Yes, I know it might not be practical to do this without errors and there’s reasons like running utilities through and quality control with inexperienced workers, but technically speaking, could you make stronger structures with less materials using stronger structural shapes? Maybe it’s just more pleasing to our eyes everything being straight and square and such, but what about utility canopies and tents where you want to have your structural members as light and portable as possible? Why do we not have tetrahedron shaped tents that have 3 small, collapsible, yet rigid poles and a firing they go in at the top instead of having long flexible ones?
In: Engineering
Triangles aren’t magical. They have one very specific use – they get rid of bending force. You try to bend a triangle, you just end up stretching one aide and squishing another. This only works if the force is in the right direction – if it pushes sideways (up or down on the sheet of paper where you drew your triangle) then there’s still just as much bending and the triangle is no good.
If you wanted to use triangles to improve floor joists then you’d have to make them into trusses, and while trusses do see some use it would take up more space or money than using regular old I or H beams.
So we see trusses in many roofs, where space is free, but in the floor not so much.
Your basic building plan is a square. The shortest distance across the square is straight across. Lumber cost increases greatly as length goes up. So you want your floor joists to be as short as possible, which is straight across.
A Typical pattern would be a 30×30 square with 16 foot joists. They overlap each other in the center over some sort of support. (15’ from each outer wall to the inner support wall.)
The triangle is also the strongest shape against external forces. Floor joists just push against gravity. They do have not have to oppose forces in multiple directions. So the triangle isn’t needed.
It’s standard [in roofing](https://www.menards.com/main/building-materials/trusses-i-joists-engineered-lumber/roof-trusses/c-5658.htm), which requires cross-support to both hold itself up, and only exert downward force on the walls (a simple sloped roof without support would put outward force on the walls, which they’re not designed to resist.)
It’s [a thing](https://trimjoist.com/) in joists as well. It’s just not economical – the additional labor in constructing them is significantly more than the materials cost of just buying a solid piece of wood of equivalent size. They mainly get used in long, unsupported spans, where you can’t really get a single piece of lumber of the appropriate length and strength.
The purpose of joists is to carry the weight to the ends, not to keep the floor square, that is done by the subfloor that goes on top of the joists, and you kinda still need that even if you have diagonal joists, because that’s what transfers the weight from your foot to the joist. Beam deflection is related to the cube of length. So to carry the same load you’d have to make it much stronger.
Now, that’s not to say stronger shapes don’t exist. You often see wooden joists in the shape of an I beam, putting more material where it matters for the loads a joist carries.
>Why do we not have tetrahedron shaped tents that have 3 small, collapsible, yet rigid poles and a firing they go in at the top instead of having long flexible ones?
Because the goal isn’t to make the tent as strong as possible inside a given weight, it’s to have as much usable space as possible inside a given weight.
Because everything only needs to be strong enough for the intended usage.
We rarely optimize for strength over everything else. And when we do, it’s still generally not a tetrahedron. The loads and fixed points are assessed and a truss like structure is designed that is suited for the various multiple important loading scenarios, and the design is the best fit to handle those while complying with other requirements such as being manufacturable and deployable, costs being minimized or meeting budget requirements, optimizing for some other parameters such as minimum weight or maintenance requirements, handling some anticipated kinds of impacts or (mis)handling loads or incidental damage types, having a sufficiently long service life in an environment with chemicals or cyclic loads or UV or whatever else is going on, and so on.
A now-getting-old mechanical engineering code named Optistuct might be an interesting google run for you. It’s one attempt to make it easy to obtain a generic near-ideal structural design for any component. It won’t always get it, but if you were to learn the details, the methodology they use has broad enough applicability and is well enough implemented that it can usually be an effective tool to improve the structural optimization of a mechanical design.
In addition to what everyone else said about sheathing/plywood/subfloors already providing the membrane action you’re looking for, it also means you need to either use deeper timbers, or you need to have a gradient of depths.
