Deflection calculation for overhanging tabletop - assessing need for support

Question

I'm planning the construction of a table I want to build in the near future. I'm pretty new to calculating beam and plate deflections, and I can't seem to find the information I'm looking for.

In short, the table has rails to expand the tabletop in both directions, from 1000x1500mm (collapsed) to 2000x2500mm (fully extended). I am having trouble calculating the deflection of the overhanging tabletop, and assess if there is a need for additional support. I am particularly worried about the corners.

• Planning a 26mm thick Oak board as the material (12,5 GPa MoE)
• Fully extended tabletop is 90 kg (a total of 882,9 N, or 176,58 Pa)

Centrally will be a 750x1250mm storage box with legs at each corner, supporting the tabletop (shown on image below). Since the support structure doesn't expand, this will give increasing overhangs from 125mm to 625mm in both directions. I am only calculating for fully extended, as lesser will presumably also be fine then.

By my calculations these wooden beams will be more than fine for the weight (but I have considered adding a crossbeam in both directions within the box for even more support)

• Two 750x116x26 beams at 882,9 N/2m (441,45 N/m) will deflect 0,02151mm (20522 N/m for 1mm)
• Two 1250x116x26 beams at 882,9 N/2,5m (353,16 N/m) will deflect 0,13278mm (2659,7 N/m for 1mm)

An extension rail is fixed to both sides. These rails will carry a wood beam construction as shown on the image below.

The crossing beam will carry a second rail, attached directly to the tabletop. These beams should also be plenty for the weight requirements.

• metal rail set can carry up to 90 kg loads, according to seller (45 kg for each side; I am considering 2 rails for better support)
• Two 600x110x26mm cantilever beams at roughly 353,16 N/m will deflect 0,07936mm (4450 N/m for 1mm)
• One 800x110x26mm beam at roughly 441,45 N/m will deflect 0,06531mm (6789 N/m for 1mm)

In addtion to allowing movement this will also provide a bit of additonal support for the shortside overhangs, as illustrated on the image below

This still leaves both longsides as "pure" overhangs, and this is where I'm stuck. Particularly for the corners, as they aren't quite as supported as the overhang adjacent to the central support

Inputting the longside overhang into Sagulator as a floating 'shelf' of span 2500mm, depth 625mm, thickness 26mm and uniform load of 50 kg, I get a sag of 8,88 mm total, which is obviously too much, but that also assumes that the entire span is fixed at one end, which isn't quite the case.

Trying to calculate the overhang as a cantilever beam doesn't quite work, as it is too wide (calculation claims only 0,41672mm deflection at 1000 N/m, which feels clearly wrong).

But I can't find resources online for overhanging plate deflections, and the (free) online calculators I can find doesn't seem to allow for this particular case.

I'm reasonably certain that the components won't break under the stress required of this table, but I would still like it to also not tip over when guests place their elbows on the edge, or bend so much that our stuff slides off.

I have been considering adding extra legs to the second rail, which would then move with and support the corners better, but I'm not sure if this is necessary, and that is the thing I would like to figure out. My question is about calculating deflection for overhanging wooden plate. Can anyone help point me in the right direction?

Answer 1

This design will not work.

The table frame: While the basic frame appears reasonable for a table design, the extensions will not work. It is not clear how they will attach to the main platform frame. What is clear is that they only connect the main frame for several inches in the expanded position. Think of this as a hinge point with a very long lever arm extending to the outside edge. Any weight on the outer edges of the table will put high stresses on the connections back at the leg points. As a general rule, structurally the extension rails should be in contact with the main frame side rails for approximately 2/3 of their length.

The table top: As bowlturner mentioned in a comment, the individual top pieces should be supported near both ends in at least one direction. You have too many pieces that are relying on some sort of connection to adjacent pieces rather than resting upon the frame. Think of each tabletop leaf joint as a potential hinge point (a point of weakness). You should not depend upon adjacent panels to support each other. There should be some sort of pins to help keep the various leaves aligned, but they do not bear weight.

Look at designs of tables in furniture stores as a reference. Notice that if the table extends in length, the support rails extend a significant length along the main frame so that when extended they still have significant connection with the main frame. Also note that the tabletop is generally two large panels that open in the center to allow filler leaves to be placed in the opening. The individual leaves extend beyond the edge of the side rails, but usually a maximum of foot +/- (the same basic 2/3 supported standard I mentioned above). These tables never expand in both directions (side to side and front to back) without some attachable frame extensions.

One other thing to consider for a table. Practically, the center of the table should be accessible for a person standing at the sides in either length or width without bearing weight on the top.