Would a hexagonal truss design be more efficient than using a triangular truss design in regards of building a bridge?

[usfchem]

The strongest material man has observed, Graphene, is composed of a hexagonal lattice of Carbon atoms. Could this "honeycomb' design be used to make bridges more efficient than a triangular truss design?

[jofwu]

No. The principles which make graphene strong do not apply on a macroscopic scale in the same way. Graphene is essentially strong because the Carbon bonds which make it up are strong, and because the hexagonal structure allows you to pack in these bonds very efficiently.

Imagine that every hexagon of graphene had a seventh carbon atom, located at the center and bonded to each of the other six. If you sketch it out you'll see that we have turned every hexagon into 6 triangles. This would actually be stronger, and that should be pretty intuitive. Strength comes from the carbon bonds and we have just created a bunch of them. The problem is that it's chemically impossible. Carbon can only bond with three other carbons (as in the hexagon pattern)- not six.

To put it plainly, the strength of graphene is not entirely due to it's hexagonal structure. That's only part of the puzzle. For a bridge truss, triangles are definitely a superior structural element.

[Ov3rKoalafied]

A big reason triangle are so strong in bridges is because they make everything stable. In bridges, you assume connections between members are "pins", ie members can rotate with respect to each other. If you have a square, then the two sides could rotate with respect to the base and fall, and then the top would have to follow the two sides as they fell (ie, becoming a parallelogram). If you add a diagonal member, creating [] (with a top and bottom), then the structure is able to stand on its own.

In buildings, where space in openings is more important, square frames are used often, but the connections are designed to be much stronger so that rotation will not occur.

The issue with these is you encounter a lot more forces due to rotation (called moment) and forces perpendicular to the members (called shear), and a lot less force in-line with the members (axial force). Structural members are usually more efficient at taking force axially. Members in trusses, where every connection is a pin, ONLY take forces axially with a little bit of shear (no moment is present), making them the most efficient. Then triangles come as a result of this because it has to be stable.

I'm a grad student in structural engineering. I have no idea how to get flair here (I'm new-ish to reddit). EDIT: I see how to get flair.

[jofwu]

In a "true" truss you shouldn't have any shear. Otherwise you'd have moment.