A gusset will do it. 2x6 or 2x8 with 45’s each end attached on the inside.

 

There are metal table leg braces that I would prefer over wood, since it may split on the larger screws.
Disregard the leg mounting brackets:

Amazon.com : leg brackets for table

You can make the kerfs after assembly with a handsaw, double blades hack saw, or saber saw.

 

A gusset with 45's on each side. You can notch the 4x4 to a 45 to create a flat surface for the gusset to sit flat against or you can cut a v groove with opposing 45's in the gusset to accept the corner of the 45. I would recommend the first. If you notch the gusset too deep you will weaken it.

 

Notching the tops of the posts to snugly receive the horizontal 2x4s and then glue and screw them will add a lot of stiffness to the structure without further bracing. However, you can also add suggested gussets.
Unfortunately, the 4 screws alone don't offer much resistance to racking. If you notch the tops of the posts half the thickness of the 2x4s and then notch the ends of the 2x4s half thickness (similar to a half lap joint) and then glue them, you will then have two shoulders and the glue line to resist racking. A plus will be that the outside surfaces of the posts and 2x4s will be flush.

 

Thank you for the advice.
I can imagine yomonbill's notching explanation but I cannot imagine DrRobert's and woodnthings's gussets with 45s. Would it be possible to explain further or to provide an image?

 

Corner braces, whether wood or metal are attached in much the same way:

https://www.youtube.com/results?search_query=attach+metal+leg+braces

 

I’m talking about the braces shown above, except the wood is turned 90 degrees. You do not need notches. I hope the drawing makes sense.

U

 

I hope the drawing makes sense.

Doc, we need to have a "zoom" meeting and work on your drawing techniques. or lack there of?
Perspective is a big help.
Dark outlines separate objects.
Like this:

and this:

 

If the 2x4's were glued and screwed I don't think it needs re-enforcing. I have four work benches put together that way and they are steady.

 

Yeah, it's pretty awful, isn't it?

How about this:

 

Thank you for all the advice.
I gather that I should either:
1) Add gussets horizontally as per DrRobert
2) Add metal table leg braces as per woodnthings
3) Add gussets horizontally and notch either the posts or the gussets as per B Coll
4) Notch the posts (and beams) and screw and glue (and add horizontal gussets) as per yomanbill
5) No need to reinforce if beams are screwed and glued as per Steve Neul

I need this to be able to be dismantled so I will not be using glue only screws.

No-one has suggested it but would vertical gussets like I have at the base, turned 90degrees and screwed horizontally into the posts and horizontally into the sides of the beams be a solution?

This is what I have at the base of the posts:

The base of the posts and floor beams (?) are notched and screwed together.

 

No-one has suggested it but would vertical gussets like I have at the base, turned 90degrees and screwed horizontally into the posts and horizontally into the sides of the beams be a solution?

Yes, and a good one. Using the screws in that orientation, but predrilling for pilot holes first will help prevent splitting the wood.

 

I think that’s what I was trying to convey. Dr. Woodnthings has diagnosed my Aphantasia 😁😁

 

I learned that word about 3 days ago while watching a You Tube woodworking video.
Never knew such a condition even had a name for it.

You Tube has a bunch of videos on that:

https://www.youtube.com/results?search_query=aphantasia

 

Yes. Do at the top what you did at the bottom. There are some improvements to that you can make depending on how often you need to assemble/disassemble it, but that should adequately stiffen the structure.

 

I don't think I communicated what I meant well when I asked about "vertical gussets....turned 90degrees and screwed horizontally into the posts and horizontally into the sides of the beams".
Here is a bad drawing that I hope helps:

 

Those will work also.
Any brace is better than no brace.
The diagonals are the best, because they have more resistance over a great length.
The longer the leg of the brace away from the post, the greater the strength.
The fasteners are the "weak link" because they can shear or bend off or away.
The wood itself will not fail, but the fasteners may split out.
We are not talking "gobs" of force here, so moderation is OK.

 

This is an update.
I have reinforced the joints with braces like these:

I would like to thank everyone who helped me.

 

👍 I’d throw a third screw in there.