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You're missing way too much information to provide a qualified answer. Without knowing how much weight you're trying to support, the thickness of the table top, or how much deflection (sag) is acceptable, it's impossible to tell.
I'm guessing you're just looking for a rough answer though so... no. It won't. Go by you're local home store and grab a 6' or 8' 2x4. Set it on something so that it's supported on the ends but not in the middle. Put something that weighs ~20 pounds in the middle to simulate a monitor. See how much is flexes? Thats called deflection. If you can see it flex, it's a good indication that it's not supported enough. You can see if they have 2x2 hardwood pieces to do the same test with. A hardwood like maple or oak would provide a a lit more strength but I'd still guess it isn't enough.
You'll likely need to build some kind of structural framework like TeeJay88 did.
You're missing way too much information to provide a qualified answer. Without knowing how much weight you're trying to support, the thickness of the table top, or how much deflection (sag) is acceptable, it's impossible to tell.
I'm guessing you're just looking for a rough answer though so... no. It won't. Go by you're local home store and grab a 6' or 8' 2x4. Set it on something so that it's supported on the ends but not in the middle. Put something that weighs ~20 pounds in the middle to simulate a monitor. See how much is flexes? Thats called deflection. If you can see it flex, it's a good indication that it's not supported enough. You can see if they have 2x2 hardwood pieces to do the same test with. A hardwood like maple or oak would provide a a lit more strength but I'd still guess it isn't enough.
You'll likely need to build some kind of structural framework like TeeJay88 did.
Yeah this is true, Im not sure of the rigidity of the wood you will buy but a little support will never hurt anything just a 2x6 under the backside would work well.
A single 2x6?
This is literally (if I built it, it would look EXACTLY like it) this desk. I found the design online and fell in love with it. It'll have the same wood top and square tube steel legs (2x2 at 28 inches tall).
That desk is 80~x30. Mine will be 60-72x24.
That's a nice looking table. Two pieces of high quality plywood laminated together will be plenty strong to use as a desk. The problem is that hardwood veneer plywood is usually not very strong as it often has a low ply count and voids, especially the stuff from the home centers.
Don't use a 2x6 or 2x4 as a stiffener. You may one day wish to use the table somewhere other than against a wall and it would look silly. It would also be a knee banger if it was anywhere but along the back edge. Not good.
There are a few different ways I would go about building a table such as pictured.
One way would be to use two pieces of flat 9 ply cabinet grade plywood laminated together. Then veneer it with my material of choice; hardwood, formica, metal, or whatever you like. Band it with hardwood to dress up the edges and bolt on some legs. Not the best method as almost no plywood is perfectly flat and even if it is flat when you buy it it may not stay that way.
The second and preferred way, since you are working with steel tube for the legs anyway, would be to assemble a steel frame from 1x1 tube that serves as the structure and attachment points for the legs. Then construct a single layer top with a thickened edge that drops over the steel frame. The frame will keep a single layer top nice and flat. I would guess that this is how the pictured table is constructed.
Another way, if the quality of materials available is limited, is to incorporate 1x1 steel tube into a two layer laminated plywood or MDF top. This is simple to do by routing out a 1/2" deep by 1" wide groove into the mating faces of each of the two pieces of plywood. Drop the steel into place as you are gluing up and apply a hardwood edge band to hide everything.
It is all quite a bit of work but nothing too difficult. The decision to make is if you want a strong, good looking table that will last several lifetimes or just something disposable to get you by for a while. There are definitely advantages to either choice.
I said to lay the 2x6 flat... Not silly at all.
I wasn't really addressing your post but have a look at any table or desk such as the one depicted in the post I quoted and tell me if there is a piece of framing lumber screwed to the bottom.