I am covering a portion of my house in 4x8 sheets of hot rolled steel. How much will it expand and contract?

The steel is 3/16 thick and the summer time highs reach 90 F and winter time lows -30 F. Is the relationship linear? Would a 2x4ft sheet expand and contract half as much?

Answer:
I remember the rule: 50 microinches per inch per degree Fahrenheit.

You have a 120 degree swing. Each sheet is 96 inches long. By that rule, the expansion would be:
50*10^-6 * 120 * 96 = 0.576 inches.

That's a lot of size changing.
The cooefficient of thermal expansion for Carbon Steel is 6E-6 in/in deg F, meaning that for each change in temperature of 1 degree faraheit, each inch of steel will elongate 6e-6 in.

The relation is linear thus, by length i.e. you 2x4 ft sheet will change dimensions 1/2 of your 4x8.

If we consider the full ltemperature swing, -30 -> 90 that is 120 degree delta. You maximum size is 8x12" = 96 in, thus from one extreme to the other you will see:

96*120*6e-6 = 0.07" difference in length. (a little more than 1/16th of an inch).

Now of course, you probably would install the sheets some where in the middle of the temperature range, so your average change is less. Also, the change will be restrained by your fastening system, so instead of seeing it, instead forces will build up on your nails/screws.

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