Is a 1/8" AR400F steel plate strong enough, for 4,000 lbs?

I have a Ford F350 cab & chassis and a gooseneck trailer. For the gooseneck hitch I want to use a steel plate.
The steel plate will be BOLTED to the frame, above the rear axle And the gooseneck ball will be welded to the steel plate.

The distance between the frames is about 34". So the plate Is going to be 34"long x 8" wide.

The trailer is 16,000 lbs GVWR. And a maximum tongue weight of 4,000 lbs (at 25%)

A regular A36 steel plate, 3/8" thick, will bend under load. (A36 mechanical properties: Brinell=112, Tensile=58,000 psi, Yield=36,000 psi)

So I'm thinking to use a 1/8" thick, high strength steel ASTM 514 / AR400F (Tensile Strength=184,000 psi, Yield Point=150,000 psi, Elongation = 23% in 2",Brinell Hardness = 360/444)

Is a 1/8" AR400F steel plate strong enough, for maximum 4,000 lbs?

If not, what do you think about AR400F 3/16" thick ?

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