The best source of information on weld nuts that I have seen is the following standard:

DaimlerChrysler Corporation Process Standard No: PS-1804, WELD NUTS - PROJECTION WELDING

I can probably give you some numbers if you provide some additional details:

What type of nut are you interested in using? hex vs. round, pilot vs. non-pilot, how many projections, etc.

The nut in question is GM #11503319 M8X1.25 Thread.  There are three weld projections per nut.  Each projection has a radius and each nut has a pilot for hole location.  

I could not find that particular weld nut in my GM catalog, so I am guessing it is an older part number for the hex-style, type E weld nut.  Anyway, the data that I have for push-off strength or torsional strength requirements of a weldnut is given as a function of mating material thickness, not projection height.  Obviously one would use the longer projection height when welding into a thicker sheet material.  For an M8, the following should be considered minimum requirements:

Push-off strength
  metal thickness from 0.76-1.27 mm :  3830 N
                                1.30-1.85 mm :  5960 N
                                1.88-2.44 mm :  8010 N
                                2.46-3.28 mm : 10320 N
                               >     3.30 mm : 12460 N

Torsional strength : 113 Nm

I hope this helps.

Correction.  The nut in question is a M8 X 1.25 thread square nut with four radius projections and a pilot. Using the PS-1804<S> standard from Daimler Chrysler, what is the class, i.e., A, E, EE, F or G?  Thanks.

I think it is a type A, but I don't know for sure.  If you have access to the DCX standard fastener catalog, you can check actual weld nut drawings, which has the type listed at the top.

fgarver,

Perhaps it is too late for changes, but I would recommend against the square four-projection nut.  The main reason is that three points define a plane, so the fourth projection is routinely not touching the mating component, and therefore has a deficient weld.  GM does not recommend using those anymore, instead they prefer the round, three-projection weld nuts.  For the M8x1.25 size, the GM part numbers are 11517412 (plain) and 11517413 (with thread masking).