How to compute the deflectifon of a beam
First you need to know:
The length of the beam in meters, L
The weight supported by the beam in newtons, W
(If you know the mass supported in kg, multiply by 9.8 (gravity) to get the weight in newtons)
The elasticity, or Young Modulus, of the material in N/m^2, E. For steel this is about 200 x 10^9.
You also need to know a parameter called the second moment of area, I; this is a function of the dimensions and shape of the cross-section of the beam. There are standard formulas for things like rods, tubes, solid and hollow bars etc. Here's a calculator that will work it out for your angle:
http://www.calcresource.com/moment-of-inertia-angle.html . Entering your dimensions, it tells me that I = 1.48 X 10^-7. (There are separate values for x and y, and I'm a bit confused about which we need; but I think that your orientation is less rigid than if it were rotated by 90 degrees, so I've chosen the smaller value.)
Finally there is a constant that depends on how the beam is supported and loaded; if it's supported at the ends by resting on something and loaded evenly the value is 5/384.
Putting that all together, the deflection d is
d = 5/384 x W x L^3 / ( E x I )
In your case, that's
5/384 x 450x9.8 x 4^3 / ( 200x10^9 x 1.48x10^-7 )
= 0.124m
That's quite a lot more than the 5mm you were hoping for!
One thing to note is that the deflection increases very quickly as the length of the beam increases - it increases with the cube of the length. So if you halved the length of the beam, e.g. by using 2 2m sections, the deflection would decrease 8-fold to about 15mm. But you can do better than that; if you have a single 4m piece of steel that's supported at the middle it's more rigid than two separate 2m pieces - I think by a factor of about 2.5 (the 5/384 parameter becomes 0.0052). So that would get you quite close to the 5mm you're looking for.
(Edit - oops, I forgot that the weight is also halved in these cases, further reducing the deflection.)
Of course, I'm not a structural engineer, and what a structural engineer (or rather the software he uses) can do is also quantify other aspects such as torsion - as tony1851 mentions. Maybe long before it has deflected by 124mm it will twist, unless something is holding it back.
