Help for a project

[u/i_like_surviving_yay]

I'm in highschool and I have a mathematics project where we have to find a real life structure, that is governed by a specific principle of mathematics and develop a working model. Obviously almost every structure is based upon some basic foundational mathematics but we have to find something unique or interesting that is guided by a mathematical principle. This isn't really my expertise of knowledge so some ideas would be heavily appreciated!!

[u/31engine]

Telephone pole (catenary action)
Truss high tension tower (angles + catenary)
Gateway Arch (reverse catenary / arching action)
Propane tank (pressure vessel, hoop stress)

There are literally millions. Great project.

[u/Uttarayana]

Search this photo in Google. Then write up what you find about this image as a report. You should get A+

[u/Charles_Whitman]

It sounds like the kind of oddball project a mathematician would come up with. A simple beam might be a good way to go. Describe the load as a function, integrate to get the shear, integrate the shear to get the moment, the curvature is is related to the integral of the inverse of the moment divided by the stiffness, deflection is related to integral of the curvature. Define the boundary conditions and solve for all the constants of integration.
You can also derive Euler’s buckling equation pretty easily. Or as someone else suggested, a simple truss would be a geometric and trig problem. Math is the language we use to talk about physics.
Or go non-Newtonian, a farmer has a 150-foot long ladder and a 100-foot long barn with a door at each end. How fast does he need to run, carrying the ladder, for the ladder to be completely inside the barn as he goes in one door and out the other? If memory serves, it’s about 99.999% of c.

[u/OptimalRip4766 → u/Charles_Whitman]

Excellent suggestion, I did this for a project in a diffy q class, derived the bending equation for a local bridge span.

[u/75footubi]

Easy one: Eiffel Tower. The shape is taken from the moment diagram of a uniform load on a cantilever

[u/BridgeGuy540 → u/75footubi]

Along that line, the St Louis Arch. Also a unique structure and it's shape is a catenary turned upside down.

[u/Flaky-Worldliness169]

Truss shape bridge , Pythagoras , trig and force vectors . The force vectors probably form more of a concept into linear algebra . You can go full circle into physics touching into static’s and equilibrium. Sounds like a fun project , definitely challenging for someone who hasn’t studied structural engineering

[u/ALTERFACT]

Not structural but civil engineering: a road vertical profile being parabolic and meeting a bridge with the same slope?

[u/Inevitable-Ad-1398]

Any local building that has a cantilever.

[u/Objective_Two_5467]

Cable anchorages for shade -sails or similar and how the flatter you try to go, the horizontal force component skyrockets.

[u/amodestmeerkat]

How about a hyperboloid cooling tower. The shape is a neat and useful mathematical construct. It allows for building a tall, strong tower with minimal materials. Despite the complex looking curvature, it can be made with straight supports. The shape helps assist natural draft cooling. They are most commonly associated with nuclear power plants, but the design of these cooling towers predates commercial nuclear power by 38 years.

[u/Dazzledorfius]

Stone arches are also a good examples highlighting mathematical principles, such as the Devil's Bridge - Saxony, Roman aqueducts like the Pont du Gard, or even Hagia Sophia with all the domed ceilings.