Yes, concrete provides great compressive strength, but is not very strong given tensile loading.
Rebar provides the tensile loading support that concrete alone lacks.
In reinforce concrete beams the bending causes compression on the top and tension on the bottom. Since concrete is weak in tension (maybe 1/10 of compression strength), the rebar at the bottom will carry the tension. When you do the design calculations, some approximations are made like concrete carries no tension on bottom half of beam and how the stress is distributed on the top portion. Then with iterative analysis you can converge on an solution. Then once you got the basic design, there will other rules like displacement, buckling conditions.
Here is an example design calculation I could find: https://civilengineeringbible.com/subtopics.php?i=32
Overall, I really liked this as an art project. I'm not sure what the artist wants to communicate with the bike, but I found it very satisfying.
"I paid a lot of money for an architecture degree I'm not using."
Sorry for being negative about an art project. I think I was projecting my own biases, but it sounded like an engineering project and then I didn't learn anything.