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This is the basic requirement of the wooden door frame:

enter image description here

The requirement is to make sure that the door frame does not skew or deform.

Questions:

  • What's the minimum number of wooden pieces to be added inside the frame, so that the frame of the door remains solid, and doesn't deform?
  • What's the principled approach to handle this? Because currently I mostly use eyeballing and intuitive thinking.

1. My guesses so far

1.1. Extend from corners at 45 degrees

enter image description here

1.2. Extend from corners to opposite, regardless of degree

enter image description here

2. Surprises

I'm a bit surprised about how others do their frames, without angular pieces. For example, checkout this: enter image description here

No angular pieces at all. What's wrong? Am I missing something? Or are the engineers missing something?

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    $\begingroup$ you need to add some constraints on the wood piece dimensions, and even then the bonding process will have a significant effect. $\endgroup$
    – NMech ♦
    Aug 13, 2021 at 16:18
  • $\begingroup$ Where are the other forces (i.e. hinges)? What is the load you are interested in? Usually for simplicity, doors are constructed with just horizontal bracing, sometimes a vertical in the middle $\endgroup$
    – Pete W
    Aug 13, 2021 at 16:33
  • $\begingroup$ @PeteW - yes, hinges, and mild kicks/pushs on the corners. E.g. if I mildly punch the door from the lower corner, how much will it wobble/skew? $\endgroup$
    – caveman
    Aug 13, 2021 at 16:48
  • $\begingroup$ @NMech - screws/nails with glues. Can we abstract it independent of the dimensions of the wood pieces? E.g. wouldn't the thicker dimensions just make the better structure even better? So if we cancel out the dimensions, we may at least reach the same conclusion about the strengths of different shapes? $\endgroup$
    – caveman
    Aug 13, 2021 at 16:53
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    $\begingroup$ @caveman IMHO this is too open a problem to be addressed here. To be honest, the obvious answer for me to the title of your question "what is the minimum number of wooden pieces" is just plain 1. Apologies for not being able to be more helpful. $\endgroup$
    – NMech ♦
    Aug 13, 2021 at 17:01

2 Answers 2

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One

A gate like that will have a single diagonal from upper right to lower left. All you really need to do is turn the rectangle into triangles.

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  • $\begingroup$ Interesting. If the frame is skewed such that the top moves to left, while bottom is stationary, I see how this will try to compress the diagonal. However, if it skews to the other direction, then it will be a pull effect. I guess a pull effect is not friendly to nails/screws. Any idea how to solve this pull effect? E.g. should I add an opposite diagonal to the opposite direction similar to my 2nd suggestion? Or should I use different screws? Or am I missing something even better than all these options? $\endgroup$
    – caveman
    Aug 14, 2021 at 0:33
  • $\begingroup$ By "triangles", do you mean just 2 triangles? Or do you mean a more general concept of partitioning it recursively into more triangles if more strength is needed? Also, is there any reason why triangles? Why not other shapes? $\endgroup$
    – caveman
    Aug 14, 2021 at 0:36
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    $\begingroup$ @caveman Triangle is the most geometrically stable shape other than a perfect circle. If you want to make the door stiffer, the next choice is to provide a horizontal in mid-height, and two diagonals, one each in the rectangle above and below. $\endgroup$
    – r13
    Aug 15, 2021 at 18:43
  • $\begingroup$ @r13 - Does angle of the diagonals matter? E.g. 45 degree diagonals (like X) as opposed to non-45 degrees depending on how wide the door frame is? $\endgroup$
    – caveman
    Aug 16, 2021 at 2:15
  • $\begingroup$ In general, 45 degrees would be ideal. But giving door width to length ratio, it is neither likely to occur nor necessary. I would say, it is effective as long as it is not laying flatter than the 2:1 ratio. For rectangle door, I personally prefer to divide it into 2 or 3 rectangles and provide the diagonals in the spaces (usually 2 is adequate). $\endgroup$
    – r13
    Aug 16, 2021 at 3:17
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Doors are built as strong as needed. Depending on their utility. For example for a residential exterior door they use solid core oak or similar wood.

For interior they use hollow core with a frame around, similar to the one that you have and fill the rest with either particle board, egg crate hex cardboard, or hard foam.

The formica or finish grained sheething cover functions as a shear panel. Hence one doesn't need any diagonal bracing.

There are however, security doors that are built with hardened steel ribs that extend into a solid steel jam and have thick bomb proof plates and are sealed against toxic fumes, all covered in wood veneer to disguise.

The type and structure of door one can use is regulated by fire and building safety codes.

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