Math CentralQuandaries & Queries


Hi there, We are rollforming steel roofsheeting in 65M lengths and the question of linear expansion has cropped up.I would like to know what the expansion rate of this sheet would be over a temperature rise of say 40degree mm per Meter or whatever the norm is. The sheet is 0.53mm thick and is 700mm in width,I hope this is sufficient info to enable you to do your calculation.Many thanks, in anticipation.

Hi Ken,

The formulae for linear and area thermal expansion are as follows:

where α is the thermal coefficient for a material, ΛT is change in temperature, ΛL is change in length, ΛA is change in area, Lo is the initial length and Ao is the initial area. Similarly change in volume would be


The thermal coefficient for steel is 13.0 ×10-6 m/m K. You have to make sure all of your units are the same and a change of 40F is about 4.4K. You can just plug in all of values and solve for ΛL, ΛA or ΛV to find thermal expansion.

Hope this helps,


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