Thermal radiation
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The Problem:

How to decide the colour (light gray or orange) to paint the top surface of the STEEL girders of a Truck Scale [two girders of 25m long each with the top surface exposed to sunlight; in the middle part is the concrete pavement of 3m wide and 0.25m of thickness] like this ][=====][ The ][ are the steel girders and the ==== is the concrete platform. Mass of each girder: 1,300kg; top exposed surface of each girder: 5 sq.m

The objective is to control or minimize the thermal expansion of the structure to avoid it to "stuck" at the end walls on hot summer (ambient of 40C) and to prevent it to stay too loose on winter (15C). Of course my first argument was / is : light gray is of course the best ... end of question... but why??
The subsequent question: how much will it expand if painted light gray and if painted black?

But reasoning further ... after a while on the sun it does not matter the paint colour because both (if I compare gray and black paints) will reach thermal equilibrium and both will expand the same amount, only one will take more time than another. Is it true? If the rate of absorption is the same as the emission then the gray will always be cooler and expand less ... or not?

How do I justify this phenomena, or the final solution, using Kirchoff and Boltzman concepts / equations (if applicable...) or any other law of Physics, without carrying an experiment? I tried and was unsure ....too rusted after my engineerig graduation back in 64, but still eager to learn...

Best Regards