Bench design

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I have started on a small stool for by the back door to sit on when I put on my "outdoor shoes" with a shelf below to store those shoes. I had a walnut board that was calling to be used for a project (i.e., not so pretty, but yet nice enough for a little project for myself).

I thought I had my general plan in place, but now I'm struggling with the design details...and could use some help.  

I started by planning and jointing the board so I could do a glueup of the top.  The board is only about ¾ to and inch so I thought I would beef up the front and back edges by wrapping a strip of the board to give a feel of a thicker top.  I now think that might have to be undone as I'm struggling with how to design/attach the base.

I glued up legs that are about 1.75 square.

I was thinking of making the legs proud to the outside and then somehow provide a support running under the top that would allow that to be secured. Not sure how to do that in a way that is strong enough for me to be sitting on this.  
Then thought I tucking the legs inside the edges of that wrapped section, but then realized that any wood movement would be an issue. 

Or tucking a bit and then adding connections to attach the top.
SIGH...now contemplating just cutting off those wrapped pieces so I have a flat top again, although thinner than I had hoped.  

Also still need to figure out how to attach a shelf for shoes underneath - Dominos is my current thought.

Current "pieces"

Any other suggestions on the based/top connection.  
Food for thought:

Figuring out how to do something you have never done is what makes a good challenge.

If you’re worried about movement, and I don’t really think you need to be, leave smallest space in between your decorate ‘under pieces’ and the legs. That panel is small enough, overall, that I just don’t see having enough seasonal movement for it to be an issue. The fact that it’s going to live outside may temper that opinion a bit, but a small gap would fix the issues. 

As for your option of leaving the legs on the outside and proud: you could run an apron between the legs, then set the seat portion on top of the apron. If I was worried about strength, which I don’t think I would be if you’re using dominoes or M&T, you could also run a domino between the seat panel and the leg…so you’d have a domino connection between the apron and leg, supporting the seat on top of the apron, and an extra domino connecting the seat and legs. That’s a lot of contact points, especially if the whole this is also glued up. If you wanted to do something kinda decorative, you could do an exposed half lap joint for the apron into the legs…or maybe even a half lap decorated as a dovetail or something. A half lapped joint is damn near bullet proof, especially if it’s supported/glues against the seat. 

Just thoughts….

Ryan/// ~sigh~ I blew up another bowl. Moke told me "I made the inside bigger than the outside".

I don't think the top will require any reinforcement.
At first with the supports attached, I thought of notching the leg tops so they lap over the supports to be flush with the front of the stool. An apron (domino'd) to the legs between.
Bently's  design is great! Has style and function.
You could add aprons to the sides and rear if it seems too wobbly.
Ryan – the wood movement issue is likely greater than might be typical as this will be in a garage in Missouri, so will have significant swings in temperature and/or humidity.  Still, as you note, this isn’t that wide so I may be over concerned (haha… what’s new?).  I was initially thinking of how to get a “floating” type of appearance, but knowing my weight will be on the top, I felt I needed better support.  Having multiple connections as you note should address that. 

Bentlyj – you provided a visual that I couldn’t get pulled together in my head (as an aside, I said to my husband that having Sketchup skills would be very helpful as trying to clamp in various configurations was cumbersome at best…so THANK YOU for doing the drawing).  I think this would be the most straightforward approach – solid yet visually pleasing with the legs proud on the top.  Having parallel panels would get around the wood movement concern.  I had thought of trying to incorporate some sort of slats or even a metal grid for the shelf, but that would bring back the wood movement issue (top would move, shelf would not). I may have enough from the board to make one more panel for that bottom shelf. 

Splintergroup – I was trying to think through an apron, but in my mind, that was making it look “heavy” with those added strips I glued on the top (the sections I “wrapped” around the edge to make the top look thicker).  That had led me to consider cutting those strips off to return to the original board thickness, and then use an apron that should give a pretty balanced look. 

Will let this all rumble around in my head.  Right now leaning toward Bentlyj’s design suggestion as fulfilling the purpose (i.e., a sturdy stool on which to sit), as well as having the “flare” of the proud legs on top for a bit of a unique design. 

THANK YOU for the brainstorming and suggestions!!  My pups were helping my husband wash the truck so I was on my own in the shop just when I needed some fresh ideas. 😉😁
All views show the legs mounted on the top's end grain, I wouldn't think wood movement will present a problem. 
If you are concerned about wood movement though, here or other projects, try this calculator for potential dimensional changes:  https://kmtools.com/pages/wood-movement-calculator