Triangles are the most stable simple geometric structure. Without triangulation (or a shear plane which is really just a special case), squares have no lateral support. They fold over with any significant force applied from any direction. Just take a box and open the ends (which would otherwise form a shear plane) and see how well it maintains it’s shape. So basically, all the roll cages (and “sport bars”) you see that look like a box with no diagonals, will fold relatively easily in any direction that does not have a diagonal.
The strongest case (fore a given material) is when the diagonal meets at the perpendicular (or otherwise) joints forming a “node”. When a proper “node” is formed, any force not having a significant component perpendicular to a span and located between the nodes will be directed into compressive or tensile force vectors along and parallel to the other tubes. And, even when force component is applied perpendicular to a span, the bar can not give very far because bending the bar attempts to pull in the ends, effectively shortening the bar. This in turn pull on the nodes which transfer the forces as described above because triangles can not deform without deformation of one or more of the sides, which don’t want to deform because forces are transferred parallel to those spans. This is the strongest way to form a stable structure, but it must have proper triangulations to withstand impact forces and direct them along the spans rather than deforming.
And, this is why coarse, angular cages (if designed properly) are much stronger than cool monkey bar cages with “aesthetic bends” in spans to make it look “cool”. Those bends cause the transferred forces to have some leverage on the span and (assuming the bend is not restrained, i.e. a node) it can collapse. Try this, take a welding rod that is straight and stand it on its end on a hard surface standing vertically. Now push straight down on it from above. It will probably go through your hand long before bending. Now make a small 15* bend or so and repeat. Big difference eh? That’s what happens then you have arbitrary bends in the middle of a structural span, it becomes much weaker when nodes transfer forces, or when it takes a hit in the right direction.
Gussets are a degenerative case (no nodes) that also lend additional strength to the “nodes” they brace, reducing the chance of failure at or near a node.
And you can forget FEA without an engineering degree and a mortgage on the house. Good quality packages shoot quickly over $10k, and those are generally add ons to AutoCad and such which in turn cost more than many new cars. Never even played with one, but they are the shiznit when it comes to figuring out EXACTLY how a structure will respond to various simple point loads and as well as more complex scenarios. Paying someone to do it will not save you much given the investment required (the degree and time to model as well as equipment overhead) unless you have a very close friend who owes you a lot. Me, I have to use a model, my finger pushing on it, and my imagination…
This is my best stab at an explanation based on what I think I understand of what I’ve seen and “learned” over the years, but I’m certainly no engineer. There are others here who could probably give a better and more accurate description in fewer words.
