I am building a sofa table out of 3/4" walnut using mortise and tenon construction for the back and side aprons. The stretchers connecting the legs on the left and right sides (front to back) lower will also use mortise and tenon joinery.
I plan on using a piece of 3/4" walnut approximately 10" wide by 45" long to act as both a lower shelf and to act as a center stretcher connecting the two lower leg stretchers. There will be a cleat on the interior of both the left and right lower leg stretchers which will support the shelf.
I am not planning on placing anything heavy on the shelf but I am concerned about possible sag.
I thought about gluing lips on the front and back of the shelf which would span the entire length. I know that this is effective on bookshelves but I rejected this idea since I want the shelf thickness to equal the table top thickness (3/4")
Since the bottom of the lower shelf will be about 7" above the floor and not readily visible I thought about glueing two 3/4" runners to the shelf the same length as the lower shelf on either side of the cleats supporting the shelf. Or milling two shallow dadoes about 1/4 deep by 3/8 wide and inserting splines which would sit about 1/2" proud of the bottom surface
Any one have any comments on this approach? Any one see any problems?
All the best