# Deflection calculation for overhanging tabletop - assessing need for support

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?

• I don't think you want that many small pieces making up your table. I also don't think you want any of the pieces to be free floating, you have 10 boards that are only being supported by their neighbors, this is a recipe for disaster. In all honesty I would think every board would need to be supported at 2 ends for best results and I would use larger pieces (with fewer table size options or a LOT more interchangeable pieces). Commented Nov 21, 2023 at 13:56
• Hi, welcome to Woodworking. As a general observation, and as I often do with questions of this type, I'd caution not to reinvent the wheel. You appear to have designed your table starting from scratch, with no reference at all to existing table design principles or examples..... why??? This is partly reflected by what you call beams here, which I (and presumably others) found very confusing initially as I expected extension supports/leaf supports (as on conventional extendable tables) which could be called beams, but there aren't any in your design. Commented Nov 22, 2023 at 8:22
• Now the above aside, I'm very confused by how you intend the extension to the larger size to happen in relation to the smaller initial tabletop — the initial 2x2 grid top from the left of the image seems to disappear in the larger or extended tabletop, with the central area now being a 2x3 grid.... Commented Nov 22, 2023 at 8:30
• @bowlturner Thanks, that's a good observation, I'll take it into consideration. I had considered the many plates as a possible failure point. I got a carpenter friend to take a look at the design yesterday and he suggested something similar. So larger extention plates are in consideration. Though can you elaborate what you mean by "more interchangable pieces"; the design as detailed above only have pieces that are identical, specifically so they can be interchanged. Only the corner plates, which are fastened to the structure are a different size. Thanks! Commented Nov 22, 2023 at 10:36
• @Graphus Hi, thanks for the comments. I see I may not have explained myself ideally. To your first comment; basically I was unfamiliar with basic table design principles. Searching for "design table", "calculations tabletop" or similar gave me either: designing a mathematical table, or businesses giving a calculations for price in their store - neither being what I need. So I found construction terms and formular for beams and columns and assumed that those also apply for furniture. I can definitely see how that creates confusion. 1/2 Commented Nov 22, 2023 at 10:40