Imagine a square, 4mx4m. Assuming 600cts, you can use 6 joists, of whatever depth you need. It’s an easy calculation, since theyre all the same span, so one size fits all. Now try doing it diagonally. Instead of the max span being 4m, it’s now 5.7m. So span is up 50%, so our timbers need to be deeper to account for that. But what about the rest of the joists? Do we use the same depth of timber throughout, and spend that much more money on material, or do we make the tradie hate us, and specify a gradient of timbers depending on span.
Both of these solutions will result in a structure that’s more expensive, time consuming, and results in a deeper ceiling-floor cavity than your traditional joists + floor sheathing will.
And if for whatever reason you don’t want to use floor sheathing, strap bracing is both cheap and very easy to install
The strength that a diagonal joist would add would be strength against racking of the structrure when viewed from above. Essentially if you had a square house, it would resist a force that was trying to move parallel walls in opposite directions, like trying to turn it into a parallelagram.
But in reality there are not really many things that are going to apply that sort of force to the structure. A wind is going to hit an entire side of the buildilng pretty evenly. Nothing is really going to be pushing on one wall with a force that is parallel to that wall.
Its more important to deal with racking on the vertical walls where you have a pivot at the bottom created by where the wall meeets the foundation. In that case, wind blowing on one wall will create a racking force in the two perpedicular walls as the leverage from the wind tries to blow the wall over.
The force a floor has to deal with is downwards force on the floor itself. A triangle laid flat isn’t going to help with that.
The reason you see decks with diagonal decking is because often times they are very far from the foundation and anchored to the house at one end. In that case, you can get a racking force because it pivots at the house and the force the foundation exerts is pretty limited because it might be on tall supports.
If you run joists diagonally to the beams, it increases the span of the joists, which would make the floor or ceiling weaker. To combat this, you have to put the beams much closer together, which would require more beams, which would cost you in material.
In this scenario any extra strength you gain would be from the addition of the beams. The joists running on diagonals wouldn’t make it any stronger. The reason is because a floor joists receive sheathing, typically plywood in residential construction. The plywood ties it all together and provides the lateral strength, the resistance to “rocking,” that a triangular shape has.
Joists are there to provide specific kinds of strength or strength in specific directions relative to the forces acting on the structure. In residential construction ceiling joists, for example, do a few things:
-They provide a nailing surface and support for whatever sheaths the ceiling.
-They’re nailed to the tops of walls to keep them the correct distance apart and prevent them from moving.
-They keep the tops of exterior walls from being pushed outward by the roof.
All of these functions are made worse if the joists are running diagonally to the walls and or roof. If you want to stop something from moving away from you, it’s much better if the force you apply to it is perpendicular to the direction it is trying to move. If you’re at an angle, it’s much less effective. There’s also the fact that the roof’s rafters in most cases lie alongside the ceiling joists. They overlap, and the rafters are frequently nailed to the side of the joist as well as the top of the wall they’re sitting on. Not only would this be impossible if the joists were diagonal to the walls, but it might not even be possible to set the rafters in place on top of the walls on a proper layout. In fact it would certainly be impossible. It’s hard to explain why, but it’s the nature of the geometry of it all. You’d run into situations where the bottom side of the rafter hits the top of a ceiling joist.
The triangle shape is strong because it resists “rocking.” You can’t move any of the vertexes relative to the other parts without breaking something. The lengths and angles are locked in. In a rectangle, the angles aren’t locked. You can shift the top to one side and make it into an increasingly exaggerated diamond shape all the way until it is basically flat, but the lengths of all the sides are all still the same. The angles changed, but nothing broke apart. Triangles are “stronger” because they can’t do that.
The floor of a house isn’t really vulnerable to that kind of force to start with, especially once the plywood subfloor is on. Those kinds of shear forces are things that walls have to deal with, and they get that triangular strength from the sheathing put on them.
We do see that triangle shape in one place in residential construction, though. The roof. Once we get to a point where something has to hold itself up, like a roof, we make a triangle. If you go inside an attic above a certain size, you will probably see horizontal braces connecting every third rafter (or so) to the one directly across from it, creating a full triangle.
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