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I want to build a standing shelf that will stand on my desk around my PC monitors and want to be able to stand my PC case on top of it.

I'm planning on using 28mm solid pine boards.
The shelf dimensions will be 1400mm wide, 400mm deep. The "legs" will be 650mm high, 350mm deep and be placed 72mm from the outside edge to create a 1300mm distance between them.
The brace on the back will be 200mm high and 22mm from the back edge.
Below is the design I made using CAD software from various angles.

Using this design is the brace on the back of sufficient size to prevent lateral movement or should it be taller?
And if not how tall should it be?
Should it be offset further "inwards" or will it provide sufficient support at the current position.

Will the overall design be strong enough to support 50kg? (About 110 pounds.)
And if not, how/what support could I add that it will support such a load? Or if it's not possible to answer is there a calculator or something I can use to calculate the possible loads and/or deflection?

Perspective view: Perspective Front view: Front Top view: Top Back view: Back Side view: Side

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    Hi, welcome to Woodworking. Yes we absolutely accept Questions like this, but for future reference the body text needs to not have so many individual sub-queries. Obviously they are all interrelated here, but remember the basic rule is one query per Q. Some of these sub-queries can be folded in together as an overall design question, but once you get to asking about screws only, whether to use dowels, whether to glue, those are very much separate queries that deserve their own Q (but if you do a search internally on that you should be able to answer it to your satisfaction).
    – Graphus
    Mar 20 at 17:11
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    This is a very good, well asked question. The diversion into other (related) topics, as noted by Graphus, can be easily forgiven in consideration of the abundance of drawings included without having to ask for them!
    – FreeMan
    Mar 20 at 18:04
  • Thanks. I'm not usually the one asking new questions so I'm "new" to this. I'll try to remember to limit the questions for future reference.
    – yetanothercoder
    Mar 20 at 20:15

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Using this design is the brace on the back of sufficient size to prevent lateral movement or should it be taller?
And if not how tall should it be?
Should it be offset further "inwards" or will it provide sufficient support at the current position.

It's almost certainly fine, in all respects.

Will the overall design be strong enough to support 50kg? (About 110 pounds.)

Yes. Even without support the shelf would nearly be strong enough for a distributed load.

And if not, how/what support could I add that it will support such a load?

Your "brace" (rail, q.v. rails and stiles on tables) acts like a beam and just like the rails on tables will support the top and prevent or greatly lessen sagging under load. Some shelves in bookcases have similar rails, or strengthening edging/lips at the front, for the same purpose.

Your rail is more than sufficient for the expected load, even if all the weight were placed right in the centre, because in order for the shelf to bow at all it would have to bend the rail board sideways, or tear it free from the legs which is essentially impossible — build it right and without any change to the pieces you could use this as a seat for two!

is there a calculator or something I can use to calculate the possible loads and/or deflection?

There is, the much-linked-to the Sagulator :-)

Use with caution though — I would suggest greatly exaggerating loads (I often double, and sometimes triple!) any time you have the least doubt about the strength to give a wide margin for error, mainly because of variations in material strength (wood varies, a lot). But beyond that, look at the design of existing furniture that you see (especially older pieces) and plans in books and magazines, to give an idea of what is considered sufficiently strong in real-world applications.

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