What's up with triangles?

Indeed.

Jul 13, 2023

I just got home from helping my friend Tom on a timber frame in Oregon. It was a western style frame with chunky knee braces, so I thought this an opportune time to talk about triangles(!)

I figure the best way to tackle triangles is to highlight some visible and hidden triangles in everyday construction and how they’re doing their job, hopefully enabling you to have less wobbly stuff in your life.

Now, I get most readers here aren’t building houses. But, I’d wager many of you might build a tomato trellis or a pergola.

Or want to put up a fence.

Or fix a sagging gate.

Or perhaps you’ve just wondered just how necessary that nailed-in-place flimsy-as-hell fiberboard backing on your Ikea bookcase is. Spoiler: It’s what keeps your bookcase from wobbling. Because triangles.

Triangle basics and the walls of your home

Structures get their rigidity from triangles. (Yes, even square buildings.) Take a triangle of sticks with a nail at each corner. Apply force to the side of it. It won’t wobble. Can’t fold. Do the same with a square and push one corner of it. It’ll fold into a rhombus and flatten out.

Triangles can't be compressed. They can't flex at their connection points. They're rock solid.

If you’ve seen the open studs of modern home construction you might wonder where the triangles are. Good question, since typical 2x4 or 2x6 stud framing is just rectangles. Horizontal boards slapped across that framing might feel reassuring, but for the most part that’s just more rectangles.

Case in point: Sometimes you’ll see old garages or barns with horizontal siding nailed across studs and frequently they’ll be collapsing to their sides, doomed to flat-pack for decomposition.

In properly built modern stud framing the triangles are hidden in the plywood sheathing that encases the building. Yes, the sheet is a rectangle, but the nails that run along the edges and through the middle (aka “the field”) and into the studs, form triangles. A lot of them. And when the wall of that building tries to wiggle side to side (known as shear force, or racking) the force that is transferred through the plywood does so diagonally from nail to nail, across many dozens of triangles.

Effectively there are a hundred triangles, big and small, between every nail across the whole sheet. I can’t draw them all. But you get the idea.

You can tell how important plywood is in holding the shape of stud framed walls because, until the plywood goes up, walls are braced with temporary (wait for it…) triangles.

In older stud framing that doesn’t rely on plywood you'll find more obvious triangles, such as diagonal blocking, diagonal board sheathing, or let-in bracing.

And while we’re still on house framing, note that roof trusses, and rafters and tie beams, both take the form of triangles. Lots of triangles go into keeping your house house-shaped.

Timber framing

In western timber frames triangles exist as fairly obvious diagonal knee braces. But also keep in mind the many hidden triangles in timber framing.

An 8x8 timber with a tenon nearly as wide, passing through the mortise of another timber, is creating an 8” triangle with all those connection points. And there are a lot of those intersections in the frame. (This is why Japanese timber framing, which doesn’t rely on knee braces, still works. Though these frames also allow for more flex by design… different schools of thought…) By contrast, a 2x4 nailed to the underside of another 2x4 creates almost no triangle at all.

Obvious triangles. Hidden triangles. Note that while I only drew one on there—where the post passes through the beam—there’s actually several at each timber connection, resisting force in multiple directions.

Gates

Sagging gates that are all rectangle and no triangle are a common frustration. Gravity pushes down on the far end and, over time, you find yourself having to lift a dragging gate to get it to latch.

The gate pictured below has a diagonal brace added in the correct direction to resist that compression force.

You can also solve the problem with a cable and turnbuckle, which has the added benefit of being able to be tightened over time as things settle. But note that the force on the cable only works in tension, so you have to run it from the tall corner of the hinged side, down to the low corner of the free-swinging side.

Fences

Let’s say you have a fence to put up that requires tension— stringing chicken wire, or chainlink, or barbed wire. The fence material has to pull against something. If all it’s pulling against is posts, those will flop over. You need some triangles at the end of each line of fencing and at the corners.

Here’s an “H brace” and a “double H brace.” These use wood, the tension of diagonal wire, and the Earth, to form triangles.

Decks

If a deck is up off the ground and on posts you’ll generally see some bracing. Here’s some knee braces on deck posts.

However, this builder found that the deck still had a lot of sway. Triangles are good, but they’re not impervious. Those posts are long levers that can really test the resistance of small knee braces. So they added long bracing, creating larger triangles.

Also, look closely you’ll see that some diagonal bracing was added to the underside of the floor joists. Sure, the bracing on the posts keeps the deck from rocking back and forth, but that triangular bracing along the underside of the joists prevents the whole structure from twisting on its axis. Much more solid feeling for those on the deck.

Play Structure

My friend Jay Nelson designed and built this gorgeous redwood play structure. I helped him for a few days and I thought it was a good example to share because it’s so open and because, coincidentally, much of the work I did was installing diagonal bracing.

See all those horizontal slats? Those serve basically no structural function. Their function is looking great and keeping kids contained.

Behind and under them you’ll see diagonal bracing, which combines with the horizontal and vertical framing to form a couple dozen triangles, resisting those shear forces left to right and front to back. And up top you’ll see some cross bracing that is keeping the structure from twisting. Rock solid.

Final thoughts

Basically my hope here is that you’ll see the forces a bit more clearly and this will help you troubleshoot the minor wobbles in your life.

A sleek floating bookshelf bracket might look cool, but it will never be as rigid as an old school triangular one. Your potting bench would feel sturdier with some knee braces. Your shade canopy at the beach will probably stop flopping over if you stake out some diagonal line at the corners. Because… triangles.

All hail the mighty triangle.