joist span calculation conundrum

I wonder if anyone can point me in the direction of a formula for calculating the maximum span of a joist?
The 'knowns' are these (I'm in the UK, by the way, so everything is in SI units):
spacing (mm) load per unit length (kN/m) fibre stress of timber (N/mm2) breadth of joists (mm) depth of joists (mm)
The 'unknown' is what maximum span would result for a given set of parameters - I assume it would be possible to derive it from the data available...
For example: joists centres: 353mm load per unit length: 0.9kN/m fibre stress of timber: 7.5N/mm2 breadth of joist: 47mm depth of joist: 200mm span of joist: ?
The reason for this is that I'm (trying to) draw up a set of tables for preliminary joist sizing (UK span tables only provide metric spacing - I'm doing a set with imperial spacing for use with alterations of old buildings).
Hope somebody can help with this one!

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In a previous post John says...

There are three parts to your question: bending strength,shear strength and deflection limitations.
For floor joists with normal floor loading we can generally ignore the shear calculation, so that leaves flexure and deflection.
For flexure, the bending formula is fb = M/Sx or
fb = (wl^2)/8Sx where Sx = (bd^2)/6 fb = (6wl^2)/(8bd^2)
L = sqrt[(8bd^2)*fb/(6w)] make sure your units are compatible
For deflection of floors:
L/360 = (5wL^4)/(384EI) where I= (bd^3)/12
I will leave you to work out the math.
Your "maximum" span is the smaller of the two L's
Bob Morrison, PE, SE
R L Morrison Engineering Co
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