I think they use the 'Direct Stiffness Method'. You can read about here:

https://en.wikipedia.org/wiki/Direct_stiffness_method

Really good free university course is here:

https://www.colorado.edu/engineering/cas/courses.d/IFEM.d/

I know that the original Bridge Builder uses particles + springs with very small timesteps to keep things stable, similar to this paper: http://www.uni-weimar.de/~caw/papers/p7-kacic-alesic.pdf

Other games have used a similar approach, for example I would bet that Rigs of Rods works the same way since they've mentioned that their simulator runs at 1000hz. The game is open source so you can poke around and see how it works: https://github.com/RigsOfRods/rigs-of-rods

Interesting! I was sure when I read about introductions for FEM that Bridge Constructor was mentioned as an example using DSM. It is such a great use case for this method. 

I did structural analysis with simple physically inspired approaches, and I always got bad results. Simple geometric approaches worked good for me (e.g. to detect unstable overhangs). 

On 1/15/2018 at 5:44 PM, Dirk Gregorius said:

Interesting! I was sure when I read about introductions for FEM that Bridge Constructor was mentioned as an example using DSM. It is such a great use case for this method. 

I meant the *original* Bridge Builder game https://en.wikipedia.org/wiki/Bridge_Builder It's quite possible Bridge Constructor is using FEM!

Gish also uses penalty-method + really tiny steps, since it's by the same author.