A steel beam 10m long is installed in a structure at 20 C?

What is the beam's change in length when the temperature reaches (a) -25 C and (b) 45 C


Best answer:

Answer by gintable
No, it does not depend on the "density" of steel. It depends on the thermal expansion coefficient.

And, among the materials that are called "steel", other than stainless steel, it doesn't really vary much among all of the alloys. So you can pick a general value for steel.

According to this page, the linear expansion coefficient of steel is 13*10^(-6) lengths per Kelvin. And you know that Kelvin is the same size of degree increments as Celsius.
http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html

Our temperature increase is 45C - (-25C) = 70 C.
Our length is 10 meters
Our coefficient is 13e-6 1/C.

deltaL = alpha*L*deltaT

Result:
delta L = 0.0091 meters

This is pretty significant. About the width of a person's pinky finger. That is how much, this 10 meters of steel, will expand and contract over a typical environment's entire temperature range.

A hot summer day, could be 45 C in direct sunlight. And could be as cold as -25 C on a winter night. Maybe it was installed in the winter, so you need to prepare for its expansion when summer comes.

Generally, for steel structures, the expansion limit is about 30 meters. At least, this is the requirement for steel electrical conduit, according to the National Electric Code. Every 30 meters, you install a gap of about 1 inch. And this is consistent with the answer above.

Aluminum is more expansive than steel, and therefore needs expansion joints at smaller intervals. Typically it is listed as 12 meters or 40 feet.




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