
  • #1
chawki
506
0

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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  • #2
chawki said:

The Attempt at a Solution


Is it 1.79m?

Seems a bit unlikely. Show your work.
 
  • #3
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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  • #4
That looks better!
 
  • #5
Wow, my answer is correct?!
 
  • #6
You sound surprised.:smile:
 
  • #7
yes iam. i lost some self-confidence
 
  • #8
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 ?
 
  • #9
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!
 

Related to Linear Expansion of Steel Girder Due to Temperature Change

What is linear expansion of solid?

Linear expansion of solid refers to the increase in length of a solid material when it is heated. This phenomenon occurs due to the increase in the average distance between the atoms or molecules in the solid, which causes the material to expand in length.

What causes linear expansion of solid?

Linear expansion of solid is caused by the increase in temperature. When a solid material is heated, its atoms or molecules start to vibrate at a higher frequency, which causes the average distance between them to increase. This increase in distance results in the expansion of the material.

How is linear expansion of solid measured?

Linear expansion of solid is measured using the coefficient of linear expansion (α). This coefficient represents the change in length of a material per unit length per degree change in temperature. It is usually expressed in units of 1/°C or 1/K.

What is the formula for calculating linear expansion of solid?

The formula for calculating linear expansion of solid is: ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length of the material, and ΔT is the change in temperature. This formula can be used to calculate the expansion of a solid material for a given change in temperature.

What are some practical applications of linear expansion of solid?

Linear expansion of solid has several practical applications. It is used in the design and construction of bridges, buildings, and other structures to account for the expansion of materials due to temperature changes. It is also used in the manufacturing of precision instruments, such as thermometers and thermostats, to ensure accurate temperature readings. Additionally, it is utilized in the production of everyday objects, such as cookware and pipes, to prevent warping or cracking due to temperature changes.

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