What is the formula for bending stress of a plate with a central point load

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I have a steel deck (a) 2000mm x (b) 4200mm overall comprising 12.5mm durbar plate (grade S275) welded to RSA ribs at 400mm spacings, the plate is unsupported in the other plane (4200mm span) with the exception of end plates.
I wish to drive a forklift truck over the plate with a wheel load of 37.5KN max, which will result in a concentrated load over a small area midspan (a1) 250mm x (b1) 50mm.

I wish to check the bending capacity of the plate by hand (as opposed to FEA) and my question is therefore what would be a suitable approach/calculation for this check ??

I have looked at Roarks formulas but struggled to find a suitable support condition for the plate, so have pondered if a simplistic approach would be to determine a section modulus (bd 2/6 for the plate based on a 45 deg dispersion from the concentrated load to the supporting rib, can anybody see a problem with this ?
 

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