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Background

I'm building a table using 4 table legs and a table top. The table top, made out of wood, tends to be quite elastic. Yet, I want the table to be able to hold heavy objects without worrying about the positioning of these objects.

Problem

How does one horizontally position the leg pairs optimally, such that the weak spots of the table top are reduced as much as possible?

More specifically, how does one determine n as indicated in the following picture, such that we avoid the situation depicted in "Bad example A" and "Bad example B"?

For the sake of demonstration, let us assume that the legs have a diameter of 0 cm and that the table cannot tip over.

Problem

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closed as off-topic by Bill N, GiorgioP, Jon Custer, Kyle Kanos, M. Enns Jun 12 at 19:48

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  • $\begingroup$ Check that you'd need two small weights (on the borders) to get "bad example A", but one big weight (on the center) to get "bad example B". The solution of "optimal distribution" does depend on the weight shape (unless you relax the 4-leg condition). What are the weights you're planning to put on the table? $\endgroup$ – FGSUZ Jun 8 at 11:08
  • $\begingroup$ As far the flexibility as you depicted is considered the four legs should be, starting from a position in which they are equidistant from them as well the outer edges of the top, somehow displaced to the outer. I don't know how much, tough. $\endgroup$ – Alchimista Jun 8 at 11:09
  • $\begingroup$ From a practical point of view, indeed, more legs may be required and the 4 legs would not be a restriction. In the end, I can't change the material of the table top. I would like to be able to find the theoretical optimal solution, however, and use that as a base to judge whether or not it will be sufficient for the weights that'd it should hold. $\endgroup$ – Mr. Pixel Jun 8 at 11:32
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    $\begingroup$ A good question ... for Engineering SE! $\endgroup$ – Bill N Jun 8 at 12:51
  • $\begingroup$ If the table top is really so flexible that you have to be concerned about the flatness of the top surface, then it will also be so flexible that it will the legs of the table inward or outward when it flexes and not simply maintain the legs in the vertical orientations shown in your diagrams. You really need to design a rigid table foundation involving all four legs using horizontal beams and struts, and then attach the flexible table surface on top of that rigid foundation. $\endgroup$ – Samuel Weir Jun 8 at 19:19

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